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Force Outline
Physics Chapter 4
I. Changes in motion
A. Force:
1. Examples:
2. Units:
B. Contact force:
1. Example:
C. Field force:
1. Example:
D. Force diagrams:
1. What is the importance of drawing free-body diagrams?
2. In order to draw the free-body diagram, you must first isolate and identify all the forces
acting on the car
3. Steps in drawing free-body diagrams
a. Draw diagram isolating just the object
b. Draw and label vector arrows representing all external forces acting on the
object
c. Draw gravitational force acting on the object, directed toward the center of the
Earth
d. The upward force applied on the object
e. The backward force of friction
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2. Newton’s First Law
A. Before 1600, what was believed to be the natural state of most objects?
B. How did Galileo, revise this theory?
Newton’s First Law of Motion
C. Inertia:
D. Why is Newton’s first law referred to as the law of inertia?
E. How do we determine the acceleration of an object?
F. External force:
G. Net external force:
H. How is the net external force determined?
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Example 1: Four forces act on a box as shown. Find the net external force acting upon the box.
5120 N
950 N
1520 N
4050 N
Example 2: A dog pulls on a pillow with a force of 5.0 N at an angle of 37o above the horizontal and
gravity pulls the pillow down with a force of 2.0 N. Find the net external force acting upon the pillow.
Set 4A
1. What are the two types of forces and give two examples of each.
2. A man is pulling on his dog with a force of 70.0 N directed at an angle of 30.0o to the horizontal. Find
the x and y components of this force.
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.
a. Find the net external force in the x direction.
b. Find the net external force in the y direction.
c. Find the magnitude and direction of the net external force on the crate.
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4. A gust of wind blows an apple from a tree. As the apple falls, the force of gravity on the apple is 9.25
N downward, and the force of wind on the apple is 1.05 N to the right. Find the magnitude and
direction of the net external force on the apple.
5. The wind exerts a force of 452 N north on a sailboat, while the water exerts a force of 325 N west on
the sailboat. Find the magnitude and direction of the net external force on the sailboat.
6. The sensor in the torso of a crash-test dummy records the magnitude of the net external force acting
on it. If the dummy is thrown north with a force of 130.0 N while simultaneously being hit from the
east with a force of 4500.0 N, what force will the sensor report?
I. Describe why mass is a measurement of inertia.
J. Describe how a seat belt works.
K. Equilibrium:
3. Newton’s second and third laws
Newton’s Second Law
A. In equation form:
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Example 3: Roberto and Laura are studying across each other at a wide table. Laura slides a 2.2 kg book
toward Roberto. If the net external force acting on the book is 2.6 N to the right, what is the book’s
acceleration?
Example 4: A 7.5 kg bowling ball initially at rest is dropped from the top of an 11 m building. It hits the
ground 1.5 s later. Find the net external force acting on the falling ball.
*In solving problems, it is often easier to break the equation for Newton’s second law into components.
The sum of the forces acting in the x direction equals the mass times the acceleration in the x direction.
Set 4B
1. Can an object be in equilibrium if only one force is acting upon it?
2.
If a car is traveling westward with a constant velocity of 20.0 m/s, what is the net external force
acting on it?
3. The net external force on the propeller of a 3.2 kg model airplane is 7.0 N forward. What is the
acceleration of the airplane?
4. The net external force on a golf cart is 390 N north. If the cart has a total mass of 270 kg, what are the
magnitude and direction of its acceleration?
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5. A car has a mass of 1.50 x 103 kg. If the force acting on the car is 6.75 x 103 N to the east, what is the
car’s acceleration?
6. A 2.0 kg otter starts from rest at the top of a muddy incline 85 cm long and slides down to the bottom
in 0.50 s. What net external force acts on the otter along the incline?
7. A soccer ball kicked with a force of 13.5 N accelerates at 6.5 m/s2 to the right. What is the mass of
the ball?
Newton’s Third Law
B. Alternative statement:
C. Action-reaction pair:
D. Give an example of this law using a hammer and nail.
E. Explain how a helicopter works.
IV. Everyday forces
A. Weight:
B. Normal force:
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C. Describe what direction the normal force is in.
D. How do you calculate the normal force?
E. Static friction:
F. Kinetic friction:
G. Adhesion:
H. Coefficient of friction:
1. The coefficient of kinetic friction
2. The coefficient of static friction
Example 5: A 24 kg crate initially at rest on a horizontal floor required a 75 N horizontal force to set it in
motion. Find the coefficient of static friction between the crate and the floor.
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Example 6: A 91 kg refrigerator is at rest on the floor. The coefficient of static friction between the
refrigerator and the floor is 0.95 and the coefficient of kinetic friction is 0.90. Find the force required
setting it in motion and the force required to keep the refrigerator in motion.
Set 4C
1. Explain the relationship between mass and weight.
2.
