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AP® Practice Problems 331

(a) Refine Gwen’s symbolic and graphical representations ∆∆ x (cm) ∆∆ t (ms)

of the relationships among force, spring compression,
and speed to critically evaluate Gwen’s explanation. 2 40.0
(b) Allison has persuaded Gwen that the speed is pro- 4 16.7
portional to the compression length but she can’t 6 10.9
remember how the speed depends on m and k .
Construct the representation using dimensional 8 9.6
k
analysis to confirm that the dependence is m .

To test the prediction, Allison and Gwen deter- (c) Construct from these data a graph that tests the

prediction in part (b).
mined the mass of the cart (m = 0.25kg) and placed it

on the air track. A photogate timer was placed in the (d) Analyze the data to obtain the value of the spring
middle of the air track. A piece of cardboard with a constant in units of N/m.
length of 1 cm was mounted on top of the cart to inter-

rupt the light beam of the photogate. The following (e) Evaluate the evidence provided by the data in terms

data were obtained where ∆x is the spring compres- of both Allison’s model and Gwen’s original model
sion from the equilibrium position and ∆t is the time and evaluate the reliability of the data.

that elapses as the cart breaks the photogate beam.
AP PRACTICE PROBLEMS Prep for the AP ® Exam
®
Multiple-Choice Questions 2. A single force is exerted on an object in the

Directions: The following questions have a single correct x direction. Shown is a graph of that force and the
answer. displacement of the object in that direction. What
amount of work is done for the 30 m shown?
C
(A) 30 J (B) 45 J (C) 50 J (D) 60 J
D D D D D D D D D D B B B B B B B B B B Initial Final
String String
A

v = 0
i
1. A ball is projected up an incline and rolls around a m

track as shown above. At which labeled point is the s
work being done on the ball by the gravitational m v f
force as the ball moves through that point zero?

(A) A (B) B (C) C (D) D 3. An object of mass m hanging from the end of
a light string is initially at rest. It is lowered by
Force 3.0 v .

(N) the string a distance s and reaches a speed f
How much work was done on the object by
the string?
2.0 1
2
(A) mv
2 f
1
2
1.0 (B) − mv
2 f
1
(C) mv 2 f − mgs
0 2
0 10 20 30 1
Displacement (m) (D) − mv 2 f − mgs
2

(Continued)

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

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