LABORATORY MANUAL PHYSICS 1401 - Al Akhawayn UniversityPhysics_Lab/labman/Phy1401_Lab... · 2009-07-01 · 1. Report to the laboratory promptly, ready to work. Expect to remain for

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School of School of School of School of Science &Science &Science &Science & Engineering Engineering Engineering Engineering

LABORATORY MANUAL

PHYSICS 1401

Cours : Phy 1401

Semester : Fall 2008

By : Dr.Khalid Loudyi

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Table of Content

INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES....3 PHYSICS LABORATORY RULES ......................................................................................................... 4 LABORATORY SUPPLIES & EQUIPMENT ........................................................................5

The experiments:

GRAPHS AND GRAPHICAL ANALYSIS .............................................................................6 THE MEASUREMENT OF MASS, LENGTH AND TIME ...................................................11 VECTORS AND EQUILIBRIUM.........................................................................................19 ONE DIMENSIONAL MOTION ..........................................................................................25 ATWOOD'S PULLEY.........................................................................................................32 WORK AND ENERGY IN THE SIMPLE PENDULUM .......................................................38 ELASTIC PROPERTIES OF DEFORMABLE BODIES......................................................43 ROTATIONAL INERTIA, ANGULAR MOTION ..................................................................48 THE SIMPLE PENDULUM ................................................................................................54 BUOYANT FORCES..........................................................................................................61 LINEAR EXPANSION OF A SOLID MATERIAL ................................................................66 GAS LAWS ( BOYLE’S AND GAY-LUSSAC’S LAW) ........................................................71

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INFORMATIONS AND INSTRUCTIONS FOR GENERAL PHYSICS LABORATORIES

In science, no idea is accepted, no theory is believed, until they have been tested, then tested

again. Only then can the truth of the theory emerge. The ultimate test of any physical theory is by

experiment. This reliance on experiment differentiates science form other important human activities.

Unfortunately the beginning student often misses the importance of experiment to physics. Years or

centuries after the crucial experiments have been done, the student finds scientific truth by studying a

textbook. To show the student the importance of experiment in establishing "truth", we provide the

Physics Laboratory as part of your General Physics Course. The physical laws make predictions. We

do experiments to see if these predictions hold true, and, if they do, then, and only then, can we have

confidence in the truth of the laws.

The goal of any science is to arrive at a simple and universal explanation of natural events.

These explanations start out as theories, and they become physical laws if they are shown to be true by

comparing their predictions with the results of many experiments. Your experience in the physics

laboratory will, in a way, be similar to that of scientists in research laboratories around the world.

However, our laboratory differs form the research laboratories of professional scientists in that we

already know what theory will be applied to explain the experimental results. This means that you will

probably not discover any new physical laws this semester in the physics lab. However, you will learn

some of the methods of experimental physics used by scientists at the forefront of physics research.

While taking a physics laboratory; you will learn how to make scientific measurements and

how to present and understand these measurements by means of graphs and tables. You will also learn

the inherent limitations of measurements by discussing error analysis. These techniques can be applied

to problems in a large number of fields, other than physics such as the social, behavioural, and life

sciences.

Finally, we want you to enjoy yourself in the physics laboratory. Those of you who plan to

make a career of science will find it immensely satisfying to verify the predictions of a scientific

theory. We also hope that those of you who do not go on to become practicing scientists take with you

the excitement of "doing" physics.

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PHYSICS LABORATORY RULES

The following suggestions will help you do your work in the physics laboratory:

1. Report to the laboratory promptly, ready to work. Expect to remain for the full lab period.

2. Your laboratory station should have everything you need to complete the lab assignment. If you

encounter a shortage (or damaged equipment), notify your instructor immediately. Never borrow

any apparatus from another station even though it may not be in use. At the end of the lab period,

check your station and leave it in good order. Again, call attention of the instructor to any

equipment problems you may have encountered. Space at the lab station is limited. You should

have only the laboratory manual and one or two sheets of clean scratch paper at your workstation.

Books, coats, hats, large purses, etc. should be stored elsewhere.

3. No food, drink, or tobacco in any form is permitted in the laboratory.

4. Each student working on his own conducts laboratory work.

5. The laboratory is a working area. Feel free to get up and stretch or go out for a drink of water. Talk

with your fellow students or your instructor. Consult your instructor when you have a question

about your work.

6. Do not waist time. Report to your work area, review the previous week's work and return it to the

instructor (5 minutes), and then get involved in the experiment activity. Do not wait for the

instructor to tell you what to do.

7. Be prepared before you come to the lab. Read the experiment as well as any helpful information

provided in the introductory portion of the laboratory manual before you attend lab. Failure to be

prepared will cause delays and you may not be able to complete the experiment in the allotted time.

8. Always keep your emphasis on quality of work and completeness of understanding. Do not set a

high priority on the amount of work accomplished in a laboratory period.

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LABORATORY SUPPLIES & EQUIPMENT

This laboratory manual contains write-ups of experiments to be performed during the semester,

as well as materials explaining laboratory policies and generally accepted laboratory practices.

In addition to the laboratory manual, every student should bring the following supplies to

each lab session:

• One or two pencils (We prefer that you use pencil instead of pen in the laboratory.)

• A good eraser

• A combination straightedge and protractor.

• Bring your own calculator and DO NOT plan to borrow one from your laboratory partner

NOTE: We do not allow students to fail to buy these materials and then borrow them

from other students during the lab. There will be no need to carry your physics textbook to the

laboratory. The current experiment should be read before coming to each lab period.

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EXPERIMENT 1

GRAPHS AND GRAPHICAL ANALYSIS

INTRODUCTION

In the physics laboratories the student is often asked to make a graph of the data he has gathered, and

usually the graph is the technique by which the data is analysed. It is therefore important for the student to have a good idea of how to go about plotting a graph, and how a graph may be used to analyse (particularly, non-linear) data.

In this experiment you will: (a) learn to quickly, and accurately plot a graph. (b) Learn using graphical techniques to analyse laboratory data.

THEORY

1. What is to be plotted?

When the student is told to plot, say, S versus (vrs) t, it is accepted that this means: 1) S is the dependent variable, plotted on the "y" or vertical axis; and, 2) t is the independent variable, to be plotted on the "x" or horizontal axis. This is a convention (agreement) which should be memorised.

2. Choice of Scale.

The scale of a graph is the number of (usually) centimetres of length of graph paper allotted to a unit

of the variable being plotted. For example, 1 cm for each 10 seconds of time. In general the scales for the x and y axes may be different. There are two criteria for choosing the scale of a graph, range of the variable, and convenience in

plotting:

a) range of the variable: Suppose the range of values of S is from 5 cm to 125 cm. We then need a scale for S that allows us to plot values from 0 to values somewhat greater than 125 cm. Notice that (unless told to do so by the instructor) we do not choose to suppress the zero of the graph and start the S scale from 5 cm. The reason is that we may later need to use the graph to find values extrapolated (continued) to the zero.

Also we usually try to allow space on the graph for values somewhat greater than the largest value (in this example, 125 cm) because we may take a little more data in the experiment, with larger values, or we might want to extrapolate the graph to larger values.

Finally the scale should be chosen to most nearly use the whole of the graph paper. Just because a choice of, say, l cm to represent 1 sec of time makes the graph easy to plot, we should not do this if it makes the graph only occupy a small part of the whole paper and be hard to read and use. b) Convenience in Plotting: It turns out (as we shall see in an exercise in this lab) that scales of 1, 2, 5, and 10 (and multiples of 10 of these) per centimetre are easiest to use; a scale of 4 per centimetre is somewhat more difficult, but can be used; but scales of 3, 6, 7 , 9, etc.. per centimeter are very difficult and should be avoided. In choosing scales it sometimes helps to turn the paper so that the "x-axis" is either the long or short dimension of the paper.

3. Label the Axes and put a title to the graph

The vertical and horizontal axes of the paper should carry labels of the quantities to be plotted, with units. In our previous example the label on the y-axis would be: S(cm). The graph itself should have a title. In our example the title is: Plot of S vrs t.

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4. Circle your Data Points

Each data point should have a neat circle drawn around it. If more than one experimental trial is used one can use circles, triangles, squares, with a legend to distinguish these.

5. Put a Smooth Solid Curve through the Data Points

This can be done "by hand" or with a plotting aid. Ignore any points that fall far outside the curve

(after checking that they are plotted correctly). A dashed line should indicate extrapolations to larger or

smaller values, outside of the range of data taken.

6.Graphical Analysis

Often we have data (x, y) which we believe follows the theoretical relation y = rnx + b; we can verify

this relation if we obtain a straight line when we plot y vrs x. Also, the plot obtained allows us to find the

values of m and b as follows: b = y-intercept of graph (value of y when x = 0) m = slope of graph = ∆y/∆x = (Y2-Y1)/(X2-X1 )

Other times we have data that we believe follows a non-linear theoretical relation. For example consider S = (1/2)at². We can verify this relation by plotting S vrs t². If this relationship holds then the graph will be a straight line with intercept zero. The slope of the graph then gives the constant a/2. remarks: The points chosen to determine the slope should be relatively far apart. Points corresponding to data points should not be chosen, even if they appear to lie on the line.

EXPERIMENTAL PROCEDURE

Exercise 1.

Consider the following data:

S (m) 0.27 1.08 2.43 4.32 6.75 9.72

t(sec) 0.10 0.20 0.30 0.40 0.50 0.60

• On a sheet of graph paper draw 5 lines parallel to the y-axis, each separated by a few centimetres. Plot

the values of S on the 5 lines to the following scales (with some scales you may not be able to plot all points):

a) 1 m equivalent to l cm.

b) 1 m equivalent to 2cm.

c) 1 m equivalent to 3cm.

d) 1 m equivalent to 5cm.

e) 1 m equivalent to 7 cm.

• Which scales are easy to plot?

• Which scales are difficult? Explain why.

