Welcome toPhysics 40!

What IS Physics?

The science that deals with matter, energy, motion and force.

- Random House Dictionary

Physics is...

Objectives of Physics

• To find the limited number of fundamental laws that govern natural phenomena

• To use these laws to develop theories that can predict the results of future experiments

• Express the laws in the language of mathematics

• Physics explores the full spectrum of the cosmos from subatomic particles to clusters of galaxies, to the edge of space and time...

From Subatomic Particles….

…to atoms ….

to stuff on Earth….

…creating new technologies….

…and super power ….

exploring Earth, Moon, Sun and planets….

to the stars and beyond …

to clusters of Galaxiesfar, far away in space and back in time….

to the beginning and end of space and time ….

Physics seeks a single theory of Everything….

Bubble Universes

Superstrings

Theory of Everything (TOE)

Physics 40 ISClassical Mechanics!

Study of the motion of objects and mechanical systems that are large

relative to atoms and move at speeds much slower than the speed of light.

•Laws of Physics are statistical.•Space and time are relative.•The speed of light is absolute.•Particles are wave-like•Waves are particle-like

•Laws of Physics are deterministic.•Space and time are absolute.•Particles are Localized in Space and have mass and momentum.•Waves are non-localized in space and do not have mass or momentum.•Superposition: Two particles cannot occupy the same space at the same time! But Waves can! Waves add in space and show interference.

Classical vs Modern

Modern Physics:Quantum Physics & Relativity

You can’t get to Modern Physics without doing Classical Physics!

The fundamental laws and principles of Classical Physics are the basis Modern Physics.

Physics 40: Mechanics•Kinematics: The physics of motion•Newton’s Three Laws of Motion•Energy: Kinetic and Potential•Linear & Angular Momentum•Conservation Laws•Newton’s Universal Law of Gravity•Physics 41: Waves, Thermo, Optics•Physics 42: E &M•Physics 43: Modern Physics

Physics 40 ISNewtonian Physics!

Isaac Newton(1642 -1727)

In Principia (1687 ) Newton •Invented Calculus•3 Laws of Motion•Universal Law of Gravity

The force of gravity is Universal: The same force that makes an apple fall to Earth, causes the moon to fall around

the Earth and the planets to orbit the Sun.

Our Goal….

Celestial Mechanics!

How to Succeed in this Class•Come to Class!•Read the Book/Outline the book BEFORE lecture.•Take notes during class & rewrite them after.•Check out the power point lectures online.•Try the Homework Problems before Discussion Section•COME TO MY OFFICE HOUR!•Join MESA & Use the Tutorial Center!•Form study groups and make regular meeting dates!•Use the Phys/Eng Library to study in! •Use other textbooks for more solved problems.•Make up practice exams and practice taking tests!•PRACTICE! PRACTICE! PRACTICE!•No NEGATIVE TALK! LOVE PHYSICS!

Booze and Pot make you Stupid!•Heavy drinking affects the hippocampus of the brain, which is involved in memory and learning.

•The short-term effects of marijuana can include problems with memory and learning; distorted perception; difficulty in thinking and problem solving; loss of coordination; and increased heart rate.

•Both booze and pot effect brain function days after you drink or smoke!

SRJC Student Guide...a successful student must dedicate 2-3 hours outside class for every hour in class. In other words, a student taking 12 units is spending 12 hours in class and 24-36 hours outside of class in order to succeed.

A full time student has a full-time job just being a student.

Schedule your time so you study/solve hw problems when you are at your mental best. Do everything else (work, shop, exercise, sleep, etc.) during your less productive times.

Learn how you Learn!

Physics for Scientists and Engineers

Chapter 1 & Appendix B.8

Quantities & Units • In mechanics, three basic quantities are used

– Length, Mass, Time• Will also use derived quantities

– Ex: Joule, Newton, etc.• SI – Systéme International

– agreed to in 1960 by an international committee

Length: Meter

• Units– SI – meter, m

• Defined in terms of a meter – the distance traveled by light in a vacuum during a given time

Table 1.1, p. 5

Mass: Kilogram

• Units– SI – kilogram, kg

• Defined in terms of a kilogram, based on a specific cylinder kept at the International Bureau of Standards

Time: Second

• Units– seconds, s

• Defined in terms of the oscillation of radiation from a cesium atom

Prefixes

• The prefixes can be used with any base units

• They are multipliers of the base unit

• Examples:– 1 mm = 10-3 m– 1 mg = 10-3 g

Density: A derived Quantity

• Density is an example of a derived quantity• It is defined as mass per unit volume• Units are kg/m3

mV

ρ ≡

Problem 1.5Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius.

343

V rπ=

343

m V rρ ρ π= =

3 3

3 3

4 35

4 3s s s

rm rm r r

ρ πρ π

= = =ll l

( )3 5 4.50 cm 1.71 7.69 cmsr r= = =l

For either sphere the volume is:

And the mass is:

Divide the equation for the larger sphere by the same one for the smaller sphere:

Solve for rl:

To convert from one unit to another, multiply by conversion factors that are equal to one.

