Lecture 1 - eavdlsum.files.wordpress.com · Lecture 1 > Introduction > Measurement, Trigonometry Giancoli, Physics 6/e Serway & Vuille, College Physics 8/e Serway & Jewett, Physics

Lecture 1

> Introduction

> Measurement, Trigonometry

Giancoli, Physics 6/eSerway & Vuille, College Physics 8/eSerway & Jewett, Physics for Scientists & Engineers, 6/eTippens, Physics 7/eYoung, Freedman & Ford, University Physics 14/e

1Villacorta--DLSUM-SCITECS-L01-1819Term01

Nature of Science

> Aim of science: ideas from data, observations; collecting facts, making theories

> Observing nature, performing experiments + Aristotle, Galileo on the moving cart + Observation & experimentation + Formulating a theory + Testing the theory + Accepting the theory, range of the theory

> Theories: attempts at explaining observed phenomena + Observations lead to theories about how they came about + Theories are tested by further experiments and observations

2Villacorta--DLSUM-SCITECS-L01-1819Term01

Introduction to Physics

> Physics: expt'l science, sci method + Observe nature + Find patterns

> Physical theories: patterns observed in nature;

Laws, principles: well established & widely used physical theories

> Galileo on falling objects + Experiment ~ Light, heavy ~ Rate of falling ~ Weight-independent

+ Experimental process, tests

+ Range of validity: ignoring air resistance

3Villacorta-DLSUM-SCITECS-L01-1819Term01

Galileo Galilei1564-1642

> Falsifiability + Testing theories through experiments + New experiments: refine or discard + How to disprove a theory: find an observation inconstent w/ it

https://en.wikipedia.org/wiki/Galileo_Galileihttps://en.wikipedia.org/wiki/Aristotle

Aristotle384-322 BC

Introduction to Physics contd

4

> Physics: the study of matter and energy + Most basic of the sciences + Classical: motion, fluids, heat, sound, light, electricity, & magnetism + Modern: relativity, atomic structure, condensed matter, nuclear physics, elementary particles, & cosmology and astrophysics + Physics is related to many fields: mathematics, biology, chemistry, etc

> Picturing & explaining nature + Model: using simplified, known ideas & applying it to other phenomena + Theory: more expansive, testable results + Law: natural behavior + Principle: specific behavior + Prescription (setting limits) vs. description (describe as observed)

Simplified

Real object

Point particle

Young, Freedman, c01Villacorta-DLSUM-SCITECS-L01-1819Term01

Measurement and Uncertainty

5

> Uncertainty from the inaccuracy of measuring devices

> Accuracy (closeness to the true value)

vs Precision (measurement repeatabilty)

Ruler: ½ of 1/10 of a centimeter or 0.05 cm

Vernier caliper: ½ of 1/10 of 1/10 of a centimeter or 0.005 cm

https://en.wikipedia.org/wiki/Rulerhttps://en.wikipedia.org/wiki/Calipers

Villacorta-DLSUM-SCITECS-L01-1819Term01

Measurement and Uncertainty contd

6

> Significant figures: number of reliable digits + Since measuring devices can never be completely accurate, the measurements taken using them cannot be 100% reliable.

+ Non-zeroes are always significant.

+ Zeroes are significant when these are between significant digits.

→3.21 cm 3 significant figures→14.77 kg 4 significant figures

+ Zeroes to the right of the decimal point are significant.

+ Zeroes to the right of a significant digit and to the left of a decimal point are NOT significant.

→504.8 in 4 significant figures7001.9 s –> 5 significant figures

→7.00 km 3 significant figures→1.0400 m 5 significant figures

→5600 lb 2 significant figures7090 m2 → 3 significant figures



7

> When adding measures, the final answer must have the same decimal places to the right of the decimal point as the addend with the least number of decimal places.

> When multiplying measures, the final answer must have the same number of significant figures as the factor with the least number of significant figures.

Ex. What is the total mass of three objects:14.0 kg, 18.33 kg, and 5.790 kg?

Ans. Simple addition

14.0 kg + 18.33 kg + 5.790 kg = 38.12 kg

Since 14.0 kg has one decimal place w/c is the least among those given, then the final answer should be

38.1 kg,w/c also has one decimal place.

Ex. What is the area of a triangle that is 12.0 cm tall and has a base 35.25 cm wide?

Ans. Use the formula for the traingle area:

A = (½) b h = (½) (35.25 cm) (12.0 cm) = 211.5 cm2

Since the height measure only has three significant figures (sf), then the final answer should be

212 cm2, w/c also has three sf.



