Theories and Experiments
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The goal of physics is to develop theories
based on experiments
A theory is a “guess,” expressed
mathematically, about how a system
works
The theory makes predictions about how a
system should work
Experiments check the theories’
predictions
Every theory is a work in progress
Units
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To communicate the result of a
measurement for a quantity, a unit
must be defined
Defining units allows everyone to
relate to the same fundamental
amount
Systems of Measurement
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Standardized systems
• agreed upon by some authority, usually
a governmental body
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SI -- Systéme International
• agreed to in 1960 by an international
committee
• main system used in this text
• also called mks for the first letters in the
units of the fundamental quantities
Time
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Units
• seconds, s
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Defined in terms of the oscillation of
radiation from a cesium atom
US “Official” Atomic Clock
Length
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Units
• SI – meter, m
• US Customary – foot, ft
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Defined in terms of a meter – the
distance traveled by light in a
vacuum during a given time
Mass
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Units
• SI – kilogram, kg
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Defined in terms of kilogram, based
on a specific cylinder kept at the
International Bureau of Weights and
Measures
Standard Kilogram
Multipliers
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Prefixes correspond to powers of 10
Each prefix has a specific name
Each prefix has a specific
abbreviation
Larger: kilo(k), Mega (M), etc
Small: milli (m), micro(), nano(n)
Speed
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The average speed of an object is
defined as the total distance traveled
divided by the total time elapsed
x
v
t
The total distance and the total time
are all that is important
SI units are m/s
Speed, cont
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Average speed totally ignores any
variations in the object’s actual
motion during the trip
The total distance and the total time
are all that is important
SI units are m/s
Example
Car travels 350 km in 7 hours. What is
its speed?
Speed
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Instant Speed v: speed at any
particular instant
Constant Speed: Speed v does not
change during motion
2 hours at 75km/h
1h at 50km/h, then 1h at 100km/h
Same average speed
Velocity
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Both speed and direction of motion are
specified
Represented by a Vector quantity
Magnitude (speed)
Direction
graph
Vector: velocity, force, electric field
Scalars:speed, temperature, time, energy
Acceleration(a)
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Time rate of change of the velocity
v  vo
a
t
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Units m/s² (SI)
Instant acceleration: at any particular
instant
Constant acceleration: same at any
instant
graph
Average Acceleration
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Vector quantity
When the sign of the velocity and the
acceleration are the same (either
positive or negative), then the speed
is increasing
When the sign of the velocity and the
acceleration are in the opposite
directions, the speed is decreasing
Linear motion (one dimension)
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Constant velocity v: x= vt
Constant acceleration a:
v  vo
a
t
1 2
x  vot  at
2
Linear Motion Summary
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(1)
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(2)
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(3)
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(4)
v  vo
a
t
1 2
x  xo  vot  at
2
v  vo
x  xo 
t
2
v 2  vo 2
a
2( x  xo)
Example
An antelope moving with constant
acceleration covers the distance
between two points A and B, 60 m
apart in 6 s. Its velocity as it passes
the second point is 15 m/s. What is
the acceleration? What is the velocity
at point A?
Problem 1
A speedboat increases its speed at a
constant rate of 2m/ s².
a.
b.
c.
How much time is required for the
speed to increase from 8m/s to
20m/s
How far the boat travel during this
time
Average speed
Galileo Galilei
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1564 - 1642
Galileo formulated the
laws that govern the
motion of objects in
free fall
Also looked at:
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Inclined planes
Relative motion
Thermometers
Pendulum
Free Fall
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All objects moving under the influence of
gravity only are said to be in free fall
• Free fall does not depend on the object’s
original motion
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All objects falling near the earth’s surface
fall with a constant acceleration
The acceleration is called the acceleration
due to gravity, and indicated by g
Acceleration due to Gravity
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Symbolized by g
g = 9.80 m/s²
• When estimating, use g 10 m/s2
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acc is always directed downward
• toward the center of the earth
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Ignoring air resistance and assuming
g doesn’t vary with altitude over
short vertical distances, free fall is
constantly accelerated motion
Free Fall – an object dropped
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Initial velocity is
zero
Let up be positive
Use the equations
• Generally use y
instead of x since
vertical
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Acceleration is g =
9.80 m/s2
vo= 0
a=-g
Free Fall – an object thrown
downward
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a = -9.80 m/s2
Initial velocity  0
• With upward being
positive, initial
velocity will be
negative
Free Fall -- object thrown
upward
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Initial velocity is
upward, so positive
The instantaneous
velocity at the
maximum height is
zero
a = - 9.80 m/s2
everywhere in the
motion
v=0
Thrown upward, cont.
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The motion may be symmetrical
• Then tup = tdown
• Then v = -vo
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The motion may not be symmetrical
• Break the motion into various parts
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Generally up and down
Non-symmetrical
Free Fall
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Need to divide the
motion into
segments
Possibilities include
• Upward and
downward portions
• The symmetrical
portion back to the
release point and then
the non-symmetrical
portion
Example of falling object
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y-axis points up
vo = 15 m/s
After 1s
After 4s
Maximum height
Time to reach maximum height
Velocity 6m above starting point
Falling object motion example
A ball is thrown vertically down from a
100 m tall building with a speed of
10m/s.
 How long will it take for the ball to
reach ground?
 What is the velocity of the ball just
before hitting the ground?
 What is the acceleration?