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Forces and the Laws of Motion
Force, Mass, and Acceleration
PVHS Physics
Objectives
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Students should be able to analyze situations in which a particle
remains at rest, or moves with constant velocity, under the
influence of several forces.
Students should understand the relation between the force that
acts on an object and the resulting change in the object’s velocity
Students should understand how Newton’s Second Law, , applies
to an object subject to forces such as gravity, the pull of strings, or
contact forces
Students should be able to analyze situations in which an object
moves with specified acceleration under the influence of one or
more forces
Students should understand the significance of the coefficient of
friction
Students should understand the effect of drag forces on the motion
of an object
Students should be able to apply Newton’s Third Law in analyzing
the force of contact between two objects that accelerate together
A little review…
 What is acceleration?
 What causes
acceleration?
 What are the types of
forces?
What we know…
 Inertia…
 Is an object’s
resistance to a
change in motion
 it is the tendency of
an object to maintain
its state of motion
 Mass is a measure of
inertia
 More mass… more
inertia
 Less mass… less
inertia
What we know…
 The Law of Inertia …
“An object at rest
tends to stay at rest
and an object in
motion tends to stay in
motion with the same
speed and in the same
direction unless acted
upon by an
unbalanced force”.
 Net Force…
 The vector sum of all
the external forces
acting on an object
What we know…
 Forces are Vectors
 Equilibrium…
 The state in which there
is no change in an
object’s motion
 The sum of all forces
equals zero

F0
What we know…
Finding the Net Force…
What happens when the Net Force is not zero?
 List givens and draw a
free-body diagram
 Establish x-y axes
(frame of reference)
 Resolve vector
components
 Sum the vectors in
each direction
F
F
y
0
x
 13N  11N  2N
Forces and Motion
 Forces cause an object’s velocity to change…
 Since acceleration is the rate of change in
velocity…
 Force causes acceleration
 The acceleration is directly proportional to the
force
 The bigger the force, the greater the acceleration
 The smaller the force, the smaller the acceleration
accelerati on  Force
or,
F
aF
F
Mass and Motion
 Inertia…
 Is an object’s resistance to a change in motion
 Inertia resists acceleration
 Mass is a measure of inertia
 Acceleration in inversely proportional to
mass
 More mass, less acceleration
 Less mass, greater acceleration
accelerati on 
or,
a
1
m
1
mass
m
m
Force, Mass, and Motion
 Combining the effects of mass and force…
1
accelerati on  Force, accelerati on 
mass
then ,
or,
Force
accelerati on 
mass
a
F
m
 This is Newton’s Second Law
Newton’s Second Law
 “The acceleration of an object as produced by a net
force is directly proportional to the magnitude of the
force, in the same direction of the force, and inversely
proportional to the mass of the object”
 The 2nd Law is commonly written as:
SF=ma
“The sum of the forces on an object equals mass
times acceleration”
Note: it is the Net Force that causes the acceleration
Application…
 The net force on the propeller of a 3.5kg model
airplane is 7.0N. What is its acceleration?
 A 2.0kg otter starts from rest at the top of an incline
85 cm long and slides to the bottom in 0.50s. What is
the net force on the otter?
Who is pushing who?
Newton’s Third Law
 “For every action, there is an equal and opposite
reaction” … Newton’s 3rd Law
 Forces always exist in pairs called ActionReaction Pairs
 When two objects interact they exert forces on
one another that are equal and opposite
 This includes field forces and physical forces
 Action-Reaction Pairs don’t cancel
 Each force acts on a different object…
 This law explains why both cars are dented
in a car accident. (Can you think of any other
examples of Newton’s Third Law?)
Newton’s Third Law
Newton’s Third Law
Lets Talk about Friction…
 Friction always resists motion
 Two types of Friction
 Static… no motion/ stationary and forces in
equilibrium
 Kinetic… object in motion, forces may or may not be
in equilibrium
 Static friction force is greater than Kinetic friction
force
Friction
 Do you think friction
forces vary with the
type of surface?
 Do heavy objects
have more friction
than lighter
objects? Why?
Friction
 Normal Force… the force
perpendicular to the contact surface
between two objects
Normal Force (N)
W
Normal Force (N)
W
Friction
 Friction is proportional to the normal force
Ffriction  Fnormal
or,

Ffriction
Fnormal
  is the coefficient of friction and depends on
the type of surface
Friction
 Typical coefficients of friction… depends on the type of
surface
Coefficient of Friction
Surfaces
Static Friction
Kinetic Friction
Steel on steel (dry)
0.6
0.4
Steel on steel
(greasy)
0.1
0.05
Teflon on steel
0.041
0.04
Brake lining on cast
iron
0.4
0.3
Rubber tires on dry
pavement
0.9
0.8
Metal on ice
0.022
0.02
Rubber tip of crutch 0.7
on rough wood
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Newton’s Laws and Friction
 Useful Equations…
 Net force: SF = ma
(units… newtons = kg m/s2)
 Gravitational force: W = mg
 Frictional force: Ffriction = Fnormal
Practice #1
An applied force of 50 N is used to accelerate an object to the right
across a frictional surface. The object encounters 10 N of friction. Use
the diagram to determine the normal force, the net force, the mass,
and the acceleration of the object. (Neglect air
resistance.)
Practice #2
An applied force of 20 N is used to accelerate an object to the right
across a frictional surface. The object encounters 10 N of friction.
Use the diagram to determine the normal force, the net force, the
coefficient of friction (µ) between the object and the surface, the
mass, and the acceleration of the object. (Neglect air resistance.)
Practice #3
A 5-kg object is sliding to the right and encountering a friction force
which slows it down. The coefficient of friction (µ) between the object
and the surface is 0.1. Determine the force of gravity, the normal force,
the force of friction, the net force, and the acceleration. (Neglect air
resistance.)
Practice #4
 Demo… A 2.0 kg block accelerates down a 35 degree
ramp. If it travels 2.0 m in 4 seconds, what is the
coefficient of friction?
Practice #4
 Do… A 1.0 kg block slides down a down a 30 degree
ramp with a coefficient of friction of .15. How long will it
take to slide 2.0m?
What about Air Resistance?
 Air Resistance is a friction force
 In general, Air Resistance (aka Drag) is
proportional to velocity or the square of velocity
Fdrag  Av
or
Fdrag  Bv 2
A and B depend on type of fluid, density,surface area, shape, etc...
What is Terminal Velocity?
 As an object falls through a fluid, its velocity and Drag (air
resistance) increases
 At a certain velocity, the drag equals the force of gravity
and the object stops accelerating… equilibrium is reached
and the net force is zero
 When equilibrium is reached the object has attained
Terminal Velocity
at Terminal Velocity,
 F  0  Av
T
 mg
mg
A
similarly, if Drag  v 2
 AvT  mg or, vT 
vT 
mg
B
Air Resistance and Terminal Velocity
 Create qualitative x-t, v-t and a-t graphs of a
falling object with air resistance…
What we know…
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How does force affect the motion of an object?
How do free-body diagrams help in analyzing forces
and motion?
What are Newton’s Laws of Motion?
How can you determine forces required for
equilibrium?
How is mass related to motion?
What are action-reaction pairs and why don’t they
produce equilibrium?
What is the difference between mass and weight?
What is a normal force?
How can you determine the force due to friction?
Questions?