PowerPoint Lectures
to accompany
Physical Science, 6e
Chapter 2
Motion
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Motion
Its description and explanation
Overview
Description
Explanation
• Position
• Velocity
• Acceleration
• Forces
• Newton’s laws
Applications
• Momentum
• Circular motion
• Newton’s law of
gravitation
• Horizontal motion on
land
• Falling objects
• Compound (2-D) motion
Applications
The motion of this
windsurfer, and of other
moving objects, can be
described in terms of the
distance covered during a
certain time period.
Measuring motion
Two fundamental
components:
• Change in position
• Change in time
Three important
combinations of
length and time:
1. Speed
2. Velocity
3. Acceleration
Speed
• Change in position
with respect to time
• Average speed most common
measurement
• Instantaneous
speed - time interval
approaches zero
The bar means "average"
distance
distance
d
speed = v = t
time
Average speed
time
Example: average speed
Calculate average speed between trip times of
1 h and 3 h
150km
50km
50km
d
?
v=
v= t = =
h
2h
?
Velocity
• Describes speed (How fast is it going?) and
direction (Where is it going?)
• Graphical representation of vectors: length =
magnitude; arrowheads = direction
Acceleration
•
•
•
•
Rate at which motion changes over time
Speed can change
Direction can change
Both speed and direction can change
v f - vi
a=
t
(A) This graph shows how the speed changes per unit of
time while driving at a constant 30 mi/hr in a straight line.
As you can see, the speed is constant, and for straightline motion, the acceleration is 0.
(B) This graph shows the speed increasing to 50 mi/hr
when moving in a straight line for 5 s. The acceleration,
or change of velocity per unit of time, can be calculated
from either the equation for acceleration or by
calculating the slope of the straight line graph. Both will
tell you how fast the motion is changing with time.
– Example
• if a car changes velocity from 55 km/hr to 80 km/hr
in 5s, then
• acceleration=80km/hr-55km/hr = 25 km/hr
5s
5s
• acceleration = 5km/hr/s
• usually convert km/hr to m/s, to keep units the
same for time
• then get 1.4 m/s/s or 1.4 m/s2
• represented mathematically, this relationship is:
• a = Vf-Vi
t
Forces - historical background
Aristotle
Galileo and Newton
• Heavier objects fall
faster
• Objects moving
horizontally require
continuously applied
force
• Relied on thinking alone
• All objects fall at the
same rate
• No force required for
uniform horizontal
motion
• Reasoning based upon
measurements
Force
• A push or pull
capable of changing
an object’s state of
motion
• Overall effect
determined by the
(vector) sum of all
forces - the “net
force” on the object
Horizontal motion on land
“Natural motion” question:
Is a continuous force
needed to keep an
object moving?
• No, in the absence of
unbalanced retarding
forces
• Inertia - measure of an
object’s tendency to
resist changes in its
motion (including rest)
Balanced and unbalanced
forces
• Motion continues
unchanged w/o
unbalanced forces
• Retarding force
decreases speed
• Boost increases
speed
• Sideways force
changes direction
Falling objects
• Free fall - falling under
influence of gravity w/o
air resistance
• Distance proportional to
time squared
• Speed increases
linearly with time
• Trajectories exhibit
up/down symmetries
• Acceleration same for
all objects
m
a = "g" = 9.8 2
s
v f = at ft 2
= 32 2
s
1
d = at
2
– Example:
• A penny is dropped from the Eiffel Tower
and hits the ground in 9.0 s. How far is if to
the ground.
• d=1/2gt2
• d=1/2(9.8m/s2)(9.0s)2
• d=(4.9m/s2)(81.0s2)
• d= (ms2)
s2
• d= 396.0m
Compound motion
Three types of motion:
Projectile motion
1. Vertical motion
2. Horizontal motion
3. Combination of 1. and
2.
•
An object thrown into
the air
Basic observations:
1. Gravity acts at all
times
2. Acceleration (g) is
independent of the
object’s motion
Projectile motion
Vertical projectile
Horizontal projectiles
•
•
•
•
• Horizontal velocity
remains the same
(neglecting air
resistance)
• Taken with vertical
motion = curved path
Slows going up
Stops at top
Accelerates downward
Force of gravity acts
downward throughout
Fired horizontally versus
dropped
• Vertical motions
occur in parallel
• Arrow has an
additional horizontal
motion component
• They strike the
ground at the same
time!
Example: passing a football
• Only force = gravity
(down)
• Vertical velocity
decreases, stops
and then increases
• Horizontal motion is
uniform
• Combination of two
motions = parabola
Three laws of motion
• First detailed by Newton (1564-1642 AD)
• Concurrently developed calculus and a law of
gravitation
• Essential idea - forces
Among other accomplishments, Sir Isaac Newton
invented calculus, developed the laws of motion,
and developed the law of gravitational attraction.
