Forces and Friction

Foundation Mechanics Forces and Friction H10FM1 & H10FM2

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UNIVERSITY OF NOTTINGHAM

FOUNDATION MECHANICS

LABORATORY 1

FORCES AND FRICTION

Aims:

1. To use vector addition to prove equilibrium of a series of forces 2. To investigate the Laws of Friction

Introduction

This laboratory is split into two sections, each one should take you about one hour to

complete. They are based on the self contained Leeds Mechanics Kit.

NOTE:

Before you come to the laboratory session, you should complete the attached worksheet

to help you understand some of the concepts.

The report should be written according to the material available on WebCT in the Study

Skills lecture on writing laboratory reports. You are STRONGLY advised to use the

report writing template and adapt it.

You should include a copy of the sheet obtained during part (1). You only need to add

any method if you did something different to the method in this laboratory sheet.

Remember that you have ONE WEEK to complete the report.

You need to submit the report electronically via the Turnitin option on the WebCT site

for Foundation Mechanics.


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Part 1 Vector addition of forces

Equipment

Leeds Mechanics Kit

A selection of masses

Length of inelastic string

Pulleys

Mass hangers

Sheets of paper

Blutak or other self-adhesive fixing agent

Ruler

Protractor

Method

1. Lift the lid of the box into the upright position and fix it in position using the support inside the box.

2. Place each of the two pulleys into two of the holes along the edge of the lid (see figure 1)

Figure 1 Leeds Mechanics Kit as a Force Board

3. Attach a piece of paper to the lid (as shown in figure 1) using the Blutak.

4. The inelastic string is hung over the pulleys and the mass holders are attached to each of the three ends.


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5. Select three masses to attach to each of the mass holders that will enable the system to attain equilibrium.

6. Mark the position of the string onto the paper. Note the TOTAL mass on the end of each of the mass holders.

7. Now repeat the set up for another four sets of different masses, so that each of you has at least one original set of results to include into your report (note, you will

also need the results of the other members of your laboratory group.

Analysis of results

Once you have obtained the direction of the string on your piece of paper, draw the

SPACE DIAGRAM showing the position of the string during the experiment.

Measure the angles s shown in figure 2.

Knowing the masses applied to the end of the string, mark on the Space Diagram the

tension in each of the strings.

From this space Diagram construct the VECTOR DIAGRAM or use the ideas of

resolving forces to analyse the results (i.e. resolve each of the tensions into its vertical

and horizontal component and use these components to mathematically establish

equilibrium), and if the calculations suggest that equilibrium hasnt been established, look at the experimental set up and ask is there a net force on it?

What you should obtain, for each test is something like this:-

F2 F3

2 3

F1

Figure 2 Angles to be measured

The loads F1, F2 and F3 are assumed to be the same as the weights attached to the string

(if there is no friction over the pulleys is this a valid assumption?)


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The angles 2 and 3 can be measured from the vertical extension of the line of action of load F1.

If we now resolve horizontally

F3 sin 3 = F2 sin 2

Resolving vertically should give

F1 = F2 cos 2 + F3 cos 3

What you need to do is calculate the percentage differences from the two equations for

EACH test.

For example, if we had the following results

F1 = 16 N, F2 = 12 N, F3 = 16 N, 2 = 40o and 3 = 45

o, then

Horizontally 16 sin (45o) 12 sin (40o)

There is an error here as the left hand side does not equal the right hand side. You can

find the error by taking away the two results and dividing it by one of them.

Thus

Error = 16 sin (45o) - 12 sin (40

o) x 100 = 18.7 %

16 sin (45o)

Vertically Calculated F1 = 16 cos (45o) + 12 cos (40

o) = 20.5 N

Now calculate (F1 Calculated F1) x 100 = (16 20.5) x 100 = -28.2% F1 16

This will give you a percentage error. The question is that you must address is is this significant? Now discuss this in the discussion!

Points for discussion

1. Why is each string assumed to be light and each pulley smooth? 2. Why is the string assumed to be inelastic? 3. Within reasonable experimental error, has equilibrium been established? 4. How can two forces be combined to produce a resultant?


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Part 2 Friction

Equipment

Leeds Mechanics Kit

Friction plane

Wooden block

Masses of various sizes

Mass holder

Method

1. Find the mass of the wooden block by weighing it.

2. Set up the apparatus as shown in the figure below (figure 3)

Figure 3 Friction experiment

3. Start off with the plane horizontal.

4. Place the wooden block on the friction plane. Add masses to the mass holder until the wooden block is JUST on the point of sliding (you may find that light tapping

on the wooden block helps determine this point).

5. Record the mass (M1) of the wooden block and the mass applied to the mass holder to just start the block moving (m).

6. Increase the mass of the wooden block by adding masses to it. Find the new mass that has to be applied to the mass holder to JUST start the wooden block moving

(m).

7. Repeat the procedure (5) and (6) for 5 more different masses (M1), recording the applied mass to the mass holder (m) to JUST start it moving.


