Physics 114A Mechanics Lecture 1 T

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Physics 114A - MechanicsLecture 1 (TM Chapter
1)Units and VectorsMarch 30, 2009

• John G. Cramer
• Professor of Physics
• B451 PAB
• jcramer_at_u.washington.edu

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Lecture Schedule (Part 1)
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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. ExamplesMass - kilogra
ms (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 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

Units for almost all other physical
quantities can be constructed from mass, length,
and time, so these are the fundamental units.
Unit
Conversions 1 in 2.54 cm 1 cm 0.3937 in 1
mi 1.609 km 1 km 0.621 mi 1 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 has a weight of 2.2046 pounds
at standard gravity.

English Units(Used only in USA, Liberia,and
Myanmar)
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The SI Time Unit second (s)
Cesium Fountain Clock
13th Century Water Clock
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.
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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 Earths
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. Avagadros number of
carbon-12 atoms (6.02214199 x 1023) has a mass
of exactly 12 kg.
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Scientific Notation
How manysignificantfigures?
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Prefixes
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Dimensions and Units
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Dimensional Analysis (1)
Any valid physical equation must be
dimensionally consistent each side must have
the same dimensions.
From the Table Distance velocity
time Velocity acceleration time Energy mass
(velocity)2
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Dimensional Analysis (2)
Example
The period P (T) of a swinging pendulum depends
only on the length of the pendulum d (L) and the
acceleration of gravity g (L/T2). Which of the
following formulas for P could be correct ?
P 2? (dg)2
(a)
(b)
(c)
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Dimensional Analysis (3)
Remember that P is in units of time (T), d is
length (L) and g is acceleration (L/T2). The both
sides must have the same units
Try equation (a).
Try equation (c).
Try equation (b).
(a)
(b)
(c)
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Some Approximate Magnitudes
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Order of Magnitude Calculations

• Make a rough estimate of the relevant
  quantitiesto one significant figure, preferably
  some power of 10.
• Combine the quantities to make the estimate.
• 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 Rubber
Problem When you drive your car 1 km,
estimate the thickness of tire tread that is worn
off.

• Answer
• 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)
• Estimate the thickness of a typical tire tread
  lost on a worn tire 1 cm.
• Consider the following ratio

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

• No recipe or plug-and-chug works all the time,
  but here are some guidelines
• Read the problem carefully.
• Sketch the system.
• Visualize the physical process.
• Devise a strategy for solving the problem.
• Identify appropriate equations.
• Solve the equations. Calculate the answer.
• Check your answer. Dimensions? Reasonable?
• Explore limits and special cases.

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Scalars and Vectors
Temperature Scalar Quantity is specified by
a singlenumber giving its magnitude.
Velocity Vector Quantity is specified by
three numbers that give its magnitude and
direction (or its components in
threeperpendicular directions).
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Properties of Vectors
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End of Lecture 1

• Before the Tuesday lecture, read Walker, Chapter
  2.1 through 2.3.
• Obtain a HiTT clicker from the University
  Bookstore.
• Lecture Homework 1 has been posted on the Tycho
  system and is due at or before 1159 PM on
  Thursday, Jan. 15, i. e., one week from Thursday.