Y (units)

X (units)

(x1, y1)

(x2, y2)

∆x

∆y

y-intercept y = mx + b

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Exercise 2.

• Plot a graph of S Vs t.

• Does this plot give a straight line?

Exercise 3.

• On the same graph paper as for exercise 2, plot a graph of S vrs. t². This should give a straight-line plot.

• What is the y-intercept of this graph?

• What is the slope of the straight line? (Include units.)

Conclusion:

Conclusions are a necessary part of every experiment. The main purpose of the conclusions is to

summarise the following:

• What was investigated? i.e. relate to how the purpose was confirmed or contradicted. What was found?

i.e. outcome of graphs and main qualitative/quantitative results • What can be interpreted? i.e. significance of graphs/results and correlation to theory • Lastly, you would discuss reasons for any serious discrepancy and any major problems encountered in

the experiment (and perhaps suggestions for improvement). When comparing experimental results to expected values, it is important to quote the result together with its associated uncertainty (error). If the difference between experimental and expected values is greater than the expected uncertainty, you should note the disagreement and give possible reasons for the discrepancy (sources of errors). If the experiment deviates from theory, then you can try to explain the deviation, or perhaps, modify the theory to account for the behaviour. For example, theory often assumes idealised conditions, but in the actual experiment these ideal conditions may not be true.

EXPERIMENT 1

GRAPHS AND GRAPHICAL ANALYSIS

NAME: . DATE: .

SECTION: .

THIS ¨PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION

1. EXPERIMENTAL PURPOSE:

State the purpose of the experiment.( 5 points )

2. Answer Pre Lab Question (5 points)

:

PHY 1401 LABORATORY REPORT

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3. RESULTS AND ANALYSIS

Exercise 1:

Graphs of S with different scales in attached graph paper: (15 points)

Questions (15 points)

Exercise 2 : Graph of S vrs. t in attached graph paper: (20 points)


Exercise 3:

Graph of S vrs. t² in attached graph paper: (15 points)


Conclusions: (10 points)

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EXPERIMENT 2

THE MEASUREMENT OF MASS, LENGTH AND TIME

INTRODUCTION: The purpose of this experiment is to familiarise you with the basic measurement necessary to make physical observations. The procedures outlined illustrate the difference between basic physical quantities(e.g. mass, length and time) and derived quantities (e.g. volume, area and density). The units used to describe these quantities are also introduced, and appreciation of the

methods and accuracy by which these quantities can be measured. BACKGROUND: Physics is fundamental an observational science. All “laws”, ”theories”, ”principles”, ...etc. are based upon experimental observation. We observe nature, and then devise laws and theories, ...etc. to explain our observations. We then test our theories by using them to predict what will happen given a certain set of conditions. We set up those conditions in experiments and in this way make further observations that either support or deny our original theory. It becomes clear then that a fundamental aspect of physics is the ability to make accurate observations. The observations themselves usually consist of detailed measurements. Often, our theories stand or fall based on the accuracy with which we can make these measurements. The quantities length , mass and time are the so-called base quantities in mechanics; their corresponding units are called the base units. The word base refers to the fact that they cannot be defined in terms of any other quantities or units; they are fundamental “building blocks” of all other quantities. That is all other quantities can be defined in terms of mass, length and time. These latter quantities are called derived quantities and the corresponding units are derived units. As a simple example, the derived quantity density is defined in terms of the base quantities mass and length, thus:

Density = Mass/Volume or, similarly, speed is derived thus:

Speed = Distance/Time

Thus, the accuracy with which density (for example) can be measured depends upon the accuracy with which length and mass can be measured.

THE EXPERIMENT: 1- Experimental Apparatus:

The apparatus for this experiment consists of: plastic ruler, meter stick, electronic balance, Ohaus balance, pair of callipers, micrometer gauge, graduated cylinder, stopwatch, and a variety of objects for measurement. 2- Experimental Procedure:

A. Measurements of Regular Shaped Objects

a) Steel cylinder measurements using meter stick and pan balance:

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• Measure the length and diameter of the steel cylinder using the meter stick record the result in the data table in your laboratory report. You should make the measurement several times and then compare results - this is one of the best way to avoid careless results in the laboratory work.

• Measure the mass of the cylinder using the pan (Ohaus) balance.

• Calculate the volume of the steel cylinder. The volume of a cylinder is the product of its height (h) and its cross-sectional area, namely:

V h r= π 2

where r is the cylinder’s radius.

• Calculate the density of the steel cylinder in the space provided and record your answer in the table. SHOW YOUR WORK, showing the correct use of units and significant figures. The density of the cylinder is then its mass (M) divided by its volume:

ρ =M

V

b) Steel cylinder measurements using vernier calliper and electronic balance:

Another useful instrument for measuring length is the vernier calliper, shown schematically in Fig 1

FIGURE 1: A vernier calliper,

• Take several readings of the length and diameter of the cylinder with the vernier calliper. When you are satisfied with your answer, record the data in the second row of the table.

• Now use the electronic balance to measure the mass of the cylinder.

• Recalculate the volume and density and show your work in the appropriate section of your laboratory report.

c) Steel sphere measurements using vernier calliper and electronic balance:

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• Measure the diameter of the sphere with the vernier calliper. When you are satisfied with your answer, record the data in the third row of the table.

• Measure the mass of the sphere by using the electronic balance.

• Calculate the density of the steel sphere. Note that the volume of a sphere is given by:

V r=4

3

3π

where r is the radius of the sphere. d) Steel sphere measurements using micrometer and electronic balance: The micrometer calliper is an instrument used for the accurate measurement of short lengths (see Figure 2).

FIGURE 2: A micrometer calliper

• Measure the diameter of the steel ball using the micrometer and record it on the fourth row of Table I.

• Calculate the density of the steel ball.

• Compare this measurement with those that you’ve made earlier. B. Measurements of Irregular Shaped Objects The above measurements were straightforward because of the regular shape of the objects concerned. The volumes of these objects were easy to calculate using prescribed formulae. However, what about irregular shaped objects, such as the rock provided in this experiment? To calculate the volume of such objects is difficult, if not impossible. To determine the density thus requires a separate measurement (i.e. not a calculation) of the volume. To do this proceed by:

• Measuring the mass of the rock using the electronic balance.

• Fill the graduated cylinder about half-full of water and note the level to which the water rises in the cylinder. Fully immerse the rock fragment in the water, and note the new water level. Subtraction of two readings gives the volume of the rock..

• Calculate the rock’s density. Show all your data and your calculations in the space provided in the laboratory report.

C. Time Measurements

• Familiarise yourself with the operation of the stopwatch. Experiment to determine the shortest time interval that you can measure.

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• Construct a ramp by taping one end of the plastic ruler and elevating one end by about 1/4 of an inch. -use a pencil or a thin notebook.

• Let the steel ball roll down the ramp and on to the table, and determine the time taken for the ball to roll over a distance of 1 m on the table. Record your results in the data table.

• Repeat the measurement three times and determine the average time value.

• From this calculate the average speed of the ball The average speed, defined as:

average speed = length traveled

time taken

D. Percent Difference and Errors a) If you have measured the same quantity more than one-way, one can calculate the percent difference between the two results. This is defined as:

100tsmeasuremen twoof average

tsmeasuremen twobetween differencedifference% x=

• Calculate the percent difference in the two values you obtained for the density of the steel cylinder, the values obtained in row 1 and row 2 of the data table I.

b) If a “true” or reference value is known for the measured quantity, one calculate a percent error for the experimental result, thus:

100 valuereference

valuereferencevalue alexperimenterror% ×

−=

• Calculate the percent error in your experimental value for this quantity (use the value obtained in row 4 of the data table I). Assume the reference value for the density of steel as 7.8 g/cm3.

• List reasons (other than measurement errors) why your measured value for the density of steel may differ from the accepted value.

c) The smallest sub-division marked on a measuring instrument is sometimes called the least measure of the instrument.

• List the measuring instruments used in this experiment and note their least measure. d) When making experimental measurements one can also expect error due to imprecision in the measurement. Thus one defines:

100measured quantity theof magnitude

instrument the of measureleast error expected ×=

• Calculate the expected errors for the diameter of the steel cylinder using the meter stick, and using the vernier callipers. Also calculate the expected error in the measurement of the diameter of the steel sphere using the micrometer gauge.

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EXPERIMENT 2

THE MEASUREMENT OF MASS, LENGTH AND TIME

NAME . DATE: . SECTION: . THIS ¨PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION

1. EXPERIMENTAL PURPOSE: State the purpose of the experiment.( 5 points ) 2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points ) Briefly outline the apparatus General procedures adopted.


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3. RESULTS AND ANALYSIS A. Measurements for Regular Shaped Objects

Data (15 points )

Data Table I: Density of Selected Solids

Object Measured

Measuring Instrument

Length (cm)

Diameter (cm)

Mass (g)

Volume (cm3)

Density (g/cm3)

Steel Cylinder Meter Stick

Steel Cylinder Vernier Calliper

Steel Sphere Vernier Calliper

Steel Sphere Micrometer

Calculations Show your work Volume of cylinder (using meter stick) (5 points) Density of cylinder (using meter stick ) (5 points) Volumes of cylinder and steel ball (using vernier-callipers ) ( 5 points ) Densities of cylinder and steel ball (using vernier-callipers ) ( 5 points ) Volumes and Densities of steel ball (using micrometer ) ( 5 points )

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B. Measurements for Irregular Shaped Objects: Rock (10 points) Volume of water (before rock immersed): Volume of water (after rock immersed): Volume of rock: Mass of rock: Density of rock: C. Time measurements

Table 3 (5 points )

Average speed calculations: (5 points)

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D. Percent Difference and Error a) Density of steel; percent difference (5 points) b) Density of steel; percent Error (5 points) Reasons for percent difference and percent error (5 points) c) Least Measures (5 points )

d) Expected Errors (5 points)

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EXPERIMENT 3

VECTORS AND EQUILIBRIUM

INTRODUCTION:

The purpose of this experiment is to confirm the laws of vector addition, and to study the

equilibrium of force vectors at a point.

