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Chapter 5
Newton’s Laws of Motion
Announcements, 9/24
• Homework due Friday, 10 PM
• Next Readiness Quiz: Chapter 6, Monday
• Extra Credit Opportunity: Street Corner Science!
– Look at news item on eLearn, follow the link to two
videos. In them, a Nobel Laureate sits on a street
corner and answers science questions. Pick the
question / answer that is most interesting, do a little
more internet research, and write a 250+ word
summary of the topic in your own words. Post the file
in the dropbox labeled "Street Corner Science".
Units of Chapter 5
• Force and Mass
• Newton’s First Law of Motion
• Newton’s Second Law of Motion
• Newton’s Third Law of Motion
• The Vector Nature of Forces: Forces
in Two Dimensions
• Weight
• Normal Forces
5-1 Force and Mass
Force: push or pull
Force is a vector – it has magnitude and
direction
5-1 Force and Mass
Mass is the measure of
how hard it is to
change an object’s
velocity.
Mass can also be
thought of as a
measure of the quantity
of matter in an object.
Identifying Forces
• The first thing to do with force problems is be able to
identify the forces
• Every problem is divided into the system and the
environment
• Every force must have an agent
– An identifiable cause in the environment
– Not necessarily a person!!!
• Almost every force is a contact force
– Agent must physically touch the system
– Gravity is one of the only exceptions
Identifying Forces - Procedure
• Divide the problem into “the system” and “the
environment”
– The system is just the thing whose motion you want to
study, the environment is everything else
• Draw a picture of the problem, showing the object and
everything in the environment that touches the object.
Ropes, springs, surfaces and so on are part of the
environment
• Draw a closed curve around the system, with the object
inside the curve and everything else (mostly) outside the
curve.
Identifying Forces - Procedure
• Locate every point on the boundary of this curve where
the environment touches or contacts the system. These
are the points where the environment exerts contact
forces on the object. Don’t forget any!
• Identify by name the contact force or forces (there are
probably more than one!) at each point of contact, then
give each an appropriate symbol.
• Identify any long range forces acting on the object.
Name the force, and write a symbol for it beside your
picture
Standard Names for Some Forces
• The force
 due to gravity: Weight, often
called W
• The push up on things by floor/ground:

Normal Force, often called N

• Force of friction, often called f
• Pull by a rope/string: Tension, often
called T
Examples
Everything else is the environment
System
System
Group Exercise
• A car is pulled up a slope by a chain.
Friction is present. Draw a sketch, and
identify the forces on the car.
5-2 Newton’s First Law of Motion
If you stop pushing an object, does it stop
moving?
Only if there is friction! In the absence of any
net external force, an object will keep moving
at a constant speed in a straight line, or
remain at rest.
This is also known as the Law of Inertia.
5-2 Newton’s First Law of Motion
In order to change the velocity of an
object – magnitude or direction – a net
force is required.
An inertial reference frame is one in
which the first law is true. Accelerating
reference frames are not inertial.
ConcepTest 5.1a Newton’s First Law I
A book is lying at
rest on a table.
The book will
remain there at
rest because:
1) there is a net force but the book has too
much inertia
2) there are no forces acting on it at all
3) it does move, but too slowly to be seen
4) there is no net force on the book
5) there is a net force, but the book is too
heavy to move
ConcepTest 5.1a Newton’s First Law I
A book is lying at
rest on a table.
The book will
remain there at
rest because:
1) there is a net force but the book has too
much inertia
2) there are no forces acting on it at all
3) it does move, but too slowly to be seen
4) there is no net force on the book
5) there is a net force, but the book is too
heavy to move
There are forces acting on the book, but the only
forces acting are in the y-direction. Gravity acts
downward, but the table exerts an upward force
that is equally strong, so the two forces cancel,
leaving no net force.
ConcepTest 5.1b Newton’s First Law II
A hockey puck
slides on ice at
constant velocity.
What is the net
force acting on
the puck?
1) more than its weight
2) equal to its weight
3) less than its weight but more than zero
4) depends on the speed of the puck
5) zero
ConcepTest 5.1b Newton’s First Law II
A hockey puck
slides on ice at
constant velocity.
What is the net
force acting on
the puck?
