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Newton’s Laws
The Study of Dynamics
What is Force?
 A force is a push or pull on an object.
 Force is a vector (magnitude and direction).
 Forces cause an object to accelerate…



To speed up
To slow down
To change direction
Newton’s First Law
 A body in motion stays in motion at
constant velocity and a body at rest stays at
rest unless acted upon by a net external
force.
 This law is commonly referred to as the
Law of Inertia.
The First Law is Counterintuitive
Aristotle firmly believed this,
but physics students know better!
Implications of Newton’s 1st Law
 If there is zero net force on a body, it
cannot accelerate, and therefore must
move at constant velocity, which means



it cannot turn,
it cannot speed up,
it cannot slow down.
What is Zero Net Force?
The table pushes up
on the book.
A book rests on a table.
FT
Physics
Gravity pulls down on
the book.
FG
Even though there are forces on the book, they are balanced.
Therefore, there is no net force on the book.
SF = 0
Diagrams
 Draw a force diagram and a free body
diagram for a book sitting on a table.
Force Diagram
N
Physics
W
Free Body Diagram
N
W
Sample Problem
a) A monkey hangs by its tail from a tree
branch. Draw a force diagram representing
all forces on the monkey
FM
FG
Sample Problem
b) Now the monkey hangs by
both hands from two vines.
Each of the monkey’s arms
are at a 45o from the
vertical. Draw a force
diagram representing all
forces on the monkey.
Fa1
Fa2
FG
Mass and Inertia
 Chemists like to define mass as the amount
of “stuff” or “matter” a substance has.
 Physicists define mass as inertia, which is
the ability of a body to resist acceleration
by a net force.
Sample Problem
A heavy block hangs from a string attached to a
rod. An identical string hangs down from
the bottom of the block. Which string
breaks
a)
when the lower string is pulled with a slowly
increasing force?
Top string breaks due to its greater force.
a)
when the lower string is pulled with a quick
jerk?
Bottom string breaks because block has lots of inertia and
resists acceleration. Pulling force doesn’t reach top string.
Newton’s Second Law
 A body accelerates when acted upon by a
net external force.
 The acceleration is proportional to the net
force and is in the direction which the net
force acts.
Newton’s Second Law
 ∑F = ma



where ∑F is the net force
measured in Newtons (N)
m is mass (kg)
a is acceleration (m/s2)
Units of force
 Newton (SI system)

1 N = 1 kg m /s2
 1 N is the force required to accelerate a 1
kg mass at a rate of 1 m/s2
Working 2nd Law Problems
1. Draw a force or free body diagram.
2. Set up 2nd Law equations in each
dimension.
SFx = max and/or
SFy = may
3. Identify numerical data.
x-problem and/or y-problem
4. Substitute numbers into equations.
“plug-n-chug”
5. Solve the equations.
Sample Problem
In a grocery store, you push a 14.5-kg cart with a force of 12.0 N.
If the cart starts at rest, how far does it move in 3.00 seconds?
Newton’s Third Law
 For every action there exists an equal and
opposite reaction.
 If A exerts a force F on B, then B exerts a
force of -F on A.
Examples of
Newton’s 3rd
Law
Sample Problem
You rest an empty glass on a table.
a) How many forces act upon the glass?
b) Identify these forces with a free body diagram.
c) Are these forces equal and opposite?
d) Are these forces an action-reaction pair?
Mass and Weight
 Many people think mass and weight are
the same thing. They are not.
 Mass is inertia, or resistance to
acceleration.
 Weight can be defined as the force due to
gravitation attraction.
 W = mg
Sample Problem
A man weighs 150 pounds on earth at sea level. Calculate
his
a) mass in kg.
b) weight in Newtons.
Normal force
 The normal force is a force that keeps one
object from penetrating into another
object.
 The normal force is always perpendicular a
surface.
 The normal exactly cancels out the
components of all applied forces that are
perpendicular to a surface.
Normal force on flat surface
 The normal force is equal to the weight of an object
for objects resting on horizontal surfaces.
 N = W = mg
N
mg
The normal force
most often
equals the weight
of an object…
…but this is by no
means always the
case!
Sample problem
A 5.0-kg bag of potatoes sits on the bottom of a stationary
shopping cart. Sketch a free-body diagram for the bag of
potatoes. Now suppose the cart moves with a constant velocity.
How does this affect the free-body diagram?
Apparent weight
 If an object subject to gravity is not in free
fall, then there must be a reaction force to act
in opposition to gravity.
 We sometimes refer to this reaction force as
apparent weight.
 In 1-D force problems, the apparent weight is
the same thing as the normal force (it is the
force that a scale would read).
Elevator rides
 When you are in an elevator, your actual
weight (mg) never changes.
 You feel lighter or heavier during the ride
because your apparent weight increases when
you are accelerating up, decreases when you
are accelerating down, and is equal to your
weight when you are not accelerating at all.
Going
Up?
v=0
a=0
v>0
a>0
v>0
a=0
v>0
a<0
Heavy feeling
Normal feeling
Normal feeling
Light feeling
Wapp
Wapp
Wapp
Wapp
W
W
W
W
Ground
floor
Just
starting up
Between
floors
Arriving at
top floor
Going
Down?
v<0
a<0
v=0
a=0
v<0
a>0
v<0
a=0
Heavy feeling
Normal feeling
Normal feeling
Light feeling
Wapp
Wapp
Wapp
Wapp
W
W
W
W
Beginning
descent
Between Arriving at
floors Ground floor
Top
floor
Sample Problem
An 85-kg person is standing on a bathroom scale in an elevator. What
is the person’s apparent weight
a) when the elevator accelerates upward at 2.0 m/s2?
b) when the elevator is moving at constant velocity between floors?
c) when the elevator begins to slow at the top floor at 2.0 m/s2?
Sample Problem
A 5-kg salmon is hanging from a fish scale in an elevator. What is the
salmon’s apparent weight when the elevator is
a) at rest?
b) moving upward and slowing at 3.2 m/s2?
c) moving downward and speeding up at 3.2 m/s2?
d) moving upward and speeding up at 3.2 m/s2?