BACKGROUND:

A scalar is a quantity that has magnitude only; examples are temperature, mass, and density. A

vector is a quantity that has both magnitude and direction; examples are velocity, acceleration, and force.

A vector may be represented by a straight line in the direction of the vector, with the length of the

line proportional to its magnitude. Placing an arrowhead at the end of the line indicates the direction of the vector.

Vectors may be added. The sum or resultant of two or more vectors is defined as the single vector

that produces the same effect. Figure 1 shows the resultant of two forces A and B.

The resultant is defined as the force equal and opposite to the resultant as shown in Figure 1. If the

resultant is added to the sum of A and B the sum of the forces equals zero, and the system of forces is in

equilibrium.

Vector addition may be accomplished graphically or analytically. Using the graphical method for

more than two forces we have the polygon method of vector addition: the vectors to be added are placed so

that the tail of the second is on the head of the first vector, maintaining their original directions. The tail of

the third vector is placed on the head of the second vector, etc. when all the vectors are in place, the side which closes the polygon is the resultant of the vectors. This is shown in figure 2, for the addition of vectors

A, B, C, and D. If the polygon closes by itself, the resultant is equal to zero and the vectors, if representing

forces, are in equilibrium.

Then addition of the two vectors is most conveniently carried out by the parallelogram method shown

in figure 4.

Equilibrant

Resulant

A

B

A

B R

Figure.3: Polygon method for addition of two vectors A, B

Fig. 4. The Parallelogram method to add two vectors

A, B

180

270

90

0

Resultant

A

B

Figure 1: The resultant and

equilibrant of two forces A, B.

A

B

C

D

R

Figure 2: Polygon method to

add four vectors A, B, C, D.

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Vectors may also be added analytically, and this is preferred to the graphical method since one does

not have to make precise drawings. The method is illustrated in figure 5 for the addition of two vectors A

and B. The vectors are broken down into components:

then R = Rx i + Ry j where Rx = Ax + Bx, and Ry = Ay + By

The magnitude of R is then

R = (Rx² + Ry²)1/2 = [(Ax + Bx)² + (Ay + By)²]

1/2

while the angle that R make with the x-axis is given by

θ = tan-1(Ry/Rx) = tan

-1[(Ay + By) / (Ax + Bx)]

This method may be extended easily to the sum of any number of vectors A, B, C, etc. by just replacing the

appropriate quantities in equations (1) and (2) by sums of all the x and y components.

THE EXPERIMENT:

1- Experimental Apparatus:

Vectors and the equilibrium of forces may be most easily studied in the lab by means of the force table

shown in figure 6. The apparatus consists of: force table, weight hanger, slotted weights, ring attached to

strings, and pulleys.

2- Experimental Procedure:

θθθθA

R

A

B

θθθθB

θθθθ

iAx Ax Bx

Ay

By

y

x

Figure 5. Analytic addition of two vectors A, B

A = Ax i + Ay j B = Bx i + By j where

Ax = A cos θA Ay = A sin θA

Bx = B cos θB By = B sin θB

(1)

(2)

Figure 6: Force Table

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Part A

• Mount a pulley on the 30° mark and suspend a total of 200 g over it. By means of a vector diagram

drawn to scale (choose your own scale) find the magnitude of the components along the 0° and 90°

directions.

• Set up on the force table 0° and 90° forces you found from the diagram. These forces are equivalent to

the original force. Test this statement by replacing the initial force at 30° by an equal force at 180° away from the initial direction, and check for equilibrium.

• Have your instructor check the equilibrium

Part B

• Mount a pulley on the 20° mark on the force table and suspend a total (including the mass holder) of

100g over it. Mount a second pulley on the 120° mark and suspend a total of 200 g over it.

• Draw a vector diagram to scale, using a scale of 20 g per centimetre, and determine graphically the

direction and magnitude of the resultant using the parallelogram method.

• Check your results so far by setting up the resultant on the force table. Putting a pulley 180° from the

calculated direction of the resultant, and suspending weights equal to the magnitude of the resultant does

this.

• Have your instructor check the equilibrium

Part C

• Mount the first two pulleys as in Part B, with the same weights as before.

• Mount a third pulley on the 220° mark and suspend a total of 150 g over it.

• Draw a vector diagram to scale and determine graphically the direction and magnitude of the resultant,

(Hint: This may be done by adding the third vector to the sum of the first two, which was obtained in

Part A.) Now set up the resultant on the force table and test it as before.

ANALYSIS:

1. Calculate analytically the magnitude and direction of the resultant in part B and compare to the graphical determination.

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EXPERIMENT 3

VECTORS AND EQUILIBRIUM

NAME: . . DATE: . .

SECTION: . .

THIS PAGE NEEDS TO BE DONE AT HOME BEFORE COMING TO THE LAB. SESSION



2. EXPERIMENTAL PROCEDURES AND APPARATUS:

Briefly outline the apparatus used and the general procedures adopted. (5 points )


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3. DATA and ANALYSIS:

Part A (20 points)

Attach the graphs and the analysis

Part B (25 points)


Part C (25 points)


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QUESTIONS: (20 points)

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EXPERIMENT 4

ONE DIMENSIONAL MOTION

INTRODUCTION

This experiment explores the meaning of displacement; velocity, acceleration and the relationship that

exist between them. An understanding of these concepts is essential to a later study of more complex motion

and the relationship between force and motion. The experiment allows you to record graphically the changes

in displacement, velocity and acceleration that occur when constant forces are applied to objects, using the

computer as a data acquisition and analysis tool.

THEORETICAL BACKGROUND

Displacement (distance), velocity (speed) and acceleration are three necessary concepts to be understood before one can undertake a study of the physics of motion called “kinematics”. To describe the

motion of an object we must be able to define the direction in which the motion is occurring, the speed with

which the motion occurs; and details regarding how the speed of the object changes as the motion takes place. You will have learned form your class-work that this information is contained in three vector

quantities of displacement, velocity and acceleration.

In this experiment we will be dealing only with motion in a straight line (i.e. in one dimension). In

one dimensional movement if the distance travelled by an object is ∆x and the time taken is ∆t, then the average speed of the object is simply:

t

s,speed average

∆

∆=v

The limiting value of the average velocity as the time interval ∆t approaches zero gives the instantaneous velocity,

dt

sd

t

svv

tt

vrr

=∆

∆==

→∆→∆ 00limlim

One can define the average acceleration and instantaneous acceleration in a similar way to that

already discussed. Thus we have:

t

va

∆

∆=,onaccelerati average

and

dt

sd

dt

vd

t

vaa

tt

rrrr

2

00limlim ==

∆

∆==

→∆→∆

For the special case of constant acceleration a set of equations can be derived which relate the displacements and velocities at various times to the acceleration. The derivation of these equations is given

in your textbook as,

)x(xa2vv

2

attvxx

2

t)v(vxx

avv

0

22

2

00

00

0

0−+=

+=−

+=−

+= t

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In these equations, v0 is the original speed of the object at time, t = 0; v is the speed of the object at time t; (x

-x0) is the distance travelled in time t and a is the (constant) acceleration during this period.

Finally, we note that three quantities x, v, a can be displayed graphically as functions of time. The

figures shown below give the displacement as a function of time for two different objects. The first (object A; Figure 1) is travelling at a constant velocity such that its displacement-versus-time graph is a straight line.

The slope of the displacement-versus-time graph at any time gives the velocity at that time. Since the graph

is a straight line, the velocity must be constant and thus the instantaneous velocity must always equal the average velocity. In these circumstances, the acceleration is zero since the velocity does not change.

For object B (Figure 1) we have an example of an object undergoing constant acceleration. The

displacement versus time graph is an upward curve. This means that the object is travelling further in equal

time intervals as the motion progress -i.e. its velocity is increasing. Here the instantaneous velocity does not

equal the average velocity. The instantaneous velocity is given by the value of dx/dt -i.e. by the slope of the

tangent to the line at any point. Clearly this slope increases as time increases - in other works the object is

accelerating. To obtain the acceleration we would have to construct a velocity-versus-time curve, extracted

from the above curve, by calculating the slope of the tangent at every point. This is done in Figure 2(b) where it can be seen that the velocity-versus-time graph is a straight line.

Figure 1: Position, velocity, and acceleration as functions of time for objects A and B.

27

THE EXPERIMENT:

This experiment uses a variety of options for collecting information for the physical phenomena

described above.


The apparatus consists of a microcomputer connected to Lab Pro Lab Interface box, an Ultrasonic

Motion Detector, a Logger program for Windows, a clamp, rods, a pulley, a wooden block, a metal cart, and

weights.


• Clamp the pulley to the edge of the table using the clamps provided.

• Fasten one end of the provided string to the metal cart and put a nut to hold the mass hanger on the other

end of the string.

• Set the provided masses on the metal cart.

• Plug the Ultrasonic Motion Detector into DIG/SONIC 1 of the LabPro interface.

• Place this motion detector on the same side as the pulley at about 50-cm distance from the metal cart.

• Make sure that the image of the cart is seen on the golden coloured plate of the motion detector.

• Pass the mass hanger over the pulley and make sure that the stretched string is parallel to the table.

• Switch on the computer, and monitor.

• Open Logger Pro using the icon on the desktop.

• From the Menu Bar, choose the File menu to open the MOTION file in Physics_Experiments folder

• Click on the Collect button of the toolbar in order to start the action of the Motion Detector (MD).

While operating the motion detector emits short bursts of 40 kHz ultrasonic sound waves from the gold

foil of the transducer. These waves fill a cone-shaped area about 15 to 20° of the axis of the centerline of

beam. The MD then “listens” for the echo of these ultrasonic waves returning to it. By timing how long

it takes for the ultrasonic waves to make the trip from the MD to an object and back; distance is

determined. The MD will report the distance to the closest object that produces a sufficiently strong

echo. Objects such as chairs and tables in the cone of ultrasound can be picked-up the MD.

