Cracking the AP Physics C Exam
Chapter 6 Drill
The answers and explanations can be found in Chapter 17.
5. The coefficient of static friction between a box and a
Section I: Multiple Choice ramp is 0.5. The ramp’s incline angle is 30°. If the box is
placed at rest on the ramp, the box will do which of the
following?
1. Consider a box being dragged across a table at a con-
stant velocity by a string. Which of the following would (A) Accelerate down the ramp
be considered an action-reaction pair? (B) Accelerate briefly down the ramp but then slow
down and stop
I. The force of gravity pulling the box down
(C) Move with constant velocity down the ramp
and the normal force pushing the box up
(D) Not move
II. The force of friction on the box and the
(E) Cannot be determined from the information given
tension force pulling the box
III. The force of the box pushing down on the
table and the normal force pushing the box 6.
up
(A) I only
(B) I and II only
(C) II only
(D) I and III only
(E) III only
2. A person who weighs 800 N steps onto a scale that is on
the floor of an elevator car. If the elevator accelerates
upward at a rate of 5 m/s2, what will the scale read?
(A) 400 N
(B) 800 N
(C) 1,000 N
(D) 1,200 N
m
M
(E) 1,600 N
3. A frictionless inclined plane of length 20 m has a maxi-
mum vertical height of 5 m. If an object of mass 2 kg is Assuming a frictionless, massless pulley, determine the
placed on the plane, which is the net force it feels? acceleration of the blocks once they are released from
rest.
(A) 5N
(B) 10 N m
(C) 15 N (A) g
M +m
(D) 20 N
(E) 30 N M
(B) g
M +m
4. A 20 N block is being pushed across a horizontal table M −m
(C) g
by an 18 N force. If the coefficient of kinetic friction m
between the block and the table is 0.4, find the accelera-
M +m
tion of the block. (D) g
M −m
(A) 0.5 m/s2
(B) 1 m/s2 M −m
(E) g
(C) 5 m/s2 M +m
(D) 7.5 m/s2
(E) 9 m/s2
6. Newton’s Laws | 1 6 3
Cracking the AP Physics C Exam
7. If all of the forces acting on an object balance so that the Questions 11–12:
net force is zero and the object’s mass remains constant,
then
A 60 cm rope is tied to the handle of a bucket which is then
(A) the object must be at rest
whirled in a vertical circle. The mass of the bucket is 3 kg.
(B) the object’s speed will decrease
(C) the object will follow a parabolic trajectory
(D) the object’s direction of motion can change, but not
its speed 11. At the lowest point in its path, the tension in the rope is
(E) none of the above 50 N. What is the speed of the bucket?
(A) 1 m/s
(B) 2 m/s
8. An object of mass m is allowed to slide down a fric-
(C) 3 m/s
tionless ramp of angle q, and its speed at the bottom is
(D) 4 m/s
recorded as v. If this same process was followed on a
(E) 5 m/s
planet with twice the gravitational acceleration of Earth,
what would be its final speed?
(A) 2v 12. What is the critical speed below which the rope would
become slack when the bucket reaches the highest point
in the circle?
(B) 2v
(A) 0.6 m/s
(C) v (B) 1.8 m/s
(C) 2.4 m/s
v
(D) (D) 3.2 m/s
2 (E) 4.8 m/s
v
(E)
2
9. An engineer is designing a loop for a roller coaster. If
the loop has a radius of 25 m, how fast do the cars need 13. An object moves at a constant speed in a circular path of
to be moving at the top to ensure people would be safe radius r at a rate of 1 revolution per second. What is its
even if the safety bars malfunctioned? acceleration?
(A) 12.7 m/s (A) 0
(B) 15.8 m/s (B) 2π2r
(C) 21.2 m/s (C) 2π2r2
(D) 29.3 m/s (D) 4π2r
(E) 33.3 m/s (E) 4π2r2
10. The pulley system above requires a person to pull on the
rope with a minimum force F in order to lift the block of
mass m. An inclined plane of angle θ requires that same
force to push the block up the ramp. Assuming ideal
conditions in both situations, what is the value of θ?