1) more than its weight
2) equal to its weight
3) less than its weight but more than zero
4) depends on the speed of the puck
5) zero
The puck is moving at a constant velocity, and
therefore it is not accelerating. Thus, there must
be no net force acting on the puck.
Follow-up: Are there any forces acting on the puck? What are they?
Newton’s First Law IV
You kick a smooth flat
stone out on a frozen
pond. The stone slides,
slows down and
eventually stops. You
conclude that:
1) the force pushing the stone forward
finally stopped pushing on it
2) no net force acted on the stone
3) a net force acted on it all along
4) the stone simply “ran out of steam”
5) the stone has a natural tendency to be
at rest
Newton’s First Law IV
You kick a smooth flat
stone out on a frozen
pond. The stone slides,
slows down and
eventually stops. You
conclude that:
1) the force pushing the stone forward
finally stopped pushing on it
2) no net force acted on the stone
3) a net force acted on it all along
4) the stone simply “ran out of steam”
5) the stone has a natural tendency to be
at rest
After the stone was kicked, no force was pushing
it along! However, there must have been some
force acting on the stone to slow it down and stop
it. This would be friction!!
Follow-up: What would you have to do to keep the stone moving?
5-3 Newton’s Second Law of Motion
Acceleration is proportional to force:
Announcements, 9/26
• Homework due tonight, 10 PM
• Group Office Hours this afternoon, 1:30
PM, Room 139
• Next Readiness Quiz: Chapter 6, due
Monday
5-3 Newton’s Second Law of Motion
Acceleration is inversely proportional to mass:
5-3 Newton’s Second Law of Motion
Combining these two observations gives
Fnet
a
m
In words: acceleration equals net force over
mass
Or,
Fnet  ma
5-3 Newton’s Second Law of Motion
An object may have several forces acting on it;
the acceleration is due to the net force:

1
a  F
m
F
F
x
 ma x
y
 ma y
(5-1)
5-3 Newton’s Second Law of Motion
Free-body diagrams:
A free-body diagram shows every force acting
on an object.
• Sketch the forces
• Isolate the object of interest
• Choose a convenient coordinate system
• Resolve the forces into components
• Apply Newton’s second law to each
coordinate direction
5-3 Newton’s Second Law of Motion
Example of a free-body diagram:
5-3 Newton’s Second Law of Motion
A more complicated problem:
Practice
5-4 Newton’s Third Law of Motion
1. Every force occurs as one member of a pair
of interaction forces
2. The two members of a pair of interaction
forces act on two different objects.
3. The two members of an interaction pair are
equal in magnitude but opposite in direction.


Or, FA on B  FB on A
These forces are called action-reaction pairs.
5-4 Newton’s Third Law of Motion
Some action-reaction pairs:
5-4 Newton’s Third Law of Motion
Although the forces are the same, the
accelerations will not be unless the objects
have the same mass.
Climbing the Rope
When you climb up a rope,
1) this slows your initial velocity, which
is already upward
the first thing you do is pull
2) you don’t go up, you’re too heavy
down on the rope. How do
3) you’re not really pulling down – it
just seems that way
you manage to go up the
rope by doing that??
4) the rope actually pulls you up
5) you are pulling the ceiling down
Climbing the Rope
When you climb up a rope,
1) this slows your initial velocity, which
is already upward
the first thing you do is pull
2) you don’t go up, you’re too heavy
down on the rope. How do
3) you’re not really pulling down – it
just seems that way
you manage to go up the
rope by doing that??
4) the rope actually pulls you up
5) you are pulling the ceiling down
When you pull down on the rope, the rope pulls up on
you!! It is actually this upward force by the rope that
makes you move up! This is the “reaction” force (by the
rope on you) to the force that you exerted on the rope.
And voilá, this is Newton’s 3rd Law.
Collision Course I
1) the car
A small car collides with
2) the truck
a large truck. Which
3) both the same
experiences the greater
impact force?
4) it depends on the velocity of each
5) it depends on the mass of each
Collision Course I
1) the car
A small car collides with
2) the truck
a large truck. Which
3) both the same
experiences the greater
impact force?
4) it depends on the velocity of each
5) it depends on the mass of each
According to Newton’s 3rd Law, both vehicles experience
the same magnitude of force.