• Select the Data menu from the Menu Bar, then Delete data set.

• Select an experiment length of 5 seconds, using the Timing button in the toolbar or by choosing the

Timing option from the Experiment menu.

• Have the metal cart with its added weight at about 50-cm distance from the MD, then let the weight

hanger slide over the pulley as soon as you click on the Start button of the toolbar.

• When the collection of data is finished (the collect button turns green and the MD stops its clicking

28

sound), and once your are satisfied with the collected data, save the data file in D or USB Drive: under

the name: met_cart.exp.xmbl

ANALYSIS OF RESULTS: On the LoggerPro Program Menu Bar, the Analysis menu provides access to various options for data

review and analysis. You can turn on an examination cursor and tangent lines. You can zoom in and out on

the data, auto-scale the graph, or try to fit a function to the data. If you select a region of a graph (this is

accomplished by pressing on the left mouse key and dragging the mouse over the desired region then

releasing the left mouse key) you can get the statistics, the regression line, the integral, or try a curve fit on

just that region.

• Open the experiment file met_cart.xmbl and select a regular region of the distance-versus-time curve.

• To this region try to fit a Quadratic function by choosing the Automatic Curve Fit from the Analysis

menu. Once the fit is finished keep it.

• Select the corresponding region of the velocity-versus-time curve and try to fit a Linear mathematical

function to the data by choosing Automatic Curve Fit from the Analysis menu. Once the fit is finished; keep it and report the values of M and B to Table 2 of your laboratory report.

• For the acceleration-versus-time curve, select the same region and choose Statistics for the analysis

menu in order to determine the average acceleration of the metal cart and report the value in the data

table, then get a print out of your computer graphs corresponding to met_cart.xmbl.

4. DATA ANALYSIS

• From your computer-generated graphs calculate the followings:

a- Average velocity from the initial time(ti) to the final time(tf). Show your work.

b- Average acceleration from initial time to the final time. Show your work.

• Since the slope of a velocity-versus-time graph is acceleration, the value of M for this graph should be

close to the value of the average acceleration from the statistics of the acceleration vrs. time graph..

Examine the appropriate quantities in Table 2 and calculate percent differences.

5. CONCLUSIONS What conclusions regarding the relationships between displacement; velocity and acceleration have you arrived at as a result of this experiment? In particular, do your data agree with the predicted

relationships for acceleration given in equations (1) - (4)?

Wooden Block Motion Detector

Pulley

Weights and mass hanger Table

EXPERIMENTAL SET-UP FOR THE MOVING CART

29

EXPERIMENT 4

ONE DIMENSIONAL MOTION

NAME: . . DATE: . .

SECTION: . .




2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points )

Briefly outline the apparatus

General procedures adopted.


30

3. RESULTS AND ANALYSIS Do a sketch of the graphs obtained in your computer (30 points)

Summary of computer generated graphs . (15 points)

Table 2: (10 points)

Graph M B AVERAGE

Velocity

Acceleration

4. DATA ANALYSIS (15 points)

31

5. CONCLUSIONS (10 points)

32

EXPERIMENT 5

ATWOOD'S PULLEY

INTRODUCTION:

Newton's second law is expressed as amFrr

=∑ , where the acceleration a may vary as the force

varies. Up to now, you have been assuming that this formula is true. This experiment will allow you to

explore the validity of this assumption by testing Newton's second law for the Atwood pulley system shown

in Figure 1.


The law governing the operation of the Atwood Pulley is

just Newton's second law:

amFrr

=∑

where F = net force on the system, m = total mass of the

system, and a = acceleration of the system. Suppose that

the pulley is massless and frictionless. Considering

Figure 2, we see that each mass feels the downward force

of gravity and the common upward string tension. The

heavier mass m1 accelerates downwards with an

acceleration a while the fixed length of the string forces

the lighter mass m2 to move upwards at the same rate of

acceleration. Applying Newton's second law to each of

the masses gives:

(1) T- m1g = m1(-a) and T –m2g = m2 a

Subtracting the two equations to eliminate the string

tension T, yields:

(2) (m1 -m2) g = (m1 + m2) a.

In this equation (2) mJ - m2 is simply the total mass m, which is accelerating under the force of gravity.

(3) Fnet = (ml – m2)g.

The linear acceleration of the system is determined using the equation for uniformly accelerated motion

h = ½(at²)

where t is the time it takes the masses to move a distance h from rest.

THE EXPERIMENT:

Figure 2: Forces acting on the

systme

33


The apparatus for this experiment consists of meter stick, electronic balance, stopwatch, mass hangers,

slotted masses, pulley, rods, and stands.


Newton’s second law F = ma involves three quantities: the net force F, the total mass m and the

resulting acceleration a. In order to test this relationship, one of the three quantities must be held constant. In

this experiment the total mass m is kept constant. The force on the system F net is varied and the resulting

accelerating a is measured.

• Start the experiment with 500 plus 25 g of the slotted masses placed on one side and 500 grams on the

other side (mass of the 50-g holders included). The mass of the heavier side is m1 while the mass of the

lighter side is m2.

• Release the mass m1 from a height h (around 1.0 m) above the floor as shown in Figure 1, and record the

time of fall to the floor.

• Calculate the system acceleration a using equation (4) and the unbalanced force acting on the system Fnet

using equation (3). Take the value of g to be 9.81 m/s². Organise all your data and results on the data

table of the laboratory report.

• Decrease the force Fnet by transferring a 1-gram slot from m1 to m2. This changes the values of m1 and m2

and also Fnet while keeping the total mass (m1 + m2) constant. Since the string may stretch, the height

should be measured prior to each run.

• Release the mass m1 from a height h (around 1.0 m) above the floor, and record the time of fall to the

floor.

• Continue decreasing Fnet by successively transferring 1 gram at a time from m1 to m2, and record times of

fall through the height h. Perform the experiment for 10 different pairs of ml and m2

ANALYSIS OF RESULTS:

• Plot a graph of Fnet versus a.

• Determine the slope and the intercept of the best-fit line. The scatter of the points about the best-fit line

is an indication of the random error in the measurement of time.

• If equation (2) is the correct theoretical equation to explain the motion of Atwood's Pulley, what values

do you predict for the theoretical slope and theoretical intercept of your graph?

• Test the agreement of theory and experiment by comparing the experimental slope and intercept to the

theoretically predicted values?

• If the intercept of the graph does not agree within error of the theoretically predicted value, calculate the

mass difference necessary to produce a force equal to the intercept. Does the mass seem reasonable? If

time permits, return to the equipment and determine the mass necessary to overcome the static friction in

the pulley.

CONCLUSIONS

• What conclusions can be made from this experiment on the basis of your graphs and results?

• If experiment and theory do not agree within error, what explanation can you give to account for the

discrepancy?

Questions

34

1. Equation (2) is arranged in the format of a straight line y = mx + b. Following the suggested procedure

identify the variables and constants then show which quantities correspond to the variables y, x and the

constants m, b respectively.

2. From equation (2), the theoretical acceleration a is given by

a == g (m1 - m2)/( m1 + m2)

Calculate the theoretical acceleration a using the experimental values of m1 and m2 from your first trial.

Do the calculated and experimental values agree within error?

3. What is the tension T in the string when m1 = 525 grams and m2= 500 grams?

35

EXPERIMENT 5

ATWOOD'S PULLEY

NAME: . . DATE: . .

SECTION: . .




2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points)




36

3. RESULTS AND ANALYSIS Table 1: (30 points)

Heavier

mass, m1

Lighter

mass, m2

(m1-m2) Height of

fall, h

Time of

fall, t

Acceleration,

a

Net force,

Fnet

GRAPH (attach graph paper. 25 points)

ANALYSIS OF GRAPH (15 points)

37

4. CONCLUSIONS (10 points)

5. QUESTIONS (10 points)

38

EXPERIMENT 6

WORK AND ENERGY IN THE SIMPLE PENDULUM

INTRODUCTION: Conservation laws play a fundamental role in modern physical theory. A conservation law is a

statement that there is some property of a system, such as energy, that does not change as we study the

system in a specified way. In this experiment, we seek to verify the law of conservation of energy for a

particular, simple system.

THEORY:

When a constant force, F, acts on an object, O, and results in a

displacement, x, the work done (W) is defined as the product of force

and displacement. Since both force and displacement are vectors, the product must be found by using not F but rather the component of the

force in the direction of the displacement; i.e., Fx in the direction of x

(x being the displacement).

W = (Fx)(x)

When an object of mass m is raised a vertical distance h=hf - hi (hf

being the final height and hi being the initial height of the object) in

the earth’s gravitational potential field, the gravitational potential energy of the object changes by an amount

GPE = mg (hf - hi )

where g is the acceleration due to gravity.

An object moving with speed, v, has kinetic energy (KE) associated with it given by the relation:

KE = mv²/2

We would also like to introduce the concept of the work-energy theorem which states that when

forces act on a body while it undergoes a displacement, the total work Wtot done on the object by all the

forces equals the change in the particle’s kinetic Energy, namely

Wtot = KE2 - KE1

Finally, the work done on an object in a uniform gravitational field can be represented in terms of a

potential energy (GPE) as: Wgrav = mgy1 - mgy2 = GPE1 - GPE2

THE EXPERIMENT:

1. EXPERIMENTAL APPARATUS:

The apparatus used in this experiment is a pendulum with a spherical

bob. A string is fastened to the pendulum bob and passes over a pulley to a

weight hanger so that a known horizontal force can be applied to displace the

pendulum. A timing device (photo-gate timer), to be explained later, allows

you to measure the speed of the pendulum as it passes through the rest position. The units of work in the SI system are (force)(displacement) =

(Newtons)(meters) = joules

x0 x1

F

Fx

x

hf

hi

Bob

Pulley

Load hi

hf

xi

xf

39

2. EXPERIMENTAL PROCEDURE:

A. Measurement of the Work Done in Displacing the pendulum:

• Measure and record the mass of the pendulum bob.