(A) 0°
(B) 9.6°
(C) 21°
(D) 47°
(E) 80°
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Cracking the AP Physics C Exam
Section II: Free Response
1. This question concerns the motion of a crate being pulled across a horizontal floor by a rope. In the diagram below, the mass of
the crate is m, the coefficient of kinetic friction between the crate and the floor is µ , and the tension in the rope is FT .
pe
ro
θ
m
(a) Draw and label all of the forces acting on the crate.
(b) Compute the normal force acting on the crate in terms of m, FT , θ, and g.
(c) Compute the acceleration of the crate in terms of m, FT , θ, µ , and g.
(d) Assume that the magnitude of the tension in the rope is fixed but that the angle may be varied. For what value of θ would
the resulting horizontal acceleration of the crate be maximized?
2. In the diagram below, a massless string connects two blocks—of masses m1 and m2 , respectively—on a flat, frictionless tabletop.
A force F pulls on Block #2, as shown:
Block #1 Block #2
m1 m2 F
Solve for the following in terms of given quantities.
(a) Draw and label all of the forces acting on Block #1.
(b) Draw and label all of the forces acting on Block #2.
(c) What is the acceleration of Block #1?
(d) What is the tension in the string connecting the two blocks?
(e) If the string connecting the blocks were not massless, but instead had a mass of m, find
(i) the acceleration of Block #1, and
(ii) the difference between the strength of the force that the connecting string exerts on Block #2 and the strength of the
force that the connecting string exerts on Block #1.
6. Newton’s Laws | 1 6 5
Cracking the AP Physics C Exam
3. In the figure shown, assume that the pulley is frictionless and massless.
m1
m2
Solve for the following in terms of given quantities and the acceleration of gravity, g.
(a) If the surface of the inclined plane is frictionless, determine what value(s) of θ will cause the box of mass m1 to
(i) accelerate up the ramp
(ii) slide up the ramp at constant speed
(b) If the coefficient of kinetic friction between the surface of the inclined plane and the box of mass m1 is µ k, derive (but
do not solve) an equation satisfied by the value of θ which will cause the box of mass m1 to slide up the ramp at constant
speed.
4. A sky diver is falling with speed v0 through the air. At that moment (time t = 0), she opens her parachute and experiences the
force of air resistance whose strength is given by the equation F = kv, where k is a proportionality constant and v is her descent
speed. The total mass of the sky diver and equipment is m. Assume that g is constant throughout her descent.
(a) Draw and label all the forces acting on the sky diver after her parachute opens.
(b) Determine the sky diver’s acceleration in terms of m, v, k, and g.
(c) Determine the sky diver’s terminal speed (that is, the eventual constant speed of descent).
(d) Sketch a graph of v as a function of time, starting at t = 0 and going until she lands, being sure to label important values
on the vertical axis.
(e) Derive an expression for her descent speed, v, as a function of time t since opening her parachute in terms of m, k, and g.
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Cracking the AP Physics C Exam
5. An amusement park ride consists of a large cylinder that rotates around its central axis as the passengers stand against the inner
wall of the cylinder. Once the passengers are moving at a certain speed v, the floor on which they were standing is lowered. Each
passenger feels pinned against the wall of the cylinder as it rotates. Let r be the inner radius of the cylinder.
Solve for the following in terms of given quantities and the acceleration of gravity, g.
(a) Draw and label all the forces acting on a passenger of mass m as the cylinder rotates with the floor lowered.
(b) Describe what conditions must hold to keep the passengers from sliding down the wall of the cylinder.
(c) Compare the conditions discussed in part (b) for an adult passenger of mass m and a child passenger of mass m/2.
6. A curved section of a highway has a radius of curvature of r. The coefficient of friction between standard automobile tires and
the surface of the highway is µ s.
(a) Draw and label all the forces acting on a car of mass m traveling along this curved part of the highway.
(b) Compute the maximum speed with which a car of mass m could make it around the turn without skidding in terms of µs ,
r, g, and m.
City engineers are planning on banking this curved section of highway at an angle of θ to the horizontal.
(c) Draw and label all of the forces acting on a car of mass m traveling along this banked turn. Do not include friction.
(d) The engineers want to be sure that a car of mass m traveling at a constant speed v (the posted speed limit) could make it
safely around the banked turn even if the road were covered with ice (that is, essentially frictionless). Compute this bank-
ing angle θ in terms of r, v, g, and m.
6. Newton’s Laws | 1 6 7
