Lecture 3
Newton’s Three Laws of Motion
Homework Assignment
• A few rules to remember:
– At rest or constant velocity = no change in
motion
– No change in motion = no acceleration = No
Net Force (ΣF= 0)
Origins of Modern Astronomy
• Sir Isaac Newton
(1642-1727)
– Formulated the laws of
motion and gravitation
that govern all bodies
in the universe.
Newton’s First Law of Motion
• The Law of Inertia:
Every object continues in a state of rest or of uniform
speed in a straight line unless acted on by a nonzero
force.
• Inertia: The property of objects to resist changes in
motion.
The Earth in Motion
• Nicolaus Copernicus
(1473-1543):
– Proposed that the Earth
revolved around the Sun
from observations of the
motion of planets.
– Because the concept of
inertia was unknown at
his time, the idea of a
moving Earth was difficult
to comprehend.
If the Earth moves at 30 km/s, how can the
bird drop down and catch the worm?
Thanks to inertia, you can flip a coin in an airplane
without having it fly into your face at 500 mph.
Newton’s Second Law of Motion
• The acceleration produced by a net force on an
object:
– is directly proportional to the net force,
– is in the same direction as the net force,
– and is inversely proportional to the mass of the object.
Newton’s Second Law of Motion
Acceleration = net force / mass
a=F/m
Newton’s Second Law of Motion
• Net Force = mass x acceleration
• F = ma
• Units: 1 N = 1 kg∙m/s2
You apply the same amount of force on two separate carts;
one cart with mass of 1 kg and another with a mass of 2 kg.
Which of the following is correct?
1.
2.
3.
4.
The acceleration of the 2 kg
cart will be ½ as much as
that of the 1 kg cart.
The acceleration of the 2 kg
cart will be 2 times greater
than that of the 1 kg cart.
The acceleration will be the
same for both carts.
The acceleration of the 2 kg
cart will be ¼ as much as
that of the 1 kg cart.
0%
1.
0%
2.
0%
3.
0%
4.
A jumbo jet cruises at a constant velocity of 1000 km/h
when the thrusting force of its engines are a constant
100,000 N. What is the force of air resistance on the jet?
1.
2.
3.
4.
0N
100,000 N
1,000 N
There is not
enough
information to
answer this
question.
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4.
How much force, or thrust, must a 20,000-kg jet
plane develop to achieve an acceleration of 2
m/s2?
1.
2.
3.
4.
5.
6.
10,000 N
10,000 m/s2
20,000 N
20,000 m/s2
40,000 N
40,000 m/s2
0%
0%
0%
0%
0%
0%
1.
2.
3.
4.
5.
6.
A constant g on Earth
• Galileo was the first to
measure the acceleration
of objects in free fall, but
could not explain why
they all fall equally.
• Greater the mass =
stronger gravitational pull.
A constant g on Earth
A constant g on Earth
• g (10m/s2) is
independent of an
object’s mass.
In a vacuum, a coin and a feather fall equally, side
by side. Would it be correct to say that equal
forces of gravity act on both the coin and the
feather in a vacuum?
1. Yes
2. No
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1.
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2.
A constant g on Earth
Weight
• Calculating Weight using Newton’s
Second Law:
F = ma
Weight = mg
g = acceleration due to gravity on Earth
Falling Objects and Air Resistance
• On Earth, air-resistance must be considered for
falling objects.
• As falling speed increases so does the opposing
force of air-resistance.
Net force (ΣF) = Weight – Air-resistance
Falling Objects and Air Resistance
• Acceleration of falling object calculated
using Newton’s 2nd Law:
a = ΣF / m
a = (mg - R )/ m
R = force due to Air Resistance
mg = weight
Terminal Velocity
• Terminal velocity reached when the force of airresistance = the falling object’s weight.
a = ΣF / m = 0
a = (mg - R )/ m = 0
• No net force (ΣF= 0) = no acceleration = no
change in velocity
Terminal Velocity
• Varies from 150 to 200 km/h for a human
skydiver.
A bowling ball and a feather are dropped from the
same height at the same time. Which reaches
terminal velocity first?