• Construct a pendulum from the provided bob and strings. Allow the pendulum to hang vertically and

place the meter stick on the table with one end directly under the pendulum bob. The meter stick should

lie along the direction of the string be used to displace the pendulum. This string should go over the

pulley placed on the lab-table edge.

• Record hi, the initial height above the table of the string fastened to the pendulum bob (measure to the

center of the bob).

• Add the weight hanger to as a load to displace the pendulum bob. The string which displaces the

pendulum should be kept horizontal (parallel to the lab-table) by adjusting the height of the pulley

• Record the horizontal displacement of the pendulum bob form its initial position in the data table of your

lab-report.

• Add 10-gram mass to the weight hanger, make sure the string is horizontal by adjusting the height of the

pulley, and record (in the data table of your lab-report ) both the load (in Newtons) and the horizontal

displacement of the bob form its initial position.

• Repeat for a series of at least 10 different loads on the weight hanger (not to exceed 150 grams for the

final load), and record both the load and the horizontal displacement of the bob form its initial position.

• For the largest load only, record the final height hf of the string attached to the pendulum bob.

• Draw a graph of Fx versus x.

• Find the work done on the pendulum by measuring the area under the curve of Fx versus x.

B. Measurement of Gravitational Potential Energy of the Pendulum:

• Calculate the increased gravitational potential energy of the pendulum bob in the elevated position (refer

to the Figure for further clarifications). Show your work.

C. Measurement of the Kinetic Energy of the Pendulum:

• Position the U-shaped arm of the photo-gate timer such that the pendulum bob hangs directly in its

center when the pendulum is at rest. During subsequent motion, the cylinder must interrupt the light

beam between the U-shaped arms to activate the timer.

• With the pendulum held at an elevated position hf turn on the timer (use the “gate” setting), and release

the mass of the pendulum from this elevated position, it will pass through the rest hi position (i.e.,

equilibrium) with a kinetic energy of mv²/2. CAUTION: The attached string can also trip the timer as it falls through the beam, consider only the time for the pendulum itself to pass through the beam.

• In your lab-report record the beam-interruption time, which corresponds to the time for the diameter of

the bob to cross the photo-gate timer.

• Repeat the measurement as necessary to insure accuracy of the time (at least four measurements).

• Measure the diameter of the pendulum bob (sphere).

• Using this mass and the average photo-gate time calculate the velocity at the lowest point of the

pendulum swing.

• Calculated the maximum kinetic energy. Report your results in the lab-manual.

• In a brief paragraph, summarise the results of your experimental work.

• Calculate percent differences (between KE and W, KE and GPE, GPE and W). What does this tell you

about the meaning of work done by the variable force? How does this demonstrate conservation of

energy? Try to account for any significant difference between your results and what you would expect to

occur.

40

EXPERIMENT 6

WORK AND ENERGY IN THE SIMPLE PENDULUM

NAME: . . DATE: . .

SECTION: . .







41

3. DATA and ANALYSIS: (10 points)

Mass of pendulum bob =

Initial height of string =

Final height of string =

TABLE 1: (20 points)

Attach graph of Fx versus x (20 points)

3. CALCULATIONS:

A.Work: (5 pints)

B. GPE: (5 points)

C. KE: (10 points)

42

4. SUMMARY OF RESULTS: (5 points)

Percent differences: (5 points)

%difference (Work and KE)

%difference (Work and PE)

%difference (PE and KE)

5. CONCLUSION: (10 points)

43

EXPERIMENT 7

ELASTIC PROPERTIES OF DEFORMABLE BODIES

INTRODUCTION:

In this experiment we have two goals. Firstly, we examine a rubber strap and a steel spring to see if

Hook’s law is obeyed and, if so, determine the constant of proportionality in the law. This constant is

frequently referred to as the “spring constant” or as the “force constant”. Secondly, we investigate the

energy transformation which occur when a mass is suspended from an elastic spring and set into vertical

oscillation.

THEORY

In 1678, Robert Hook announced his theory of elastic bodies.

Now known as “Hook’s law”, the theory states that the stretch (∆y) in a wire or spring supporting a load (∆F) is directly proportional to the load, or ∆F= k(∆y) where k is a proportionality constant

Elasticity:

Elasticity is the property of an object determining the extent to

which it tries to return to its original shape and size after removal of a

deformable force. In general the deformation of an object increases as the applied force increases. If the deformation is directly proportional

to the applied force, we say the object obeys Hook’s law. For the case

of a linear stretching of an elastic material, we may write Hook’s law

in the form:

F = kY, where F is the deforming force, Y is the deformation of the

material from its original size, and the proportionality constant k is

called the force constant. The graph of this equation (F vrs. y) is a straight line and the slope is the force constant, k.

Elastic Potential Energy: The force-displacement curve for a body that obeys Hook’s

law is a straight-line, as shown. When the body has been stretched by

an amount y1 the force is ky1. In an earlier experiment, you learned

that the area under the F(y) curve represented the work done. In this

case,

ELASTIC ENERGY IN SPRING = KY²/2 (2)

THE EXPERIMENT: 1. EXPERIMENTAL APPARATUS:

To carry this experiment you lab station should have the following items: spring, rubber band, mass

hanger, slotted weights, meter stick, ruler.


• Support the spring and meter stick as shown in Figure 3.

• Record Po (the location of the bottom of the spring when no load is applied).

y1

F

y

Work

Figure 2

44

• Add a weight hanger and record the new equilibrium

position.

• Fill up the cells of Table 1 in your laboratory report with

the data corresponding to mass increments of 20 g for the

spring.

• Change the spring with the rubber band and follow the

same procedure for recording the bottom of the band when no load is applied, when the mass hanger is added, and

when new mass in increments of 200 g is added.

• Record the data in the corresponding cells of Table 1 of

your laboratory report.

• Now, support the spring and meter stick as shown in Figure

3 again, and record P0.

• Add a weight of 150 grams (weight hanger + 100 g) to the

spring and record the new equilibrium position, P2.

• Raise the mass until the lower end of the spring is now at

an intermediate position, P1, between Po and P2.

• Release the mass and observe the lowest position to which

it descends. Repeat this last observation as necessary until

P1 and P3 are measured as accurately as possible and record

the final data to your lab-report.


• From the data collected in Table 1, plot a graph of the load-versus-displacement for the spring and

the rubber band. The graph paper is provided on the worksheet. Use the same sheet for both

graphs. Use the combination of right/lower axis for the spring data and the left/upper axis for the

rubber data.

• From the plotted data determine whether or not the steel spring and the rubber tube at your lab

station obey Hook’s law as expressed in equation (1).

• Determine the force constant, if it is appropriate. Briefly summarise the results of your work.

• From the P1, P2, and P3 measurements, you should be able to fill in the data cells of Table 2 on

your laboratory report. Use the point P3 as the reference level for the GPE = mgh. The elastic

potential energy (EPE = ½ k∆y²). Take the reference point for this energy as point P2. The total

energy (TE) possessed by the spring-mass system is the sum of the kinetic energy and the two

potential energies, that is: TE = KE + GPE + EPE

QUESTIONS:

1. What kinds of errors appear in your calculations of the energies in this experiment as a result of not

considering the mass of the spring? Think carefully and answer as specifically as you can. Can you estimate the magnitude of these errors and determine whether or not they are really significant?

2. Consider Figure 2. What would it mean if the straight line had an intercept on the F axis other than

zero (0)? How might this affect your computation? 3. Will all springs made of the same steel wire have the same force constant, k? Explain.

KEY FOR FIGURE 3

P0 : no mass position .

P1: highest point of oscillation

P2: rest position with mass.

P3: lowest point of oscillation.

45

EXPERIMENT 7

ELASTIC PROPERTIES OF DEFORMABLE BODIES

NAME: . . DATE: . .

SECTION: . .



State the purpose of the experiment.(5 points)


Briefly outline the apparatus used and the general procedures adopted. (5 points)


46



SPRING RUBBER

ADDED MASS POSITION ADDED MASS EQUILIBRIUM

GRAPH: Attach the graph(20 points)

Summary of graph: (10 points)

Suspended mass: (5 points)

p0 = ; p1 = ; p2 = ; p3 = (10 points)

Calculations of energies: GPE = mgh, EPE = ky²/2, TE = GPE + EPE + KE: (10 points)

47

Table 2: (10 points)

EPE GPE KE TE

P1

P2

P3

4. CONCLUSIONS: (10 points)

5. QUESTIONS: (5 points)

48

EXPERIMENT 8

ROTATIONAL INERTIA, ANGULAR MOTION

INTRODUCTION:

The aim behind this experiment is the study of angular motion, and the concept of rotational inertia.

In particular, to determine the effect of a constant torque upon a disk free to rotate, to measure the resulting

angular velocity, and to determine the moment of inertia of a body about an axis.