Newton’s 1st law of motion
• “The law of inertia”
• Every object retains its state of rest or its
state of uniform straight-line motion unless
acted upon by an unbalanced force
• Inertia resists any changes in motion
Newton’s 2nd law of motion
• Forces cause
accelerations
• Units = Newtons (N)
• Proportionality
constant = mass
• More force, more
acceleration
• More mass, less
acceleration
Fnet
Fanet== m
ma
Examples - Newton’s 2nd
• More mass, less
acceleration, again
• Focus on net force
– Net force zero here
– Air resistance + tire
friction match applied
force
– Result: no
acceleration;
constant velocity
– The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to the mass of the object
– The unit of force used in the SI system is the
Newton (N)
– N= kgm/s2 (any other units must be converted
to
and m/s2 before a problem can be solved for
N)
– Force is equal to mass times acceleration
• F=ma
– Weight is equal to the mass of an object times
the force of gravity
• w=mg
Weight and mass
• Mass = quantitative
measure of inertia; the
amount of matter
• Weight = force of
gravity acting on the
mass
• Pounds and newtons
measure of force
• Kilogram = measure of
mass
Newton’s 3rd law of motion
• Source of force - other
objects
• 3rd law - relates forces
between objects
• “Whenever two objects
interact, the force
exerted on one object is
equal in size and
opposite in direction to
the force exerted on the
other object.”
FA due to B =FB due to A
• Newton's Third Law of Motion.
– Whenever two objects interact, the force
exerted on one object is equal in size and
opposite in direction to the force exerted on
the other object.
• FA due to B = FB due to A
• forces always occur in matched pairs
• that act in opposite directions
• and on two different bodies
• For every action there is an equal &
opposite
reaction
The football
player's foot is
pushing against
the ground, but it
is the ground
pushing against
the foot that
accelerates the
player forward to
catch a pass.
Possible due to
friction.
Momentum
• Important property
closely related to
Newton’s 2nd law
• Includes effects of
both motion
(velocity) and inertia
(mass)
p = mv
• Momentum () is the product of the mass of an
object (m) and its velocity (v).
–  = mv
• The law of conservation of momentum
– The total amount of momentum remains
constant in the absence of some force
applied to the system.
Conservation of momentum
• The total momentum of a group of interacting
objects remains the same in the absence of
external forces
• Applications: Collisions, analyzing
action/reaction interactions
Impulse
• A force acting on an object for some time t
• An impulse produces a change in momentum
• Applications: airbags, padding for elbows and
knees, protective plastic barrels on highways
impulse = Ft
Forces and circular motion
• Circular motion =
accelerated motion
(direction changing)
• Centripetal acceleration
present
• Centripetal force must
be acting
• Centrifugal force apparent outward tug
as direction changes
• Centripetal force ends:
motion = straight line
v
ac = r
2
v
Fc =ma c = m r
2
• Centripetal force. (center-seeking)
– This is the force that pulls an object out of its
straight line path into a circular path
• Centrifugal force.
– The imaginary force that is thought to force
objects toward the outside if an object is
moving in a circular pattern.
– Actually the force is simply the tendency of
the object to move in a straight line.
Newton’s law of gravitation
• Attractive force between
all masses
• Proportional to product
of the masses
• Inversely proportional to
separation distance
squared
• Explains why g=9.8m/s2
• Provides centripetal
force for orbital motion
• Objects fall due to the force of gravity (g) on
them.
– This force is 9.8 m/s2
– It is this force that gives objects weight
• w = mg
• Universal Law of Gravitation
– Every object in the universe is attracted to
every other object in the universe by a force
that is directly proportional to the product of
their masses and inversely proportional to the
square of the distances between them.
• F = G(m1m2)/d2
• G is a proportionality constant and is equal
to 6.67 X 10-11 Nm2/kg2 (Henry Cavendish)
– Usually the objects in our environment that we
interact with on an everyday basis are so smal
that the force is not noticed due to the large
force of attraction due to gravity.
The variables involved in gravitational attraction. The
force of attraction (F) is proportional to the product of
the masses (m1, m2) and inversely proportional to
the square of the distance (d) between the centers of
The force of
gravitational
attraction
decreases
inversely with the
square of the
distance from the
earth's center.
Note the weight
of a 70.0 kg
person at various
distances above
the earth's
Gravitational
attraction acts as a
centripetal force that
keeps the Moon from
following the straightline path shown by
the dashed line to
position A. It was
pulled to position B
by gravity (0.0027
m/s2) and thus "fell"
toward Earth the
distance from the
dashed line to B,
resulting in a
somewhat circular