Collision Course II
In the collision between
1) the car
the car and the truck,
2) the truck
which has the greater
3) both the same
acceleration?
4) it depends on the velocity of each
5) it depends on the mass of each
Collision Course II
In the collision between
1) the car
the car and the truck,
2) the truck
which has the greater
3) both the same
acceleration?
4) it depends on the velocity of each
5) it depends on the mass of each
We have seen that both
vehicles experience the
same magnitude of force.
But the acceleration is
given by F/m so the car
has the larger acceleration,
since it has the smaller
mass.
Announcements, 9/29
• Quiz Wednesday: On forces / free-body
diagrams. Will be similar to the first
example we do in class today and
Example 5-4 in the book
• Homework due Friday, Chapter 5
Example
• A force of magnitude 7.50 N pushes three boxes with
masses m1 = 1.30 kg, m2 = 3.20 kg and m3 = 4.90 kg as
shown in the figure. Find the magnitude of the contact
force (a) between boxes 1 and 2, and (b) between boxes
2 and 3. Ignore friction
5-5 The Vector Nature of Forces: Forces in
Two Dimensions
The easiest way to handle forces in two
dimensions is to treat each dimension
separately, as we did for kinematics.
Example
• Two adults and a child want to push a wheeled cart in the direction
marked x in the figure below. The two adults push with forces F1 and
F2 as shown in the figure. (a) Find the magnitude and direction of
the smallest force that the child should exert to move the cart in the
x direction only. (b) If the child exerts the minimum force found in
part (a), the cart accelerates at 2.0 m/s2 in the +x direction. What is
the weight of the cart?
5-6 Weight
The weight of an object on the Earth’s surface
is the gravitational force exerted on it by the
Earth.
Announcements, 10/1
• Homework due Friday
• Next Readiness Quiz: Chapter 7 (Note this
is different than in syllabus)
• New Extra Credit Opportunity: Lecture
abut Dr. King, Humanities Auditorium, Wed
Oct 8th, 12:40 pm
– Attend lecture, write a 250 word essay about
what you learned, and what it meant to you
5-6 Weight
If your surroundings
are accelerating, your
apparent weight may
be more or less than
your actual weight.
5-7 Normal Forces
The normal force is
the force exerted by
a surface on an
object.
5-7 Normal Forces
The normal force may be equal to, greater than,
or less than the weight.
5-7 Normal Forces
The normal force is always perpendicular to
the surface.
ConcepTest 5.14 Normal Force
Below you see two cases: a
physics student pulling or
pushing a sled with a force F
which is applied at an angle q.
In which case is the normal
force greater?
1) case 1
2) case 2
3) it’s the same for both
4) depends on the magnitude of
the force F
5) depends on the ice surface
Case 1
Case 2
ConcepTest 5.14 Normal Force
Below you see two cases: a
physics student pulling or
pushing a sled with a force F
which is applied at an angle q.
In which case is the normal
force greater?
1) case 1
2) case 2
3) it’s the same for both
4) depends on the magnitude of
the force F
5) depends on the ice surface
Case 1
In Case 1, the force F is pushing down
(in addition to mg), so the normal force
needs to be larger. In Case 2, the force F
is pulling up, against gravity, so the
normal force is lessened.
Case 2
Summary of Chapter 5
• Force: a push or pull
• Mass: measures the difficulty in
accelerating an object
• Newton’s first law: if the net force on an
object is zero, its velocity is constant
• Inertial frame of reference: one in which the
first law holds
• Newton’s second law:
• Free-body diagram: a sketch showing all the
forces on an object
Summary of Chapter 5
• Newton’s third law: If object 1 exerts a force
F on object 2, then object 2 exerts a force –F
on object 1.
• Contact forces: an action-reaction pair of
forces produced by two objects in physical
contact
• Forces are vectors
• Newton’s laws can be applied to each
component of the forces independently
• Weight: gravitational force exerted by the
Earth on an object
Summary of Chapter 5
• On the surface of the Earth, W = mg
• Apparent weight: force felt from contact with a
floor or scale
• Normal force: force exerted perpendicular to a
surface by that surface
• Normal force may be equal to, lesser than, or
greater than the object’s weight