THEORY

The angular speed of a body is defined as its time rate of change of angular displacement, or the ratio

of the angular displacement, of the ratio of the angular distance which it has traversed to the time required to

travel that distance. If ∆θ is the small increment of angular distance traversed and ∆t the time required for

the body to travel that distance. Instantaneous angular speed ω is the limit of the ratio of the angular displacement over the time,

tt ∆

∆=

→∆

θω lim

0

If ∆ω is the small increment of angular velocity in the time interval ∆t, than the instantaneous angular

acceleration α is defined as,

tt ∆

∆=

→∆

ωα lim

0

The relation between the angular velocity (ω) and the tangential speed (v) of an object on the rotating body

at a distance r form its center is given by:

v = rω

The tangential acceleration of the same point as above on the rotating body is defined as:

a = α r

A rotating object has rotational kinetic energy given by:

(K.E.)rot. = ½ Iω²

where I is the moment of inertia of the rotating object. Now if the rotating object has translational motion

with velocity v as well as rotational motion if kinetic energy is the sum of the two kinetic energies,

K.E. = ½ mv² + ½ Iω²

A ball of radius R rolling about an axis through its center has a moment of inertia of I=2/5 MR², will have

through any point of its motion down the inclined ramp a total mechanical energy of:

T.E. = mgh+½ mv² + ½ Iω²

Angular momentum (L) is the analogue of linear momentum of a particle. For a particle with a constant

mass m, velocity v, linear momentum p = mv, and position vector r relative to the origin O of an inertial frame, the angular momentum L is defined as

vmrprLrrrrr

×=×=

Eq. 1

Eq. 2

Eq. 3

Eq. 4

Eq. 5

Eq. 6

Eq. 7

Eq. 8

49

For a rigid body with a moment of inertia, I, that is rotating around a symmetry axis with angular velocity ω

its angular momentum is given by:

vmrprLrrrrr

×=×=

When the net external torque acting on a system is zero, the total angular momentum of the system is

constant (conserved).

THE EXPERIMENT:


On you work station you will be provided with an angular momentum apparatus which consists of:

25 cm wheel that revolves on a low-friction bearing, an acceleration timer, a 40 cm metal arm with 3 cups,

metal balls, and an adjustable launching chute. You will also find a photo-gate timer, a D.C power supply, a

vernier calliper, and a ruler.


A. Measurements of the Ball Velocity:

• Place the photo-gate timer at the base of the

inclined ramp, in a position to detect the metal

ball as it leaves the launching ramp.

• Set the photo-gate timer in the GATE mode.

• Record the height (H), the start-up point in the

launching inclined ramp of the rolling ball, in

your laboratory report.

• Record the height (h), the point at which the

ball leaves the launching inclined ramp, in your laboratory report.

• Place the metal ball on the top of the launching

inclined ramp at height (H), and release it.

• Measure the time that the ball diameter took to cross the photo-gate timer

• Repeat the same measurement for at least three times (make sure that the ball is released from the

same starting point, H).

• Report the data in your laboratory report write-up.

B. Measurements of the angular momentum:

• Tape a waxed recording tape on the rim of the

rotating disc.

• Make sure that the timing motor’s chain makes

contact with the rotating disc rim.

• Release the ball from the same initial height (H)

as in part A.

• As the ball gets inside the outside cup in the metal arm, press on the red button of the timer. As the

disc rotates, there will be marks on the waxed recording tape.

• Record the time for on revolution of the disc.

• Remove the waxed recording tape from the rim the disc

• Measure the distance between the successive points and record the values in table II of your

laboratory report.

Rim of rotating disc

Rotational velocity, ω

Metal arm with ball inside one of the 3 cups

Ball rolling down an incline

H

h

v

ω

Photo-gate timer

Start-up point of the rolling ball

Eq. 9

50

DATA ANALYSIS:

A. Measurements of the Ball Velocity:

• From the data obtained in part A of the experiment calculate the linear speed of the ball as it leaves the

ramp by using the conservation of the mechanical energy given by equation 7 in the theoretical

background section.

• Compare this calculated velocity to the measured velocity obtained from the data recorded in table I (that

is find the percent difference between the two velocity values).

• Explain the reasons for any difference between the two velocities.


• Calculate the circumference of the rotating disc (C=2πr) and divide it by the distance between two

waxed tape marked points, this will give you the number of points marked on the waxed tape during a complete disc revolution.

• Divide the time for one complete disc revolution by the number of points marked on the waxed tape

during a complete disc revolution to obtain the time between successive data points.

• In a graph paper plot distance obtained from data table II versus the time. Calculate the disc’s rotational

speed.

• Using equation 8 for the system of the ball and metal arm on the disc; calculate the angular momentum

just before impact.

• Assuming that no external torque act on the system of the ball and metal arm on the disc, use the

conservation of angular momentum to find the moment of inertia of the system.

• Calculate the moment of inertia of the system.

51

EXPERIMENT 8

ROTATIONAL INERTIA, ANGULAR MOTION

NAME: . DATE: .

SECTION: .




2. EXPERIMENTAL PROCEDURES AND APPARATUS: (5 points)




52


A. Measurements of the Ball Velocity: (15 points)

The initial height of the ball as it starts at the top of the ramp (H):_________________

The height of the ball as it leaves the ramp (h):_____________________

The moment of inertia of the ball (I=2/5 MR²):_________________________

Velocity of the ball as obtained by the conservation of mechanical energy: (show your work)

TABLE I: (10 points)

Ball Diameter (cm) Time (s) Velocity (m/s)

First Trial

Second Trial

Third Trial

% Difference between measured velocity (from table I) and calculated velocity: (5 points)


TABLE II. (15 points)

TIME INTERVAL MEASURED DISTANCE (cm)

Graph: (15 points)

53

.

4. CALCULATIONS:

Time between successive data points (show your work): (5 points)

Angular velocity of the rotating disc: (5 points)

Angular momentum before impact (show calculations): (5 points)

Moment of Inertia of the system: (10 points)

5. CONCLUSION: (5 points)

54

EXPERIMENT 9

THE SIMPLE PENDULUM

INTRODUCTION The simple pendulum offers a method of measuring the constant acceleration due to gravity very

precisely. The object of this experiment is to study simple harmonic motion of the simple pendulum and to

measure the acceleration of gravity g.


A simple pendulum is defined, ideally, as a particle suspended by a weightless string. Practically it

consists of a small body, usually a sphere, suspended by a string whose mass is negligible in comparison

with that of the sphere and whose length is very much grater than the radius of the sphere. Under these conditions, the mass of the system may be considered as concentrated at a point -namely, the center of the

sphere- and the problem may be handled by considering the transitional motion of the suspended body,

commonly called “bob,” along a circular arc.

Figure 1: Diagram Analysis of the Simple Pendulum.

Consider the diagram of a simple pendulum shown in Figure 1. In its equilibrium position the bob is at the point A vertically below the point of support O. In this position the downward pull of gravity w is

counteracted by the upward pull p of the cord. When the bob is displaced to some point B, the weight w=mg

may be resolved into two components. One n normal to the arc AB which is counteracted by the pull p of the

string, and a force f tangent to the arc that tends to restore the pendulum to its equilibrium position. The

greater the displacement, the greater is this component f and the less the force p in the string, as can be seen

by comparing positions B and C. Thus the bob is subjected to a translational force f which increases with the

displacement and always tends to reduce the displacement. When the pendulum is released from a given displacement, it moves with increasing velocity toward

its equilibrium position, acquiring thereby momentum that carries it through the neutral position and

produces a negative displacement. It should be noted here that the choice of positive and negative directions is purely arbitrary. It is convenient, although not necessary, to call displacements to the right positive and

those to the left negative. Neglecting the effect of friction, the maximum negative displacement will be

equal exactly to the initial positive displacement. When the point B’ is reached, the restoring force causes a

reversal of the motion and the bob returns to B. This to-and-fro motion of a pendulum is called “vibratory”,

or “oscillatory”, motion.

The translational force f is equal to mg sin θ, as apparent from the vector diagram in Figure 1, where

θ is the angle the string makes with the vertical at the instant shown. Note that if angle θ is small, sin θ is

55

very nearly equal to the displacement, arc length x, divided by the string length l, sinθ = x/l.

fmg

lx= − ( Eq. 1)

Thus, if the amplitude of vibration is small; the resultant force on the ball is at all times proportional

to the displacement x as required for simple harmonic motion. Now, from Newton’s second law of motion,

we know that:

f ma md x

d t

mg

lx= = = −

²

² (Eq. 2)

A solution of Equation (2) requires that the second derivative of x be proportional to the negative to

x. Either the sine or cosine of some function of time will satisfy this requirement, we choose a solution of the form:

x A t= sinω (Eq. 3)

where

fmg

lx=− (Eq. 4)

is the angular velocity. The period of vibration is the time required for it to go through one cycle (i.e., the

time for pendulum to move from any point on its path back to the same point with motion in the same

direction), and is related to ω by the relation T = 2π/ω.

Tl

g= 2π (Eq. 5)

Note finally that the constant A in Equation (3) is the amplitude of the motion which measures how

far the bob swings away from the vertical -the maximum value of the displacement. This is conveniently expressed as an angle in degrees.

THE EXPERIMENT:

After you read the preceding material, you may notice that among the factors that might affect the period of a simple pendulum are the mass of the pendulum, the length of the pendulum, and the amplitude of

its swing. We shall confine our attention to these as they are easy to control experimentally.

If we are to investigate the effect of any one of these variables on the period of the pendulum, the remaining variables must be controlled (i.e., they must not be allowed to change during the experiment).

Suppose we start with an investigation of the effect of length upon the period. This means that we choose a

pendulum of fixed mass, allow it to swing always through angles of the same amplitude, and observe

changes in the period due to changes in the length of the pendulum.


The experimental apparatus consists of rods, clamps, pendulum bobs, string, metric ruler, stop watch, protector, electronic balance, computer, the LabPro interface, LoggerPro program and the Motion Detector.


A. Effect of changing length on the pendulum period: • Prepare a pendulum about 1 m long.

• Position the Ultrasonic Motion Detector so that it monitors the motion of the pendulum. Remember

that the pendulum must be placed at more than 0.5 m distance away from the motion detector.

56

Use the computer to measure the position of the ball versus time. To do this make sure the motion sensor is plugged into the Lab Pro device and the Lab Pro’s USB cable is plugged into the computer. Open Logger Pro using the icon on the desktop. Logger Pro should automatically recognize the sensors, if it doesn’t:

Click on LabPro icon, a window will open with a picture of the LabPro. Select the Dig/Sonic 1 box in the

upper right hand corner and choose the Motion Detector You can close the LabPro window now.