8

> Scientific Notation, Powers of Ten: a compact way of writing very small, large measures that keep the significant figures

> Ex. 2,300,000 kg = 2.3 x 106 kg (two s.f. before & after conversion)

> Ex. 0.000703 m = 7.03 x 10–4 m (three s.f. before & after conversion)

> Percentage Error: a measure of how far an experimental value is from an accepted, theoretical value

> Percentage Difference: a measure of how close two measurements are to each other (Ex. The same quantity measured in different ways)

Percentage Error (%E)=∣Ex. Value�Th. Value∣

Th. Value×100%

Percentage Difference (%D)=∣Meas. 1�Meas. 2∣

Average Meas.×100%


Units & Standards

9

> Physical quantity: number describing a physical phenomenon

Ex. height, weight, length, etc

Operational definition: fundamental description of a physical quantity

Ex. length: measure using a ruler time: measure using a stopwatch

> Unit: the measurement standard of a quantity + Ex. centimeters, kilometers, grams + A number is not enough to describe a quantity: the unit must be included

+ Standard: a reproducible measure for a unit

> Standard Units + Time: second = “duration of 9,192,631,770 periods of cesium atom radiation”

Young, Freedman, c01


Units & Standards contd

10

+ Length: meter = “distance traveled by light in 1 / 299,792,458 seconds”

Early defn (French Academy of Sciences, 1797):

Young, Freedman, c01

1 m=Dist from N Pole to Equator

10,000,000

+ Mass: kilogram = “mass of a platinum-iridium alloy in Paris, France”

https://en.wikipedia.org/wiki/Metrehttps://www.bipm.org/en/bipm/mass/image-ipk.htmlhttps://en.wikipedia.org/wiki/Kilogram

FR Orig in Saint-Cloud US Prototype in Maryland



11

> Systems of Units + International System (SI): metric system, cgs (centimeter-gram-second), mks (meter-kilogram-second)

+ Imperial Units: foot-pound-second

length: meters (m) 1 kilometer (km) = 1000 m = 103 m

mass: kilograms (kg) 1 metric ton/ tonne (t) = 1000 kg

time: second (s) 1 minute (min) = 60 s 1 hour (h) = 60 min = 3600 s

area: 1 hectare (ha) = (100 m)2

= 104 m2

volume: 1 liter (L) = (10 cm)3

= 0.001 m3

length: 1 inch (in) = 2.54 cm [defn] 1 foot (ft) = 12 in 1 yard (yd) = 3 ft 1 mile (mi) = 5280 ft = 1.609 km

mass: 1 pound (lb) = 4.536 kg 1 stone (st) = 14 lb 1 ton (t) = 2240 lb

area: 1 acre = 66 ft x 660 ft = 4840 yd2

= 4046 m2

volume: 1 fluid ounce (fl oz) = 28.41 mL 1 pint (pt) = 20 fl oz 1 quart (qt) = 2 pt 1 gallon (gal) = 4 qt

https://en.wikipedia.org/wiki/Metric_systemhttps://en.wikipedia.org/wiki/Imperial_unitsVillacorta-DLSUM-SCITECS-L01-1819Term01


12

> Quantities can be: + Base: defined using the standard units.

+ Derived: combination of base quantities: Ex. speed, volume, force, etc.

Serway & Vuille, Ch01

7 Base Qts:

1. Length 5. Electric charge2. Mass 6. Amount of substance3. Time 7. Luminous intensity4. Temperature


Sample Problem

13

1. (a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in µg/day.

(b) For adults, the RDA of the amino acid lysine is 12 mg per kg of body weight. How many grams per day should a 75-kg adult receive?

(c) A typical multivitamin tablet can contain 2.0 mg of vitamin B2 (riboflavin), and

the RDA is 0.0030 g/day. How many such tablets should a person take eachday to get the proper amount of this vitamin, if he gets none from other sources?

(d) The RDA for the trace element selenium is 0.000070 g/day. Express this dose in mg/day. [Young, Freedman, c01]


Measure Estimates

14

> Order of magnitude + Quick estimate of measure + Rough estimate + Ex. area of an empty lot, floor space of a room, fluid ounces of medicine, etc.

distance = (velocity) (time) or d = v t

dimension:[distance] = L {length}[velocity] = L/T {length over time}[time] = T {time}

L = ( L/T ) (T) = L,showing that the eq is consistent dimensionally

> Dimensional analysis + Equations must have the same units on both sides + Dimensions refer to the type of base quantities making up a unit + Ex. L = length, T = time, M = mass, etc.


