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Forces
Chapter 4
Forces
A push or a pull
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

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Gravitational
Electromagnetic
Weak
Strong
Sir Isaac Newton
Newton’s First Law
 An object in motion remains in motion
and an object at rest remains at rest
unless acted on by an outside force.
 Sometimes called the Law of Inertia
 Examples
 Sudden braking
 Flooring it
 Seeing stars
Inertia
 A body’s tendency to keep doing what it’s
already doing
 Measured by mass
 Does not need gravitational force.
Newton’s Second Law
 The acceleration of an object is directly
proportional to the force on the object
and inversely proportional to the mass.
F  ma
Units
m
 F  ma  kg 2  N
s
 Newtons
 English equivalent is
pounds
 4.45N=1lb
Practice
 A 2988kg elephant accelerates on a
skateboard at a rate of 2.7m/s2. If the
elephant is being pushed with a 10,000N
force, what is the force of friction?
 A 58.7N force is applied to a go kart to get it
started. If the car starts from rest and
accelerates for 4.0s covering a distance of
7.8m, what is the mass of the kart?
Newton’s Third Law
 When one object exerts a force on a
second object, the second object exerts
a force on the first of equal magnitude
and opposite direction
 Action-reaction pairs
 Switch the nouns
Weight
 Weight and gravitational force are the same
thing.
 Since acceleration due to gravity (g) is known,
we can define weight as:
Fg  mg
 In general, we will take care of directional
information (positives and negatives) in the
problem itself, so we will use +9.8m/s2 instead
of -9.8m/s2
Skydiving and Terminal
Velocity
Practice Problems
 A skydiver reaches a terminal velocity of
55m/s when in free fall. If the skydiver
has a mass of 78kg, how much force is
air resistance providing?
 When starting up the elevator, a rider
experiences an acceleration of 1.2m/s2.
If the force from the elevator floor is
650N, what is the mass of the rider?
Normal Force
 Force pushing up from a surface
 When vertical acceleration is zero and the
only two vertical forces are gravity and
normal force, normal force and gravity are
equal.
 Scales read normal force
 Elevators
 Weightlessness (Newton’s Mountain)
Friction
 Depends only on the surfaces, not on velocity
 Kinetic and static friction
 Depends on two things, normal force of the object
and the combination of surfaces
 Coefficient of friction, µ equals the ratio of frictional
force to normal force.
F fr  FN
Practice
 A 16.8 kg crate is pushed horizontally
along the floor with a force of 207N. If
the coefficient of friction is 0.62, what is
the acceleration of the crate?
 A sled is pulled across the snow with a
constant velocity. If the sled has a
mass of 32.1kg and the coefficient of
kinetic friction is 0.14, what is the
magnitude of the pull?
 A bunch of guys try to push a car out of
the mud. They push harder and harder
until it becomes unstuck and then push
with a constant force. If the coefficient
of static friction is 0.54 and the
coefficient of kinetic friction is 0.40, what
is the acceleration of the car once it
starts moving?
 A crate of chickens is pulled with 145N
of force with a rope that is inclined 30°
up from the horizontal. If the crate has
a mass of 35kg and the coefficient of
friction between the floor and the crate
is 0.43, what is:
 The normal force on the crate?
 The acceleration of the crate, assuming it
accelerates horizontally.
Tension
 Upward force coming from a string or
rope.
 All vertical ropes supporting an object
account for an equal amount of force
unless specified otherwise.
Atwood Machine Problems
•If mass 1 is 5kg and mass
2 is 7kg, what is the
acceleration of the system?
m2
m1
 Assumptions
• a1= a2
• FT1= FT2
 Pulley switches which
direction is positive.
 Consider the direction
of motion of the box to
be the positive
direction.
Box 1
FT
a
 F  ma
FT  Fg  m1a
FT  m1g  m1a
Fg
Box 2
 F  ma
FT
Fg  FT  m2 a
a
Fg
m2 g  FT  m2a
Putting it together
FT  m1 g  m1a
m2 g  FT  m2 a
FT  m1 g  m1a
m2 g  m2a  FT
m1g  m1a  m2 g  m2a
m2a  m1a  m2 g  m1g
Putting it together cont.
m2a  m1a  m2 g  m1g
(m2  m1 )a  m2 g  m1g
m2 g  m1 g
a
 1.63 m 2
s
m1  m2
Practice Problem
 m1=8kg
 m2=4kg
 Find FT
m2
m1
Sign Problems
 Equilibrium-the state where all forces are
balanced and acceleration is zero.
 Includes both stationary and constant
velocity cases.
1st Example
 If the sign has a mass of
15kg, what is the tension in
the string? What is the
force the beam exerts on
the sign?
 Assume equilibrium.
 One component at a time.
Set up equilibrium case
F
F
horizontal
vertical
0
0
Fy  FT sin 
Fx  FT cos 
Fy
FT
23
Fx
Fbeam
Fg
Equilibrium case for
vertical
F
vertical
0
Fy  Fg  0
FT sin   mg  0
mg
FT 
 376.2 N
sin 
Equilibrium case for
horizontal
F
horizontal
0
Fx  FBeam  0
FT cos   FBeam  0
FT cos   FBeam
376.2 cos 23  346.3N
Practice Problem 2
 Find the tension in
each rope.
T1
T2
Break up Components
Fy1  F1 sin 1
F1
F2
Fx1  F1 cos1
Fy 2  F2 sin  2
Fx 2  F2 cos  2
Fy1
Fy2
Fx1
Fx2
Fg
Horizontal Pieces
 Since the sign isn’t
accelerating
horizontally, we can
use:
Fy1
Fy2
Fx1
Fx2
Fg
F
x
0
Fx1  Fx 2  0
F1 cos1  F2 cos2  0
F1 cos1  F2 cos2
Vertical Pieces
 Since the sign isn’t
accelerating
vertically, we can
use:
Fy1
F  0
Fy1  Fy 2  Fg  0
Fy2
Fx1
Fx2
Fg
F1 sin 1  F2 sin 2  mg  0
Putting the two together
F1 cos1  F2 cos2
F1 sin 1  F2 sin 2  mg  0
F2 cos  2
F1 
cos 1
 F2 cos  2 

 sin 1  F2 sin  2  mg  0
 cos 1 
Putting the two together
cont.
 F2 cos  2 

 sin 1  F2 sin  2  mg
 cos 1 
 cos  2 

 sin 1  sin  2   mg
F2 
 cos 1 

F2 
mg
 cos  2 

 sin 1  sin  2 

 cos 1 

Putting the two together
cont.
F2 
47 9.8
 cos 62 

 cos 34  sin 34  sin 62



 383N
F2 cos  2
F1 
 214.6 N
cos 1
Ramp Problems
Practice Problems
 A box slides down a frictionless ramp. If the
box has a mass of 12kg and the ramp is
inclined at an angle of 32 degrees, what is the
acceleration of the box?
 A 76kg box slides down a ramp inclined at 21
degrees. If the acceleration of the box is
1.2m/s2, what is the coefficient of friction
between the box and the ramp?
Random Practice
Problems
 A 28kg box is pulled at an angle of 18o up
from the horizontal with a force of 145N.
If the coefficient of friction between the
floor and the box is .32, what is the
acceleration of the box?
 A dead pig has a µk of .21 and a µs of
.43 when sitting on a book cover, how
far will the book cover need to be tilted
to start the pig carcass moving? Once it
starts moving, how quickly will it
accelerate?




m1=13kg
m2=9kg
μk=.11
What is a?