Name
Period
Date
Energy: Worksheet 9
1. AP B 2009
In an experiment, students are to calculate the spring constant k of a vertical spring
in a small jumping toy that initially rests on a table. When the spring in the toy is
compressed a distance x from its uncompressed length L0 and the toy is released,
the top of the toy rises to a maximum height h above the point of maximum
compression. The students repeat the experiment several times, measuring h with
objects of various masses taped to the top of the toy so that the combined mass of
the toy and added objects is m. The bottom of the toy and the spring each have
negligible mass compared to the top of the toy and the objects taped to it.
a. Derive an expression for the height h in terms of m, x, k, and fundamental
constants.
Energy: Worksheet 9
page 2
With the spring compressed a distance x = 0.020 m in each trial, the students
obtained the following data for different values of m.
m (kg)
0.020
0.030
0.040
0.050
0.060
h (m)
0.49
0.34
0.28
0.19
0.18
b.
i.
What quantities should be graphed so that the slope of a best-fit straight line
through the data points can be used to calculate the spring constant k?
ii. Fill in one or both of the blank columns in the table with calculated values of
your quantities, including units.
c. On the axes below, plot your data and draw a best-fit straight line. Label the axes
and indicate the scale.
Energy: Worksheet 9
page 3
d. Using your best-fit line, calculate the numerical value of the spring constant.
e. Describe a procedure for measuring the height h in the experiment, given that the
toy is only momentarily at that maximum height.
2. 2002 AP C
An object of mass 0.5 kg experiences a force that is associated with the potential
4 .0
energy function U  x  
, where U is in Joules and x is in meters.
2 .0  x
a. On the axis below, sketch the graph of U x  versus x.
U J 
3.0
2.0
1.0
0
xm
1
2
3
4
5
Energy: Worksheet 9
page 4
b. Determine the force associated with the potential energy function given above.
c. Suppose that the object is released from rest at the origin. Determine the speed
of the particle at x  2 m .
In the laboratory, you are given a glider of mass 0.5 kg on an air track. The glider is
acted upon by the force determined in part (b). Your goal is to determine the validity
of your theoretical calculation in part (c).
d. From the list below, select the additional equipment you will need from the
laboratory to do your experiment by checking the line next to each item. If you
need more than one of an item, place the number you need on the line.
Meterstick
Stopwatch
Photogate Timer
String
Balance
Wood Block
Set of objects of different masses
Spring
e. Briefly outline the procedure you will use, being explicit about what
measurements you need to make in order to determine the speed. You may
include a labeled diagram of your setup if it will clarify your procedure.
Energy: Worksheet 9
page 5
2003 AP C (modified)
The 100 kg box shown above is being pulled with a rope along the x-axis by a
student. The box slides across a rough surface with a coefficient of kinetic friction
between the box and the surface of 0.40 and its position x varies with time t
according to the equation x  0.5t 3  2t , where x is in meters and t is in seconds.
Use g  10 N .
kg
a. Determine the speed of the box at time t  0 .
b. Determine the following as functions of time t.
i. The kinetic energy of the box.
ii. The net force acting on the box.
iii. The force of tension in the rope. Draw a force diagram of the box to start.
Energy: Worksheet 9
page 6
iv. The power output of the student.
c. Determine the change in the kinetic energy over the interval t  0 to t  2 s .
d. Indicate below whether the work done on the system by the student in the
interval t  0 to t  2 s would be greater than, less than, or equal to the answer in
part (c).
Greater than
Less than
Equal to
Justify your answer.
e. Calculate the work done by the student in the interval t  0 to t  2 s .