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8. Plot a graph of applied mass (m) against the mass of the wooden block (including any additional masses you have applied!).

9. Now remove all the applied masses from the wooden block and place it on the inclined plane. Increase the inclination of the plane to a point when the wooden

block just starts to slip (figure 4). Measure the angle of the plane from the

horizontal.

Figure 4 Inclined plane with friction

10. Now add 100g to the mass of the wooden block. Repeat the method of part (9), increasing the angle of the plane until the block just starts to move.

11. Repeat for an additional 100 g.


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Theory

Horizontal plane

A schematic diagram of the experiment

Wooden block Pulley

Plane

Mass hanger with additional mass

Assuming the block can be modeled as a particle, a free body diagram of the experiment

is

Normal reaction, N

Friction, F Tension is string, T

Mass of wooden block AND applied masses, Mg

If the string is light and inextensible, the pulley is frictionless and the block is in

equilibrium and JUST on the point of moving, we can resolve the forces horizontally and

vertically.

Horizontal F = T (1)

Vertical N = Mg (2)

For limiting friction F = N (3)

Or T = Mg

Draw a graph of the tension in the string against the mass of the wooden block and the

applied masses (i.e. T against Mg); this should give a straight line with a gradient equal

to the coefficient of friction.


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Find the coefficient of friction from this graph.

(Question: how does the tension in the string relate to the weight of the mass hanger and

the additional masses?)

Inclined plane

Assuming

1. The block is a particle 2. Limiting friction is applicable 3. The block is just on the point of slipping

4. The inclination of the plane to the horizontal is

Normal reaction, N

Friction (opposing motion) F

Mass of wooden block and any applied masses

Mg

Resolving parallel to the plane

F = Mg sin (4)

Resolve perpendicular to the plane

N = Mg cos (5)

Limiting friction

F = N (6)


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Combining equations (4), (5) and (6) gives

Mg sin = Mg cos or = tan

Analysis of results

You should draw neat tables in EXCEL and use EXCEL to draw the graphs and extract

the relevant information.

Think about what the TOTAL applied weight is on one side of the pulley and what the

tension in the string is. Also think carefully about the TOTAL mass of the wooden block!

Compare the coefficient of friction obtained from the horizontal plane to that obtained by

the inclined plane. Are there any differences? Should there be?

Points for discussion

1. How do you know when the block is just on the point of sliding? How did you ensure consistency between different experiments?

2. How close are the two values of the coefficient of friction from both parts of the experiment? Are they the same? Should they be?

3. Why is it important that the block be on the point of sliding and not actually sliding?

4. How does M relate to M1? What is missing from the assumption? 5. Should the block be placed in the same position every time? Why? 6. Why does the tangent of the angle of inclination give the coefficient of

friction?

7. Does the angle of inclination vary when the mass of the block is changed? Would you expect this?

8. Can the coefficient of friction exceed unity? 9. Where is friction useful and when is it a nuisance? 10. How could you reduce the friction?


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Worksheet for part 1

1. A swing of weight W is supported by two vertical ropes as shown below.

T1 T2

W

a) What can you say about the three forces? b) How large would T1 and T2 be?

2. A weight W is supported by two strings as shown below.

T1 T2

W

b) What can you say about the three forces? c) What is the combined effect of the three forces? d) If the two strings were removed, what single force would be required

to keep the weight in equilibrium?

e) What is the combined effect of T1 and T2?


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3. How can three forces of 50N, 40 N and 30N be placed so that they are in equilibrium? What are the angles between the forces?

4. What does it mean that a pulley is frictionless? Why are strings considered to be

light and inextensible?


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Worksheet for part 2

Take hold of a long stick (a metre rule is ideal for this) and hold is with just your fingers.

Finger 1 Finger 2

Figure A Supporting a ruler asymmetrically

Support the stick asymmetrically (as shown in fig A) with the index fingers of both

hands.

Now try to move your fingers gently towards each other and observe what happens.

Why finger moves first? Why?

Now replace one of your fingers with a pencil and repeat the procedure of moving the

pencil and the other finger towards each other.

Which moves first now? Why?


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Try again, but use an eraser rather than a pencil.

Which moves first now? Why

If a mass is at rest on an incline plane, determine the values of for which the mass remains at rest.

Block of mass M kg

Can the friction force ever be zero?


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Writing your report

Include in your report:-

1. Aims (from this lab sheet) 2. A BRIEF introduction 3. The results in a table, showing all the key points, such as the horizontally

and vertically resolved forces

4. A TYPICAL calculation (dont repeat all the calculations) 5. A discussion based on the questions posed on this lab sheet. 6. Give your results and compare them to what you would have expected. If

they are not as the theory predicts, try and explain why there are

differences (and dont just say experimental error, try to be more subjective)

7. A list of WHAT YOU FOUND OUT in the conclusions, which answer the AIMS

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Forces and Friction