Example: 32 km = ? nm

1. 1km = 103 m2 1 nm = 10-9 m

3 910 10321 1

m nmkmkm m

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

3 932 10 10 nm= × ×

133.2 10 nm= ×

1 light year = 9.46 x 1015m1 mile = 1.6 km

How many miles in a light year?

15

3

9.46 10 111 1.6 10

m milelyly m

⎛ ⎞× ⎛ ⎞⎜ ⎟⎜ ⎟×⎝ ⎠⎝ ⎠

125.9 10 miles= ×

1 light year = 9.46 x 1015m1 mile = 1.6 km

~ 6 Trillion Miles!!!Closest Star: Proxima Centauri 4.3 lyClosest Galaxy: Andromeda Galaxy 2.2 million ly

Problem 1.22An auditorium measures 40.0 m × 20.0 m × 12.0 m.  The density of air is 1.20 kg/m3.  What are (a) the volume of the room in cubic feet and  (b) the weight of air in the room in pounds?

( ) ( ) ( ) 3 340.0 m 20.0 m 12.0 m 9.60 10 mV = = ×

( )33 3 5 3 9.60 10 m 3.28 ft1 m 3.39 10 ftV = × = ×

( ) ( )3 3 3 4air 1.20 kg m 9.60 10 m 1.15 10 kgm Vρ= = × = ×

( )( )4 2 51.15 10 kg 9.80 m s 1.13 10 NW mg= = × = ×

( )( )5 4 1.13 10 N 1 lb 4.45 N 2.54 10 lbW = × = ×

a)

b)

Significant Figures

• A significant figure is one that is reliably known

• Zeros may or may not be significant– Those used to position the decimal point are not

significant– To remove ambiguity, use scientific notation

• In a measurement, the significant figures include the first estimated digit

Significant Figures, examples

• 0.0075 m has 2 significant figures– The leading zeros are placeholders only– Can write in scientific notation to show more clearly:

7.5 x 10-3 m for 2 significant figures• 10.0 m has 3 significant figures

– The decimal point gives information about the reliability of the measurement

• 1500 m is ambiguous– Use 1.5 x 103 m for 2 significant figures– Use 1.50 x 103 m for 3 significant figures– Use 1.500 x 103 m for 4 significant figures

Operations with Significant Figures – Multiplying or Dividing

• When multiplying or dividing, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures.

• Example: 25.57 m x 2.45 m = 62.6 m2

– The 2.45 m limits your result to 3 significant figures

Operations with Significant Figures – Adding or Subtracting

• When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum.

• Example: 135 cm + 3.25 cm = 138 cm– The 135 cm limits your answer to the units

decimal value

Operations With Significant Figures – Summary

• The rule for addition and subtraction are different than the rule for multiplication and division

• For adding and subtracting, the number of decimal places is the important consideration

• For multiplying and dividing, the number of significant figures is the important consideration

Rounding

• Last retained digit is increased by 1 if the last digit dropped is 5 or above

• Last retained digit remains as it is if the last digit dropped is less than 5

• If the last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number

• Saving rounding until the final result will help eliminate accumulation of errors

• Keep a few extra terms for intermediate calculations

HW Problem #30: You try it.

A rectangular plate has a length of 21.3 cm and a width of 9.8 cm.  Calculate the area of the plate, and the number of significant figures.  

A = 21.3cm x 9.8cm = 208.74cm2

A = 210cm2

How many significant figures? 2

Error in MeasurementsUncertainty arises primarily because no piece of measuring equipment is infinitely precise (sensitive) or infinitely accurate (correct).

When you make measurements in these labs, you need to estimate the uncertainty of each measurement you make, and record it in your lab report. You also need to take those estimated uncertainties and determine the uncertainty in the results you calculate.

• Uncertainty (error) is unavoidable in measurement.

• Uncertainty in a measurement, M, can have the symbol M or M

• Measured values are reported as: M M± Δ

Sources of Error

Errors arise from three major sources:

Random fluctuation – the idea that the actual quantity may vary slightly around some central value. It is assumed that the variations go in both directions equally. The way to deal with random fluctuation is to take several measurements of the same quantity and calculate the average.

Average value of n measurements of x = ∑xi /n

Deviation in xi = Δxi = xi–x avg

Average Deviation: Δx = ∑Δxi /n

Sample Problem Using Averages

Example:You have performed an experiment in which you timed the fall of a mass. You got the following values, all in seconds:12.24, 12.32, 12.25, 12.11

The average value of these times is the sum of the values, divided by 4 (the number of measurements):12.24 + 12.32 + 12.25 + 12.11 = 48.9248.92 ÷ 4 = 12.23

So 12.23 is the average value.

