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Forces and the Laws of Motion
Preview
Section 1 Newton's Second
Section 5 Extra questions
Section 1
Forces and the Laws of Motion
Section 2
Net Force - the Sum of the Forces
• This car is moving with a
constant velocity.
– Fforward = road pushing the tires
– Fresistance = force caused by friction
and air
– Forces are balanced
• Velocity is constant because the
net force (Fnet) is zero.
Forces and the Laws of Motion
Equilibrium
• The state in which the net
force is zero.
– All forces are balanced.
– Object is at rest or travels with
constant velocity.
• In the diagram, the bob on
the fishing line is in
equilibrium.
– The forces cancel each other.
– If either force changes,
acceleration will occur.
Section 2
Forces and the Laws of Motion
Section 2
Classroom Practice Problem
• An agricultural student is designing a support
system to keep a tree upright. Two wires have
been attached to the tree and placed at right
angles to each other (parallel to the ground).
One wire exerts a force of 30.0 N and the other
exerts a force of 40.0 N. Determine where to
place a third wire and how much force it should
exert so that the net force on the tree is zero.
• Answer: 50.0 N at 143° from the 40.0 N force
Forces and the Laws of Motion
Section 3
Newton’s Second Law
• Increasing the force will increase the acceleration.
– Which produces a greater acceleration on a 3-kg model airplane, a force
of 5 N or a force of 7 N?
• Answer: the 7 N force
• Increasing the mass will decrease the acceleration.
– A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg
and one with a mass of 4 kg. Which has a greater acceleration?
• Answer: the 3 kg airplane
Forces and the Laws of Motion
Section 3
Newton’s Second Law (Equation Form)
• F represents the vector sum of all forces acting on an
object.
– F = Fnet
– Units for force: mass units (kg)  acceleration units (m/s2)
– The units kg•m/s2 are also called newtons (N).
Forces and the Laws of Motion
Section 3
Classroom Practice Problem
• Space-shuttle astronauts experience
accelerations of about 35 m/s2 during takeoff.
What force does a 75 kg astronaut experience
during an acceleration of this magnitude?
• Answer: 2600 kg•m/s2 or 2600 N
Forces and the Laws of Motion
Section 4
What do you think?
• How do the quantities weight and mass differ
from each other?
• Which of the following terms is most closely
related to the term friction?
– Heat, energy, force, velocity
• Explain the relationship.
Forces and the Laws of Motion
Section 4
Weight and Mass
• Mass is the amount of matter in an object.
– Kilograms, slugs
• Weight is a measure of the gravitational force on an
object.
– Newtons, pounds
– Depends on the acceleration of gravity
• Weight = mass  acceleration of gravity
– W = mag where ag = 9.81 m/s2 on Earth
– Depends on location
• ag varies slightly with location on Earth.
• ag is different on other planets.
Forces and the Laws of Motion
Normal Force
• Force on an object
perpendicular to the
surface (Fn)
• It may equal the weight
(Fg), as it does here.
• It does not always equal
the weight (Fg), as in the
second example.
• Fn = mg cos 
Section 4
Forces and the Laws of Motion
Section 4
Static Friction
• Force that prevents motion
• Abbreviated Fs
– How does the applied force (F)
compare to the frictional force
(Fs)?
– Would Fs change if F was
reduced? If so, how?
– If F is increased significantly,
will Fs change? If so, how?
– Are there any limits on the
value for Fs?
Forces and the Laws of Motion
Section 4
Kinetic Friction
• Force between surfaces that opposes movement
• Abbreviated Fk
• Does not depend on the speed
• Using the picture, describe
the motion you would
observe.
– The jug will accelerate.
• How could the person push
the jug at a constant speed?
– Reduce F so it equals Fk.
Forces and the Laws of Motion
Friction
Click below to watch the Visual Concept.
Visual Concept
Section 4
Forces and the Laws of Motion
Section 4
Calculating the Force of Friction (Ff)
• Ff is directly proportional to Fn (normal force).
Ff   Fn

Ff
Fn
• Coefficient of friction ():
–
–
–
–
Determined by the nature of the two surfaces
s is for static friction.
k is for kinetic friction.
s > k
Forces and the Laws of Motion
Typical Coefficients of Friction
• Values for  have no units and are approximate.
Section 4
Forces and the Laws of Motion
Everyday Forces
Click below to watch the Visual Concept.
Visual Concept
Section 4
Forces and the Laws of Motion
Section 4
Classroom Practice Problem
• A 24 kg crate initially at rest on a horizontal
floor requires a 75 N horizontal force to set it
in motion. Find the coefficient of static
friction between the crate and the floor.
– Draw a free-body diagram and use it to find:
• the weight
• the normal force (Fn)
• the force of friction (Ff)
– Find the coefficient of friction.
• Answer: s = 0.32
Forces and the Laws of Motion
Section 4
Classroom Practice Problem
• A student attaches a rope to a 20.0 kg box of
books. He pulls with a force of 90.0 N at an
angle of 30.0˚ with the horizontal. The
coefficient of kinetic friction between the box
and the sidewalk is 0.500. Find the magnitude
of the acceleration of the box.
– Start with a free-body diagram.
– Determine the net force.
– Find the acceleration.