• Give the mass a small displacement from equilibrium (around 5 degrees), let it swing within the range of the motion detector, and click the Collect button to start the data collection. Make sure that the time period for data collection is long enough to accommodate at least ten periods (use the timer icon) of the pendulum swing.

• Repeat this step until you obtain a good data set.

• While you are taking these computerized data acquisitions, you should use the provided stop-watch to measure the time for the ten periods of the pendulum oscillations. This period can be determined with greater accuracy if the time to make a large number of cycles (say 10) is noted and the period calculated by dividing the total time by the number of cycles.

• Record the mass, amplitude, length, and period of the pendulum in Data Table 1.

• Decrease the length of the pendulum by about 15 cm and determine the period in the same manner, and record the results in data Table I.

• Repeat the measurement for total 5 lengths of the pendulum, the last length should be about 20 cm, and record the results in data Table I.

Remember that both the mass and the amplitude must remain the same throughout this series of

observations.

B. Effect of changing mass on the pendulum period:

• Prepare a pendulum about 75 cm length.

• Change the mass while holding the length and the amplitude constant. Displace the mass at a small

angle (around 5 degrees).

• Use the stop-watch to measure the time for the ten periods of the pendulum oscillations.

• Record the period of oscillation in data table II.

• Repeat the same procedure for three different masses, and report the results in data table II.

C. Effect of changing amplitude on the pendulum period:

• Prepare a pendulum about 75 cm length.

• Change the amplitude while holding the length and the mass constant. To start displace the mass at a

small angle (around 5 degrees).

• Use the stop-watch to measure the time for the ten periods of the pendulum oscillations.

• Record the period of oscillation in data table III.

DATA ANALYSIS:

• Using the data collected in Table I, prepare a graph of the period versus the length of the pendulum.

• What does this graph tell you about the relationship between length and the period.

• On the same sheet of graph paper, plot a graph of T² versus L (This required a different vertical scale

since a different quantity is being plotted). To avoid the confusion, place the new scale along the right

margin of the graph paper.

• What is the form of this graph? Explain the relationship between the length and the period.

• Summarise the results of your three experiments. Examine your data and graphs carefully before

writing.

• Using graphs of T² vrs. L, calculate the experimental value of g by comparing the slope of the graph with

equation 5.

57

• Show your calculation on the worksheet. Compare your calculated g value to the theoretical value of 9.8

m/s².

• Equation (3) describes the motion of the bob for a simple pendulum undergoing simple harmonic motion

(vibrating with small amplitude). From the plotter graph windows describe the motion of the pendulum

bob, and explain if you happen to see the effect of friction on this motion.

QUESTIONS:

1- Identify variables other than those investigate in this experiment which might affect the period of

pendulum.

2- Many clocks are regulated by the swinging of o pendulum. Most materials expand when heated. Would

this cause a pendulum clock to run fast or slow on a hot summer day? Explain your reasoning?

58

EXPERIMENT 9

THE SIMPLE PENDULUM

NAME: . DATE: _____________________ .

SECTION: .



State the purpose of the experiment (5 points )





59



Length, L Time for 10 cycles Period, T T²

LoggerPro Stop watch LoggerPro Stop watch LoggerPro Stop watch

TABLE 2: (10 points) TABLE (10 points):

Discussion of first graph: (5 points)

Summary of second graph: (5 points)

Summary of three experiments: (10 points)

Description of the pendulum bob movement using the data graph windows: (5 points)

60

Calculations of “g”: (5 points)

Comparison between theoretical value and experimental result of “g”, Percent error: (5 point)

Attach MPLI plotter graph windows and analysis(10 points).

CONCLUSIONS: (10 points)


61

EXPERIMENT 10

BUOYANT FORCES

INTRODUCTION:

The purpose of this experiment is to determine buoyant forces on submerged solid objects, and to investigate the dependence of buoyant forces on volumes and masses of submerged objects

BACKGROUND:

When a solid objects submerged in a fluid (gas or liquid), an upward force is exerted by the fluid on

the object. This force is called the buoyant force (B). The magnitude of the buoyant force always equals the

weight of the fluid displaced by the object (Archimede’s Principle). In other words,

B = ρf Vg

where,

ρf = Density of fluids (mass/unit volume of fluid)

V = Volume of the solid object g = Gravitational acceleration (9.81 m/sec²)

Let us examine the external forces acting on an object submerged in a fluid (see figure 1). The

object is supported by a string attached to a balance. Assuming the system is in equilibrium, then:

B = mg - T1

where T1 = Tension in the string (weight of the object when submerged).

If the same object is weighed in air and assuming no buoyant force due to air:

mg = T2

From equation 2 and 3 one can find that,

B = T2 - T1 = (weight of the object in air) - (weight of the object in fluid)

Figure 1: Set-up and Analysis of Buoyant Forces

The apparatus shown in figure 1 will be used for this experiment. The spring balance provided has a

special hook attached to the bottom. Masses to be measured should be attached to this hook, and their

weight should be read from the spring balance scale.

THE EXPERIMENT:


(1)

(Eq. 2)

(Eq. 3)

(Eq. 4)

mg

T2

mg

T1

B

- - - -

Spring balance

Container filled with liquid

Suspended sphere

62

The apparatus for this experiment consists of:

Spring balance, masses to be measured, and beaker, Vernier-calliper


A. Measurements for Different Spheres With the Same Volume:

Spheres of different masses but of equal volumes are provided for the purpose of this study. Prepare

a table to record your results as you proceed.

• Measure the dimensions of these spheres and be sure that their volumes are almost the same. Use a

vernier for these measurements.

• Attach one of the spheres to the spring balance.

• Measure the mass of the sphere in air.

• Continue to measure the masses of other spheres in air.

• Submerge one sphere in liquid measure its mass while in the liquid.

• Do the same for other spheres and find their masses while in liquid.

• Use equation # 4 to determine the buoyant force in each case.

• Record your results and include units.

B. Measurements with Different Masses:

Another set of spheres of different volumes and masses are provided for the purpose of this part of

the experiment. Again, prepare another table to record the results of this part and proceed as follows:

• Use a vernier to measure the dimensions of all masses ( except those that were used in part A).

• Find the volume of each mass.

• Measure the masses of the spheres in air.

• Submerge one sphere in liquid measure its mass while in the liquid.

• Do the same for other spheres and find their masses while in liquid.

• Use equation # 4 to determine the buoyant force in each case.

• Record your results and include units.

• Use graph paper to plot buoyant force versus volume of submerged object for each liquid.

DATA ANALYSIS:

Now with all these data at hand, you should be able to answer the following questions:

• What conclusion could by reach on the basis of the results of part A

• Do you think that the above conclusion would be reached if you use another liquid? Explain.

• Using the results of part B (slope of the graph), determine the density of water.

63

EXPERIMENT 10

BUOYANT FORCES

NAME: . DATE: .

SECTION: .







64

3. RESULTS AND ANALYSIS

A. Measurements for Different Spheres With the Same Volume:

Data (25 points )

Data Table I:

Object

Measured

Length

(cm)

radius

(cm)

Volume

(cm3)

Mass in

air (g)

Mass in

fluid (g)

Buoyant force

(N)

Calculations Show your work for one of the objects measured (5 points)

65

B. Measurements with Different Masses:

Data (25 points )

Data Table II:

Mass

Measured

Length

(cm)

radius

(cm)

Volume

(cm3)

Mass in

air (g)

Mass in

fluid (g)

Buoyant

force (N)

Calculations Show your work for one of the objects measured (5 points)

RAPH (15 points)

QUESTIONS (15 points)

66

EXPERIMENT 11

LINEAR EXPANSION OF A SOLID MATERIAL

INTRODUCTION:

Earlier this semester, we saw that the length of the pendulum effects the period. Many practical

devices, such as the mercury thermometer, work on the principle of thermal expansion. It is important for

engineers to take thermal expansion into account when designing structures. Bridges; for example, often

have joints in the roadway to allow for thermal expansion without damage.

It is found that change in length of a solid is proportional to the original length and to the change in

temperature. The constant of proportionality, which is called the coefficient of linear expansion, depends on the material of which the solid is made. It is the purpose of this experiment to determine the coefficient of

linear expansion of several metals.

THEORY:

Most solids expand when they are heated, except for those rare cases where the molecular structure

simultaneously changes to a more dense form. Ice, for example, shrinks upon melting and alloy Inver

gradually changes crystal form to a more compact structure upon heating. These few exceptions to the

general rule extend over a range of only a few degrees.

When you heat an iron rod, its molecules vibrate more violently. They shove one another away

causing the rod to expand. When the rod cools again its molecules vibrate less violently and it contracts.

It is interesting to note that each solid has a characteristic rate of expansion unique to that solid. The

rate of expansion is determined by heating a measured length of the solid through a definite temperature change and then measuring the change in length.

The coefficient of linear expansion, α, is a number which indicates the change in length per unit

length per degree of temperature change. It is a characteristic property of the material and can be calculated

as follows:

α =×

∆

∆

L

L T0

where,

∆

∆

T T T

L L L

H

H

= −

= −

0

0

TH is the hot temperature at which the new length is LH, and T0 is the initial temperature of the rod when its

length is L0.

THE EXPERIMENT:


In this experiment you will use a steam generator (boiler), heating plate, aluminium rod, brass rod,

copper rod, heating jacket, laboratory fingers, thermometer, power supply, lamp, and electrical cables.

67

Figure 1: Experimental Apparatus.


The thermal expansion of three materials will be investigated -aluminium, brass, and copper. To

operate simply

• Insert the desired rod in to the heating jacket.

• Place the heating jacket onto the base so that the water in-take valve is at the end nearest to the electrical

terminals. The thermometer should be facing up, and should be inserted in the stop-cock at the jacket

center. The water outlet valve that is near the micrometer should be placed near a laboratory sink.

• The length of the rod is found by adjusting the micrometer dial until electrical contact is established (see

Figure 1). To establish electrical contact between the rod and the lamp follow part (b) of Figure 1.