Trigonometric Functions

15

> The three trigonometric functions + Sine + Cosine + Tangent

90ºSOH – CAH - TOA

https://en.wikipedia.org/wiki/Pythagoras

Pythagorasc570-495 BC

Pythagorean Theorem

c2 = a2 + b2


Sample Problem

16

1. A high fountain of water is located at the center of a circular pool as shown...

Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 m.

Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55.0°.

How high is the fountain? [Serway, Vuille, c01]


Law of Cosines

17

> Relates the side of one triangle to the other sides and the angle opposite it

> Applicable for different kinds of triangles

c2=a

2+b2�2 a b cos γ

a2=b

2+c2�2 b c cosα

b2=c

2+a2�2 c a cosβ a

b

cγ

β

α

Note: If γ = 90º, then the cosine law for c2 is just the Pythagorean formula.

Ex. Two sides of a triangle have measures 3.0 cm and 4.0 cm and form a 45º angle. What is the length of the third side?

Ans. Use the cosine law with a = 3.0 cm b = 4.0 cm and γ = 45º

c2 = (3.0cm)2 + (4.0cm)2 – 2 (3.0cm)(4.0cm)cos 45º = 8.029 cm2

=> c = 2.834 cm

The third side is 2.8 cm long.


Law of Sines

18

> Gives the relationship between the different ratios of the sides of a triangle and the angle opposite said side

> Applicable for different kinds of triangles

a

sin α=

b

sin β=

c

sin γ a

b

cγ

β

α

Ex. Find the angle opposite 3.0-cm side and the angle opposite the 4.0-cm side in the triangle in the previous item.

Ans. Use the sine law: sin α = (a/c) sin γ and sin β = (b/c) sin γ.

sin α = (3.0cm/2.834cm) sin 45º = 0.7485 => α =48.46º

sin β = (4.0cm/2.834cm) sin 45º = 0.9980 => β =86.41º

Thus, the angle opposite the 3.0-cm side is 48º while that of the 4.0-cm side is 86º.

Note: The sine law may lead to 2 different triangles under certain conditions.


Sample Problem

19

1. You and a friend are out hiking across a large flat plain and decide to determine the height of a distant mountain peak, and also the horizontal distance from you to the peak...

In order to do this, you stand in one spot and determine that the sightline to the top of the peak is inclined at 7.5º above the horizontal. You also make note of the heading to the peak at that point: 13º east of north.

You stand at the original position, and your friend hikes due west for 1.5 km. He then sights the peak and determines that its sightline has a heading of 15º east of north.

How far is the mountain from your position, and how high is its summit above your position? [Tipler, c01]


Sample Problem contd

20

1.


Vectors

21

> Vectors, having both magnitude and direction, can be modeled using a finite ray. + The length of the ray representing the vector magnitude. + The arrowhead representing the vector direction.

> Basic vectors can be drawn in one, two, or three dimensions: + On a number line, for 1-D + On a Cartesian plane, for 2-D

> Vectors can also be written symbolically or in mathematical terms.


Vectors contd.

22

> Adding two or more vectors can be done in a number of ways. Unlike scalars that only require adding numbers using simple algebra, vectors require further steps due to its direction.

> The addition can be done either: + graphically by triangulation or head-to-tail, or + computationally by components.

> Other instances such as the negative of a vector and multiplication by a scalar are also common ways of combining vectors.


Decomposing Vectors

23

> Aside from adding vectors by graphical means, one can also combine vectors by decomposing them into their x- and y-components.

> These components come from the idea that if adding many vectors yields another vector (head-to-tail), then any vector can be decomposed into a number of vectors.

> In practice, one decomposes a vector into two perpendicular components for the 2-D case. + Horizontal, vertical components + x-, y-components


Decomposing Vectors contd.

24

> Suppose we add the following vectors: L = 5.00 u, 30.0º above the +x-axis M = 7.00 u, 45.0º below the +x-axis

> Components: L

x = 4.3301 u; L

y = 2.500 u

Mx = 4.9497 u; M

y = –4.9497 u

Rx = 9.2798 u; R

y = –2.4497 u

> Resultant: R = 9.60 u, 14.8º below the +x-axis

Lx=L cos θL ; L y=L sin θL

M x=M cos θM ; M y=M sin θM

Rx=Lx+M x

Ry=Ly+M y

R=√Rx

2+R y

2

θR=arctan∣Ry∣∣Rx∣


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Lecture 1 - eavdlsum.files.wordpress.com · Lecture 1 > Introduction > Measurement, Trigonometry Giancoli, Physics 6/e Serway & Vuille, College Physics 8/e Serway & Jewett, Physics