Physics - MechanicsLecture 1

Introduction to PhysicsSeptember 2, 2013

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Physics and the Laws of Nature

Physics: the study of the fundamental laws of nature.

● These laws can be expressed as mathematical equations. (e.g., F = m a)

● Most physical quantities have units, which must match on both sides of an equation.

● Much complexity can arise from even relatively simple physical laws.

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Units With a few exceptions, all physical quantities have units. Examples:Mass - kilograms (kg)Speed - meters per second (m/s)Pressure - pascals (P)Energy - joules (J)Electric Potential - volts (V) Rather surprisingly, the units of almost all physical quantities can be expressed as combinations of only the units for mass, length, and time, i.e., kilograms, meters, and seconds. A few physical quantities (e.g., index of refraction) are pure numbers that have no associated units.

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Standard International Units

Standard International (SI) Units (also known as MKS)

• Length: meter m• Mass: kilogram kg• Time: second s

Unit Conversions1 in = 2.54 cm 1 cm = 0.3937 in1 mi = 1.609 km 1 km = 0.621 mi1 mph = 0.447 m/s 1 m/s = 2.24 mph

Note: The English pound unit is a measure of force or weight, not mass.A kilogram of mass has a weight of 2.2046 pounds at standard gravity, but will have slightly different weights at different locations on the Earth (poles, equator).

} English Units(Used only in USA, Liberia,and Myanmar)

Units for almost all other physical quantities can be constructed from mass, length, and time, so these are the fundamental units.

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The SI Time Unit: second (s)

The second was originally defined as (1/60)(1/60)(1/24) of a mean solar day. Currently, 1 second is defined as 9,192,631,770 oscillations of the radio waves absorbed by a vapor of cesium-133 atoms. This is a definition that can be used and checked in any laboratory to great precision.

13th Century Water Clock Cesium Fountain Clock

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The SI Length Unit: meter (m)

The meter was originally defined as 1/10,000,000 of the distance from the Earth’s equator to its North pole on the line of longitude that passes through Paris. For some time, it was defined as the distance between two scratches on a particular platinum-iridium bar located in Paris. Currently, 1 meter is defined as the distance traveled by light in 1/299,792,458 of a second

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The SI Mass Unit: kilogram (kg) The kilogram was originally

defined as the mass of 1 liter of water at 4oC.

Currently, 1 kilogram is the mass of the international standard kilogram, a polished platinum-iridium cylinder stored in Sèveres, France. (It is currently the only SI unit defined by a manufactured object.)

Question: In a “telephone” conversation, could you accurately describe to a member of a alien civilization how big a kilogram was?

Answer: More or less. Avagadro’s number of carbon-12 atoms (6.02214199… x 1023) has a mass of exactly 12.00000000000… grams.

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Prefixes

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Dimensions and Units

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Any valid physical equation must be dimensionally consistent – each side must

have the same dimensions.

From the Table:Distance = velocity ×

timeVelocity = acceleration ×

timeEnergy = mass ×

(velocity)2

Dimensional Analysis (1)

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Dimensional Analysis (2)

The periodThe period PP (T)(T) of a swinging of a swinging pendulum depends only on the pendulum depends only on the length of the pendulumlength of the pendulum dd (L)(L) and and the acceleration of gravitythe acceleration of gravity gg (L/T(L/T22))..

Which of the following formulas forWhich of the following formulas for PP couldcould be correct ?be correct ?

P dg

2P dg

2(a)(a) (b)(b) (c)(c)P 2 (dg)2

ExampleExample::

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L LT

LT

T

2

2 4

4

Dimensional Analysis (3)

LL

T

T T2

2

Remember that P is in units of time (TT), d is length (L) and g is acceleration (L/T2).

The both sides must have the same units

P dg2 2(a)(a) (b)(b) (c)(c)P dg

2

Try equation (a).Try equation (b).Try equation (c).TT

TLL 2

2

P dg

2

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Some Approximate Magnitudes

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Order of Magnitude Calculations

1. Make a rough estimate of the relevant quantitiesto one significant figure, preferably some power of 10.

2. Combine the quantities to make the estimate.3. Think hard about whether the estimate is

reasonable.Example: How fast does an Olympic sprinter cross the finishline in the 100 m dash?

Analysis: Typical 100 m dash time is ~10 s, so average speed isabout 10 m/s. Sprinters “kick” near the finish line, sospeed there is faster. 50% faster? Maybe. That wouldmean the finish-line speed is ~15 m/s. Reasonable? Yes.

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Example: Burning RubberProblem:

When you drive your car 1 km, estimate the thickness of tire tread that is worn off.Answer:1. Estimate the distance require to wear down a

tire tread to the point where it needs to be replaced: ~60,000 km (or 37,000 miles)

2. Estimate the thickness of a typical tire tread lost on a worn tire: ~ 1 cm.

3. Consider the following ratio:5

71 cm of tread loss 1.67 10 cm of tread loss 2 10 m of tread loss per km60,000 km of travel 1 km of travel

Therefore, a car loses about 2x10-7 m = 0.2 m of tire tread in driving 1 km.

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Problem Solving in PhysicsNo recipe or plug-and-chug works all the

time, but here are some guidelines:1. Read the problem carefully.2. Draw a sketch of the system.3. Visualize the physical process involved.4. Devise a strategy for solving the

problem.5. Identify the appropriate equations. 6. Solve the equations. Calculate the

answer. 7.Check your answer. Dimensions?

Reasonable?8.Explore the limits and special cases.

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Scalars and Vectors

Temperature = ScalarQuantity is specified by a singlenumber giving its magnitude.

Velocity = VectorQuantity is specified by three numbers that give its magnitude and direction(or its components in threeperpendicular directions).

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Properties of Vectors

End of Lecture 1 Before the Thursday lecture, read Walker, Chapter 2.1 through 2.3. Obtain a HiTT clicker from the University Bookstore. We will use soon. Lecture Homework #1 has been posted on the WebAssign system and is due at or before 11:59 PM on Thursday, Jan. 12, i. e., on Thursday of next week.