• Answer: a = 0.12 m/s2
Forces and the Laws of Motion
The Four Fundamental Forces
• Electromagnetic
– Caused by interactions between protons and electrons
– Produces friction
• Gravitational
– The weakest force
• Strong nuclear force
– The strongest force
– Short range
• Weak nuclear force
– Short range
Section 4
Forces and the Laws of Motion
Preview
• Multiple Choice
• Short Response
• Extended Response
Section 4
Forces and the Laws of Motion
Section 4
Multiple Choice
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
1. What is the acceleration of the two blocks?
A.
a
F
m1
C. a 
F
m1  m2
B.
F
a
m2
D. a 
F
(m1 )(m2 )
Forces and the Laws of Motion
Section 4
Multiple Choice
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
1. What is the acceleration of the two blocks?
A.
a
F
m1
C. a 
F
m1  m2
B.
F
a
m2
D. a 
F
(m1 )(m2 )
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
2. What is the horizontal force acting on m2?
F. m1a
G. m2a
H. (m1 + m2)a
J. m1m2a
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
2. What is the horizontal force acting on m2?
F. m1a
G. m2a
H. (m1 + m2)a
J. m1m2a
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
3. A crate is pulled to the right with a force of 82.0 N, to the left
with a force of 115 N, upward with a force of 565 N, and
downward with a force of 236 N. Find the magnitude and
direction of the net force on the crate.
A. 3.30 N at 96° counterclockwise from the positive x-axis
B. 3.30 N at 6° counterclockwise from the positive x-axis
C. 3.30 x 102 at 96° counterclockwise from the positive x-axis
D. 3.30 x 102 at 6° counterclockwise from the positive x-axis
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
3. A crate is pulled to the right with a force of 82.0 N, to the left
with a force of 115 N, upward with a force of 565 N, and
downward with a force of 236 N. Find the magnitude and
direction of the net force on the crate.
A. 3.30 N at 96° counterclockwise from the positive x-axis
B. 3.30 N at 6° counterclockwise from the positive x-axis
C. 3.30 x 102 at 96° counterclockwise from the positive x-axis
D. 3.30 x 102 at 6° counterclockwise from the positive x-axis
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
5. A freight train has a mass of 1.5 x 107 kg. If the locomotive
can exert a constant pull of 7.5 x 105 N, how long would it take
to increase the speed of the train from rest to 85 km/h?
(Disregard friction.)
A. 4.7 x 102s
B. 4.7s
C. 5.0 x 10-2s
D. 5.0 x 104s
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
5. A freight train has a mass of 1.5 x 107 kg. If the locomotive
can exert a constant pull of 7.5 x 105 N, how long would it take
to increase the speed of the train from rest to 85 km/h?
(Disregard friction.)
A. 4.7 x 102s
B. 4.7s
C. 5.0 x 10-2s
D. 5.0 x 104s
Forces and the Laws of Motion
Section 4
Multiple Choice, continued
Use the passage below to answer questions
6–7.
A truck driver slams on the brakes and skids
6. to a stop through a displacement Dx.
A. Dx/4
B. Dx
C. 2Dx
D. 4Dx
If the truck’s mass
doubles, find the
truck’s skidding
distance in terms
of Dx. (Hint:
Increasing the
mass increases
the normal force.)
Forces and the Laws of Motion
Section 4
Short Response
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
10. How long does the ball take to hit the
ground?
Forces and the Laws of Motion
Section 4
Short Response
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
10. How long does the ball take to hit the
ground?
Answer: 6.00 s
Forces and the Laws of Motion
Section 4
Short Response, continued
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
11. How far from the building does the ball hit the ground?
Forces and the Laws of Motion
Section 4
Short Response, continued
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
11. How far from the building does the ball hit the
ground?
Answer: 72.0 m
Forces and the Laws of Motion
Section 4
Short Response, continued
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
12. When the ball hits the ground, what is its
speed?
Forces and the Laws of Motion
Section 4
Short Response, continued
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
12. When the ball hits the ground, what is its
speed?
Answer: 63.6 m/s
Forces and the Laws of Motion
Section 4
Extended Response
16. A student pulls a rope attached to a 10.0 kg
wooden
sled and moves the sled across dry snow. The
student
pulls with a force of 15.0 N at an angle of
45.0º.
If k between the sled and the snow is 0.040,
what
is the sled’s acceleration? Show your work.
Forces and the Laws of Motion
Section 4
Extended Response
16. A student pulls a rope attached to a 10.0 kg
wooden
sled and moves the sled across dry snow. The
student
pulls with a force of 15.0 N at an angle of
45.0º.
If k between the sled and the snow is 0.040,
what
is the sled’s acceleration? Show your work.
Answer: 0.71 m/s2
Forces and the Laws of Motion
Section 4
Extended Response, continued
17. You can keep a 3 kg book from dropping by pushing
it horizontally against a wall. Draw force diagrams,
and identify all the forces involved. How do they
combine to result in a zero net force? Will the force
you must supply to hold the book up be different for
different types of walls? Design a series of
experiments to test your answer. Identify exactly
which measurements will be necessary and what
equipment you will need.
Forces and the Laws of Motion
Section 4
Extended Response, continued
17. You can keep a 3 kg book from dropping by
pushing
it horizontally against a wall. Draw force
diagrams,
and identify all the forces involved. How do
they
combine to result in a zero net force? Will the
force
you must supply to hold the book up be
different for
different types of walls? Design a series of
experiments to test your answer. Identify