1. Bowling Ball
2. Feather
0%
1.
0%
2.
A bowling ball and a feather are dropped from the same
height at the same time. Which has the greater terminal
velocity?
1. Bowling Ball
2. Feather
0%
1.
0%
2.
Terminal Velocity
• Greater force of air resistance (R) needed
to cancel out the weight (mg) of heavier
objects in free fall
• Greater R requires a greater velocity
which requires acceleration for a longer
period of time.
Effect of air-resistance on falling objects
Initially velocity is 0
Air-resistance is 0
Velocity has increased
Air-resistance increases
Velocity continues to increase
Air-resistance increases
R = 80 N
R = 40 N
R=0N
Weight = 100 N
Weight = 100 N
Weight = 100 N
Net Force = 100 N
Initial Acceleration is
10m/s2
Net Force = 60 N
Acceleration is less due
to smaller net force
Net Force = 20 N
Acceleration has
decreased more
Effect of air-resistance on falling objects
Velocity no longer changes
(Terminal Velocity)
Air-resistance is 100 N
R = 100 N
No net force = no acceleration
= no change in velocity!
Weight = 100 N
Net Force = 0 N
Acceleration = 0 m/s2
A bowling ball and a feather are dropped from the same
height at the same time. Which would strike the ground first
if it were on the Moon?
1. Bowling Ball
2. Feather
3. Both at the same
time
0%
1.
0%
2.
0%
3.
Forces and Interactions
• A force is not a thing in itself but makes up
an interaction between one thing and
another.
• Force Pair: two forces that are equal in
magnitude and opposite in direction.
– Constitutes a single interaction.
Forces and Interactions
• You can only exert as much force on an object
as it can exert back on you.
Forces and Interactions
Newton’s Third Law of Motion
• Whenever one object exerts a force on a second
object, the second object exerts an equal and
opposite force on the first.
• Action force and reaction force
To every action there is always an opposed equal
reaction:
Action and Reaction
• Earth is pulled up by
the boulder with just
as much force as the
boulder is pulled
down by Earth.
• Forces are equal in
magnitude but what
about the acceleration
of the two objects?
A speeding bus and an insect experience a head-on
collision. The force of the bus on the insect splatters it on
the windshield. Is the corresponding force of the insect on
the bus greater, less, or the same?
1. Greater
2. Less
3. The same
0%
1.
0%
2.
0%
3.
What about the resulting acceleration that
the bug experiences?
1. Greater than the
acceleration of the
bus.
2. Less than the
acceleration of the
bus.
3. The accelerations
are the same.
0%
1.
0%
2.
0%
3.
Equal and opposite
forces does not always
mean equal and
opposite accelerations.
Action and Reaction
a = 20 m/s2
a = 500 m/s2
F = 10,000 N
F = 10,000 N
Cannonball = 20 kg
Cannon = 500 kg
Chuck Norris delivers a roundhouse kick with a force of
8,000 N to an opponent. Assuming that the laws of physics
apply to Chuck Norris, how much force is exerted back on
his foot?
1.
2.
3.
4.
5.
Less than 8,000 N
More than 8,000 N
8,000 N
There’s not enough
information to answer
this question.
I’m too intimidated by
Chuck Norris to answer
this question
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5.
Assume that Chuck Norris has a mass of 100 kg and his
opponent has a mass of 80 kg. The force exerted on each
was 8,000 N in the previous question. What is the
acceleration of his opponent during impact?
1.
2.
3.
4.
5.
8,000 m/s2
20 m/s2
100 m/s2
80 m/s2
640,000 m/s2
0%
1.
0%
2.
0%
0%
3.
4.
0%
5.
Defining a System
• If action and reaction forces on an object
are equal and opposite, then how can an
object accelerate?
– An acceleration of a system is only possible if
a force external to the system is involved.
Flight
• Lift: an upward reaction force that allows for
flight.
• When the force of lift exceeds an object’s weight
it will accelerate upward.
– A helicopter’s whirling blades are shaped to force air
downward and the air forces the blades up.
A bird’s wing pushes down on the air and the air
pushes back on the wing.