Understanding Vocabulary
Section 5.1
1. vector
2. scalar
3. magnitude
4. components
5. free-body diagram
Section 5.2
6. normal force
7. resultant
8. Hooke’s law
9. equilibrium
Section 5.3
10. friction
11. static friction
12. lubricant
Section 5.4
13. torque
14. rotational equilibrium
15. lever arm
Reviewing Concepts
Section 5.1
1. Force and velocity are vectors; distance and speed are scalars.
2. A force vector can be described by (1) a graph, (2) a magnitude and
angle, and (3) an x-y pair.
3. To find the components of a vector using a graph, first draw the
vector to scale and at the correct angle. Then extend the lines parallel
to the x and y axes. Last, read of the x and y components.
4.
a2 + b2 = c2
where the squares of the x and y components of a right triangle equals
the square of the hypotenuse.
5.
Section 5.2
6. The net force on an object in equilibrium is zero.
7. The word normal means perpendicular.
8. Answers are:
a. The normal force of the chair on you.
b. The normal force is directed straight up (opposite to gravity).
c. The size of the normal force is equal to the size of the force of
gravity.
9. zero; zero
10. Answers are:
a. The action force is the force your hand exerts on the spring to the
right.
b. The reaction force is the force the spring exerts on your hand to
the left.
c. The action force and reaction forces are opposite in direction.
d. The action and reaction forces are the same in strength.
11. The force increases as the spring is stretched more.
12. The spring constant of a spring is the relationship between the force
exerted by a spring and its change in length. A large spring constant
means the spring is very hard to stretch or compress and therefore it
requires a lot of force to change its length.
Section 5.3
13. static friction; sliding friction; rolling friction; air friction
14. Friction acting on a surface always acts in the opposite direction to
the movement of the surface; friction is a resistive force.
15. Static friction exists between two objects that are stationary; sliding
friction exists between two surfaces that are sliding across each other.
16. Friction is caused by the contact between the microscopic hills and
valleys on the surfaces of two objects that are interacting.
17. When the box is full of books, the tiny hills and valleys in the surfaces
of the box and the floor are pressed together with a greater force than
when then box is empty, so the amount of friction increases.
18. Lubricants and ball bearings decrease friction.
19. Sometimes we want to increase the amount of friction present instead
of decreasing it. For example, the brakes on a bicycle create friction
between the brake pads and the rim of the wheel thus allowing a rider
to slow down.
Section 5.4
20. Torque and force are similar in that torque is created by force, but are
different in that torque depends on both force and distance. You can
also think of it as if forces are pushes and pulls, torques are twists.
21. The size of the force acting on an object and the length of the lever
arm.
22. Torque is measured in newton-meters. The newton-meter used for
torque is not the same as the newton-meter for work and is not equal
to a joule. The object with a torque applied to it does not move in the
direction of the force, and therefore no work is done on it.
23. A certain amount of torque is required to loosen a bolt, and force and
the length of the lever arm are inversely related for a given torque. So
a longer lever arm corresponds to a smaller necessary force.
24. The greatest torque would be in case “c” when the shovel's handle is
pushed right so it tilts towards the ground. This creates the longest
lever arm, or perpendicular distance between the line of action of the
force and the axis or rotation. Since the force is the same in each case,
the longest lever arm creates the greatest amount of torque.
25. An object is in rotational equilibrium when the net torque applied to it
is zero.
Solving Problems
Section 5.1
1. Answers are:
2. Answers are:
3. Answers are:
a. (2.2, 2.2)
b. (6.9, 4)
c. (4, 6.9)
d. (94, 34)
Section 5.2
4. Answers are:
a. 40 N to the left
b. 25 N up
c. 11.8 m, 45°
5. Fw = mg = (20 kg)(9.8 m/sec2) = 196 N
6. Fnet = 1500 N = 400 N + 300 N + 250 N + F4
F4 = 550 N
The weight vector pushes down, the normal forces push up
7. F = -kx = -(100 N/m)(0.5 m) = -50 N
8. k = -F ÷ x = (50 N) ÷ (0.03 m) = -1666.7 N/m
F = -kx = -(-1666.7 N/m)(0.06 m) = 100 N
Section 5.3
9. force of gravity = 50 N
normal force = 50 N
pulling force = 20 N
force of friction = 20 N
10. force of gravity = 300 N
normal force = 300 N
pulling force = 50N
force of static friction = 50 N
Section 5.4
11. τ = rF = (2 m)(30 N) = 60 N-m
12. τ = rF = (0.2 m)(300 N) = 60 N-m
13. r = τ ÷ F = (200 N-m) ÷ (400 N) = 0.5 m
14. clockwise: τ = rF = (1.5 m)(10 N) = 15 N-m
counterclockwise: τ = rF = (2 m)(20 N) = 40 N-m
τnet = 40 N-m - 15 N-m = 25 N-m
15. clockwise: τ = rF = (0.5 m)(600 N) = 300 N-m
counterclockwise: τ = rF = (1.5 m) × F
τnet = 0 = (1.5 m) × F - 300 N-m
F = 200 N
Applying Your Knowledge
Section 5.1
1. If the 100 N force and the 200 N force are pointing in the same
direction, and the 300 N force is pointed in the opposite direction,
then the forces will be in equilibrium.
2. If the wall and the ground only exert normal forces on the ladder, then
the weight of the person and the ladder is balanced by the normal
force from the ground. The normal force from the wall is not balanced
by anything, therefore the ladder would accelerate and fall down.
Section 5.2
3. Sources for information on well-known bridges can be found with a
web search typing key words “famous bridges”. The web site http://
www.pbs.org/wgbh/buildingbig/bridge/webography.html is a good
source to get started.
Section 5.3
4. A web search reveals the site www.howstuffworks.com as an excellent
source for information on automobiles in general, and anti-lock
brakes specifically. The article addresses the frictional differences
between static and kinetic friction as well as the concepts of computer
feedback from brakes and wheels.
Section 5.4
5. An object is in rotational equilibrium when the net torque on the
object is zero. Torque is the product of the lever arm and a force
exerted perpendicular to the arm.
If a force is exerted on an object at its center of mass, the length of the
lever arm is zero, and therefore the net torque is zero. The object is
accelerating, but not rotationally and it is in rotational equilibrium.
If the forces are applied at 180° to one another but not coincident
upon the same point, they would create a torque. Their net force
would be zero, and they would create a non-zero torque. The body
would not be in rotational equilibrium.