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Chapter 2
Motion
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What is Motion?
Describing Motion
Three basic
concepts
1. Position
2. Speed and
velocity
3. Acceleration
Applications
• Horizontal motion
(along a line)
• Vertical motion
(falling objects)
• Compound motion
(2-D)
Explaining Motion
Basic ideas
Applications
• Forces
• Inertia and mass
• Newton’s laws
• Momentum and
impulse
• Circular motion
• Newton’s law of
gravitation
• Earth satellites
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
distance
speed =
time
The bar means "average"
distance
d
v= t
Average speed
time
Example: Average Speed
Calculate average speed between trip times of
1 h and 3 h
d
?
v= t =
?
150km
50km
50km
v=
=
h
2h
Velocity
• Describes speed (How fast is it going?) and
direction (Where is it going?)
• Graphical representation using 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
acceleration change in velocity  v
t
time elapsed
v f - vi
a= t
Problem (A) 11
How long will be required for a car to go
from a speed of 20.0 m/s to a speed of
2?
25.0 m/sWhat
if the acceleration
is
3.0
m/s
is Motion?
Movement relative to some
reference, usually a stationary
object.
Uniform Acceleration
• Constant, straight line acceleration
• Average velocity simply related to initial and
final velocities in this case
v
v f  vi
2
Example Problem 2.6
Find acceleration (deceleration) of the
automobile
in Example
2.5 (car moving
What
is Motion?
at 25.0 m/s and stops in 10.0 seconds).
Movement relative to some
reference, usually a stationary
object.
Forces - Historical Background
Aristotle
• Heavier objects fall
faster
• Objects moving
horizontally require
continuously applied
force
• Relied on thinking
alone
Galileo and Newton
• 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
Fundamental Forces
Most basic of all interactions
1. Gravitational
•
•
Mass interactions
Motions of planets, stars,
galaxies…
3. Weak force
• Involved in certain nuclear
reactions
4. Strong force
• Holds nuclei together
2. Electromagnetic
•
•
•
Charge interactions
Electricity and magnetism
Atoms and molecules,
chemistry
Horizontal Motion on Land
“Natural motion” question:
Is a continuous force
needed to keep an
object moving?
• No, if there are no
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
d = 1 at 2
2
v f  at
Problem (A) 16
A ball thrown straight up climbs for 3.0 s
before falling. Neglecting air resistance,
with what
velocity
the ball thrown?
What
iswas
Motion?
Movement relative to some
reference, usually a stationary
object.
Free Fall
• Acceleration due to gravity (free fall
neglecting
air resistance)
What
is Motion?
g = 9.8 m/s2
= 32 ft/s2
(downward)
(downward)
Movement relative to some
reference, usually a stationary
object.
Summary of Motion Equations
(see page 55)
• Average velocity
vavg = d / t
vavg = (vf + vi) / 2
What is Motion?
• Acceleration
a = (vf Movement
- v i) / t
vf =relative
vi + at tot some
= (vf - vi) / a
reference, usually a stationary
object.
• Free fall distance from
rest
d = ½at2
where, a = g = 9.8 m/s2
Compound Motion
Three types of motion:
1. Vertical motion
2. Horizontal motion
3. Combination of 1.
and 2.
Projectile motion
• 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
• Slows going up
• Horizontal velocity
remains the same
• Stops at top
(neglecting air
• Accelerates downward
resistance)
• Force of gravity acts
downward throughout • Taken with vertical
motion = curved
path
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
• Assume 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
Newton’s 1st Law of Motion
• “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
• “F = ma”
• The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to the mass of the
object.
• Depends both on the net force applied and
the mass of the object.
Newton’s 2nd Law of Motion
• Forces cause
accelerations
• Units = Newtons (N),
kg-m/s2
• Proportionality constant
= mass
• More force, more
acceleration
• More mass, less
acceleration
Fnet  ma
Fnet
a
m
Examples - Newton’s 2nd
• More mass, less
acceleration
Fnet
a
m
where, m = mb + mg
She’s not pedaling
Examples - Newton’s 2nd
• Focus on net force
– Net force zero here
– Air resistance + tire
friction match applied
force
– Result: no
acceleration;
constant velocity
Problem (A) 19
What is the resulting acceleration when
an unbalanced force of 100 N is applied
to a 5 kgWhat
object?is Motion?
Movement relative to some
reference, usually a stationary
object.
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
Momentum
• Important property
closely related to
Newton’s 2nd law
• Includes effects of both
velocity (motion) and
mass (inertia)
p = mv
Conservation of momentum
• The total momentum of a group of interacting objects
remains the same in the absence of external forces
• Applications: analyzing action/reaction interactions,
collisions
Problem (A) 22
A 15 g bullet is fired with a velocity of
200 m/s from a 6 kg rifle. What is the
recoil velocity
theMotion?
rifle?
Whatof is
Movement relative to some
reference, usually a stationary
object.
Impulse
• A force acting on an object for some time t
• An impulse produces a change in momentum
• Applications: padding for elbows and knees, airbags,
protective plastic barrels on highways
impulse  force  time
p  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
• If centripetal force
ends:
motion = straight line
v2
ac 
r
v2
Fc  mac  m
r
Problem (A) 30
How much centripetal force is needed to
keep a 0.20 kg ball on a 1.50 m string
is path
Motion?
moving inWhat
a circular
with a speed of
3.0 m/s?
Movement relative to some
reference, usually a stationary
object.
Newton’s Law of Gravitation
• “Universal Law of Gravitation”
• Every object in the universe is attracted to
every other object with 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
(Eq. 2.12)
Newton’s Law of Gravitation
• Attractive force
between all masses
• Directly proportional to
product of the masses
• Inversely proportional
to separation distance
squared
• Explains why
g=9.8m/s2
• Provides centripetal
force for orbital motion
Application of Forces
Fdrag = f(area,v,ρatm)
Fmass = mg
Fnet = ΣFi = manet
-Fthrust = Fupward
=
Fthrust
Mass decreases
with time
Application of Forces
At liftoff:
gross mass = 2.04 x 106 kg
total thrust = 30.18 MN
assume drag = 0 N
Fmass = - mg = -(2.04x106)(9.81)
Fupward = -Fthrust = 30.18 MN
Fnet = ΣFi = manet = 10.17 MN
anet = 5.0 m/s2
d(1s) = ½ at2 = 2.5 m (~8.2 ft)
Mass change = 10,400 kg/s