When electrical contact is established the lamp should light up.

• The micrometer screw should initially not be touching the rod. If there is contact, turn the dial until a

small gap exists between the rod and the screw.

• Fill the thermal expansion apparatus jacket with tab water and record the length of the Aluminium rod

and the water bath temperature.

• Turn the micrometer dial counter-clockwise for two complete turns so that there’s no electrical contact

(the light is off).

• Heat-up water contained in the steam generator to a particular temperature about 35 °C; and then pour it

in the heating jacket through the intake hose. You should use the laboratory fingers to pour the hot

water, gently, from the flask into the apparatus’ jacket. HANDLE WITH EXTREME CARE. DON’T

BURN YOURSELF!!.

• Once the jacket is filled with the hot water, allow at least 30 seconds for the rod temperature to reach

equilibrium with the water temperature, and turn the micrometer dial until the screw just makes contact with the rod, then record the micrometer’s reading for the final length, LH.

• Repeat this procedure (i.e. heating water, pouring it in the heating jacket, and measuring new length of

the rod) for four different hot water temperatures (about 50 °, 60°, 70°, and 85°).

• Record all the data in data Table 1.

For the Copper, and brass rods it is only necessary to measure ∆L obtained from the tab water bath

and at another hot water temperature. Record this data in data Table 2.


For the aluminium rod (data table 1):

68

• Construct a graph of ∆L versus ∆T.

• Calculate the slope and compare the value obtained for α with the given theoretical value.

• Discuss your graph.

From Table 2:

• Compare results.

Summarise all of your results and calculate percent errors for all α‘s.

TABLE: Linear Expansion Constants for Common Materials:

Solid αααα (Per °C)

Aluminium

Brass

Copper

Glass

Glass (Pyrex)

Invar (nickel/iron alloy)

Iron

Platinum

Quartz

Steel

Tungsten

0.000022

0.000019

0.000017

0.000007

0.000032

0.000007

0.000012

0.000009

0.000004

0.000013

0.000044

QUESTIONS:

What would happen to the coefficient of thermal expansion if the rod is not made of a pure metal?

For an Aluminium rod that is twice as long as the one used in our experiment, estimate the expected linear

expansion of this rod at the same highest temperature used in our experiment.

69

EXPERIMENT 11

LINEAR EXPANSION OF A SOLID MATERIAL

NAME: . DATE: .

SECTION: .








70



T0 TH ∆T L0 LH ∆L

GRAPH: (30 points)

Slope of Graph and ααααAl calculation: (10 points)

Discussion of Graph: (5 points)

Percent errors: (10 points)

4. CONCLUSIONS: (5 points)

5. QUESTION (5 points)

71

EXPERIMENT 12

GAS LAWS ( BOYLE’S AND GAY-LUSSAC’S LAW)

INTRODUCTION:

In order to specify fully the condition of a gas it is necessary to know its pressure, volume, and

temperature. This quantities are interrelated, being connected by the general gas law, so that if any two of

them are known, the third is determined by the mathematical relation between them.

One of the important properties of a gas is that it always tends to expand until it completely fills the

vessel in which it is placed, and thus the pressure it exerts depends on the volume it occupies. To describe

fully the condition of a gas it is necessary to give not only the volume but also the temperature and pressure,

because they are all interrelated.

The purpose of this experiment is to study two of the gas laws; that is, to develop the relation

between the volume and the total pressure of a given mass of gas when the temperature is kept constant; and to investigate the variation of the pressure, of a given mass, of gas with changes in its temperature, when the

volume is kept constant.

the volume to the pressure, and the pressure to the temperature.

THEORY

In studying the behaviour of a gas under different conditions of pressure, temperature, and volume, it

is convenient to keep one of these constant and to vary the other two. Thus, if the temperature is kept

constant, one obtains the relation between the pressure and the volume; if the volume is kept constant, one gets the relation between the temperature and the pressure.

Boyl’s law: if the temperature is kept constant, the volume of a given mass of gas varies inversely as

the pressure. This means that for a constant temperature, the product of the volume and the pressure of a given amount of gas is constant. Thus

PV = constant (Eq. 1)

or P1V1 = P2V2, where V1 is the volume of a given mass of gas at pressure P1, and V2 is the volume at

pressure P2.

The experimental test of Boyl’s law consists in observing a series of different volumes, measuring

the corresponding pressures, and observing how nearly constant the product of the two remains.

GAY-LUSSAC LAW: if the volume remains constant, the pressure of a container of a gas is directly

proportional to its absolute temperature.

THE EXPERIMENT:


To demonstrate the concept of BOYL’S LAW (pressure vs. volume) and GAY-LUSSAC’S LAW

(pressure vs. absolute temperature) you will use the Pressure Sensor and the temperature Probe with the

Vernier Logger Pro Software and its Interface (Lab Pro). You will also find your laboratory station equipped with an Erlenmeyer flask, beaker, and heating plate.


The white stem on the end of the Gas Pressure Sensor Box has a small threaded end called a luer lock.

With a gentle half turn, you may attach the plastic tubing to this stem using one of the connectors already

mounted on both ends of the tubing. The Luer connector at the other end of the plastic tubing can then be

connected to one of the stems on the rubber stoppers that are supplied, as shown in figure 1.

72

Figure 1 Figure 2 Figure 3

Preparing Logger Pro for Measurements

A. Boyl’s law experiment:

• Connect the Pressure Sensor into the LabPro interface's Ch.1; Open the LoggerPro application from the

desktop.

• Set the syringe to 20 cc volume.

• Connect the 20mL plastic syringe directly to the stem, as shown in figure 3, to secure the connection

twist the syringe with a gentle 1/2 turn. The pressure inside the syringe is now equal to atmospheric

pressure at the selected volume.

• Open Boyle’s Law file from Physics_Experiments folder

• Click the Collect button and monitor the pressure in the data table. Make sure that the pressure on the

syringe keeps the volume at 20 cc while your are collecting the data.

• When this pressure has stabilized, read the volume on the syringe and click Keep button. A data

entry box will appear allowing you to enter the volume of air in the syringe; in this box you should

record the syringe volume in cc (i.e. 20).

• Decrease the volume to 15 cc and take a new pressure measurement. Again let the pressure stabilise

before you click the Keep button.

• Collect the pressure for the volumes of 12 cc, 10 cc, and 7 cc by following the same procedure outlined

in the previous steps.

• Click Stop once you have taken all the readings

• Save this data in D drive or USB drive: under a filename that consists of six characters. The first three

characters should correspond to the first three letters in your last name and the last three characters

should be Boy. Example Rac_Boy for Rachid.

B. Gay-Lussac’s law:

• Plug the temperature probe in Channel 1, and the pressure sensor in Channel 2.

• Connect the white valve stems to one end of the long piece of plastic tubing.

• Connect the other end of the plastic tubing to one of the stems on the rubber stoppers (figure 2). This

rubber stopper should, in turn, be inserted into the Erlenmeyer flask to provide a constant-volume gas

sample.

Note: the 2nd valve on the rubber stopper is shown in a closed position. (Check this?!).

• Insert the Erlenmeyer flask in a cold water bath of the beaker (make sure that the beaker is not too full of

water, so that no water splash over).

• Open the GAY-LUSSAC file from the File menu.

• Set the experimental time to 10 minutes.

• Place the water baths on top of the heating plate, and immersed in the water you should have Erlenmeyer

flask and the Temperature Probe. Make sure that the temperature probe is not touching the walls of

the water bath.

73

• Set the heater at 3/4 of its full scale, and then turn it on.

• Click the Collect button to have the computer collect data for the change in pressure as a function of

temperature for the period of 10 minutes.

• Save this data in drive E or USB drive: under a filename that consists of six characters. The first three

characters should correspond to the first three letters in your last name and the last three characters

should be Gls, Example Rac_Gls for Rachid.

ANALYSIS OF RESULTS: A. Boyl’s law experiment:

• In a new column of the data table from the saved Boyle’s experiment file have the computer calculate the

product PV for each pressure.(Data��new calculated column)

• Leave the Graph and the Data windows on your screen and close the text window. Call the laboratory

instructor to check your results.

• Plot a second curve using the values of the pressure as the dependent variable and the corresponding

values of 1/V as the independent variable. You can easily graph pressure vs. the reciprocal of the volume by clicking on the "volume" label on the x-axis of the graph, and from the list of columns that will

appear; select "1/V" then click on the "autoscale button ".

• Using the curve fitting options in the Analyze menu, show how your results and curves verify Boyle’s

law. Explain the shape of the curves.

B. Gay-Lussac’s law:

• From the saved data file for the Gay-Lussac experiment, using the curve fitting option in the Analyze

menu, and show how your results verify the Gay-lussac’s law.

• Explain what the slope of the curve represents.

QUESTIONS:

1- Explain what effect a change in temperature will have on the Boyle’s law experiment.

2- What is the barometric pressure in Ifrane? Would you expect this value to be different than the barometric pressure in Rabat? Explain your reasoning.

74

EXPERIMENT 12

GAS LAWS (BOYLE’S AND GAY-LUSSAC’S LAW)

NAME: DATE: .

SECTION: .








75


Attach computer printouts from the Logger Pro Program with the Table window showing PV

column, and the Pressure-versus-Volume graph: (15 points)

Attach computer printouts from the Logger Pro Program with the plot of P-versus-1/V graph with

the corresponding automatic curve fit: (15 points)

Comparison of the graphs with Boyle’s law: (5 points)

Explain the shape of the curves: (10 points)

Attach computer printouts from the LoggerPro Program with the Pressure-versus-Temperature

graph and the corresponding automatic curve fit: (15 points)

Comparison of the graph results with the Gay-lussac’s law: (5 points)

Slope of Pressure-versus-Temperature graph and its physical significance: (10 points)

76

CONCLUSIONS: (10 points)


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