Average value of n measurements of x = ∑xi /nDeviation in xi = Δxi = xi–x avg

Average Deviation: Δx = ∑Δxi /n

Sample ProblemNow, to find the deviation of each measurement, we subtract this average value,12.23 from each value:Value deviation12.24 0.0112.32 0.0912.25 0.0212.11 -0.12And then we take the absolute values of each deviation, and average them:(0.01 + 0.09 + 0.02 + 0.12) ÷ 4 = 0.24 ÷ 4 = 0.06

The average deviation for this set of measurements is therefore 0.06. The value should then be reported as

12.23 ± 0.06 seconds.

Systematic error – the idea that a piece of equipment may not be calibrated or functioning correctly, or that conditions are not as you assume. All data points will vary in the same direction (all too high or too low). The way to deal with systematic error is to examine possible causes inherent in your equipment and/or procedures, and whether they may be corrected.

Human error (aka mistakes) – the idea that humans mess up. The way to deal with human error is to repeat the measurement.

Sources of Error

Uncertainty in Measurements• Uncertainty (error) is unavoidable in measurement. • Uncertainty in a measurement, M, can have the symbol M or M• Expressed in two ways: absolute or fractional.• Absolute: uses same units as the measured quantity:

(21.3 +/- 0.2) cmFractional: the uncertainty is expressed as a fraction or a percent of the measured quantity:

0.2cm/21.3cm = .009 =.9% 21.3cm +/- .9%

Uncertainty is propagated in calculations. There are two simple rules:

1) If any two quantities are added or subtracted, you add the absolute uncertainties to find the absolute uncertainty of the result.

2) If any two quantities are multiplied or divided, add the fractional (or percent) uncertainties to obtain the fractional (percent) uncertainty in the result: A L W

A L WΔ Δ Δ

= +

Problem #30: Again...A rectangular plate has a length of L = (21.3 +/‐ 0.2) cm and a width of W = (9.8 +/‐0.1) cm.  Calculate the area of the plate, including its uncertainty.  

( )( ) 221.3 cm 9.8 cm 208.74 cmA LxW= = =

0.2 0.1 .01959 .02 2%21.3 9.8

Δ ⎛ ⎞= + = ± = ± =⎜ ⎟⎝ ⎠

AA

2 2(.02)(208.74 cm ) 4.18 cm=

2 2210 cm 4 cmA = ±

Calculate the Area, keeping a few extra sig figs:

Calculate the total fractional/percent uncertainty:

Calculate the total absolute uncertainty:

Round to significant figures:

(2 sig figs in the measurements and 1 sig fig in the uncertainty.)

Standard Form

A L WA L WΔ Δ Δ

= +

HW Problem # 32The radius of a solid sphere is measured to be (6.50 +/‐ 0.20) cm, and its mass is measured to be (1.85 +/‐0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

( ) ( )( )

26.50 0.20 cm 6.50 0.20 10 m

1.85 0.02 kg

r

m

−= ± = ± ×

= ±

Givens:

Fractional error in density: 3m rm r

ρρΔ Δ Δ

= + ( )3 0.200.02 0.1031.85 6.50

= + =

( ) ( )3 3

324 3

1.85 1.61 10 kg m6.5 10 m

kgρπ −

= = ××

Calculate the density:

( ) 343

mr

ρπ

=

Calculate the total absolute uncertainty:3 3 3 3)(.103)(1.61 10 kg m .17 10 kg m× = ×

( ) 3 31.61 0.2 10 kg m± Δ = ± ×ρ ρRound & Standard Form:

You Try OneThe radius of a circle is measured to be (10.5 +/‐ 0.2) m.  Calculate the (a) area and (b) circumference of the circle and give the uncertainty in each value.

2 2346 m 10 mA = ±

( )2 2 10.5 m 0.2 m 65.97 1.25C r m mπ π= = ± = ±

2A rA rΔ Δ

=.22 .038

10.5mm

= =

( )22 210.5 m 346.36 mrπ π= =

(.038)(346) 13.18A m mΔ = =

Calculate the Area:

Fractional uncertainty in the Area:

Absolute uncertainty in the Area:

Round & Standard Form:

Circumference:

(66.0 1.3)C m= ±

Another way to do itThe radius of a circle is measured to be (10.5 +/‐ 0.2) m.  Calculate the (a) area and (b) circumference of the circle and give the uncertainty in each value.

( )22

2 2

2 2

10.5 m 0.2 m

(10.5 m) 2(10.5 m)(0.2 m) (0.2 m)

346 m 10 m

rπ π

π

= ±

⎡ ⎤= ± +⎣ ⎦

= ±

( )2 2 10.5 m 0.2 m 66.0 m 1.3 mrπ π= ± = ±

You Try One: Pre-Lab 1 HW

The radius of a cylinder is (2.50 +/- 0.10) cm, the height is (6.50 +/- 0.20) cm and the mass is measured to be (52.3 +/- 0.1) x 10-3 kg. Calculate the density of the cylinder in kilograms per cubic meter and the uncertainty in the density.

Read Chapter 2 for Monday!Yes, there will be a quiz on Ch1 HW

and Ch 2 reading!