Which is usually greater, the maximum force of static friction or the force of kinetic friction?
3. Once the crate in Example 5 is in motion, a horizontal force of 53 N keeps the crate moving with a
constant velocity. Find µk, the coefficient of kinetic friction, between the crate and the floor.
4. A 25 kg chair initially at rest on a horizontal floor requires a 365 N horizontal force to set it in motion.
Once the chair is in motion, a 327 N horizontal force keeps it moving at a constant velocity.
a. Find the coefficient of static friction between the chair and the floor.
b. Find the coefficient of kinetic friction between the chair and the floor.
5. A museum curator moves artifacts into place on many different display surfaces. Find Fsmax and Fk for
the following situations.
a. Moving a 145 kg aluminum sculpture across a steel platform (µs = 0.61; µk = 0.47)
b. Pulling a 15 kg steel sword across a horizontal steel shield (µs = 0.74; µk = 0.57)
c. Pushing a 250 kg wood bed on a wood floor (µs = 0.40; µk = 0.20)
d. Sliding a 0.55 kg glass amulet on a glass display case (µs = 0.90; µk = 0.40)
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Example 7: A student moves a box of books by attaching a rope to the box and pulling with a force of
90.0 N at an angle of 30.0. The box of books has a mass of 20.0 kg, and the coefficient of kinetic
friction between the bottom of the box and the sidewalk is 0.50. Find the acceleration of the box.
Example 8: Two students are sliding a 225 kg sofa at constant speed across a wood floor. One student
pulls with a force of 225 N at an angle of 13o above the horizontal. The other student pushes with a force
of 250 N at an angle of 23o below the horizontal. What is the coefficient of kinetic friction between the
sofa and the floor?
Set 4D
1. Describe what happens to acceleration and all of the forces as a sky diver falls through the air.
2. A student moves a box of books down the hall by pulling on a rope attached to the box. The student
pulls with a force of 185 N at an angle of 25.0o above the horizontal. The box has a mass of 35.0 kg,
and µk between the box and the floor is 0.27. Find the acceleration of the box.
3. A box of books with a mass of 33 kg moves with a constant velocity across the floor when it is pushed
with a force of 425 N exerted downward at an angle of 35.2o below the horizontal. Find µk between
the box and the floor.
Continued on next page…
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4. A clerk moves a box of cans down an aisle by pulling on a strap attached to the box. The clerk pulls
with a force of 185.0 N at an angle of 25.0o with the horizontal. The box has a mass of 35.0 kg, and
the coefficient of the kinetic friction between box and floor is 0.450. Find the acceleration of the box.
5. A 75.0 kg steal statue is being dragged across the floor with a constant velocity after being pulled with
a 120 N force at an angle of 40o above the horizontal. What is the coefficient of kinetic friction
between the statue and the floor?
6. A sled, with a mass of 50.0 kg, is accelerating across the ground after a 200.0 N force, at an angle of
25o above the horizontal, is applied. The coefficient of kinetic friction between the sled and the
ground is 0.15. What is the acceleration of the sled?
V. Inclined Planes
A. Explain how problems involving inclined planes differ from those on a horizontal surface.
B. Draw a diagram on how gravity is calculated on inclined planes.
Example 9: A block with a mass of 5.0 kg is being pulled up an inclined plane that is at a 35o angle. The
block is being pulled with a force of 50.0 N but there is 15.0 N of friction being applied to the block.
What is the acceleration of the block?
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Example 10: A 4.0 kg bucket of water accelerates down an incline plane, once it is raised to an angle of
40o. There is 9.0 N of friction also being applied to the bucket. What is the bucket’s acceleration?
Set 4E
1. A girl, with a mass of 80.0 kg, sleds down a hill that has a 30o incline. The friction between the sled
and the snow applies 15.0 N of force slowing her down. What is her acceleration down the hill?
2. A 3.0 kg block is being pulled up an inclined plane with a force of 50.0 N. There is 10.0 N of
frictional force when the incline is at 25o. What is the acceleration of the block?
3. A box of books (mass = 45.0 kg) is accelerating down an incline plane at a rate of 2.0 m/s2. How
much frictional force is present?
4. A sofa (250.0 kg) is being pushed up a moving truck’s ramp, which is at a 40o angle, with a force of
2.0 x 103 N. There is 75.0 N of friction between the sofa and the ramp. What is the acceleration of
the sofa?
5. A 6.0 kg block is being pulled up a 20o incline plane with a force of 60.0 N. The block is accelerating
3.5 m/s2 as it moves up the ramp. How much friction is present between the block and the ramp?
6. A refrigerator, mass 500.0 kg, is being pushed up an inclined plane that has a 15o angle. There is 200
N of friction between the refrigerator and the ramp. How hard must the refrigerator be pushed in
order to have an acceleration of 0.50 m/s2?
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