2009 AP B Free Response #1 Lab
Use Monster Pop-ups from Oriental Trading Company and clay. The height reached by the toy
can be estimated visually but a video makes it easier and more accurate.
1. 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.
Ei  E f
UE  Ug
1 2
kx  mgh
2
kx 2
h
2mg
2009 AP B Free Response #1 Lab
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)
h (m)
0.006
0.695
0.0085
0.535
0.0114
0.435
0.0147
0.295
0.0182
0.255
1/m (1/kg)
h (m)
166.7 
0.695
117.6
0.535
87.7
0.435
68.0
0.295
54.9
0.255
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 ?
kx2 kx 2 1
kx 2 kx 2 1
h


or m 


2mg 2g m
2gh 2g h
Since y = mx + b, Graph h Vs 1/m or m Vs 1/h
ii. Fill in one or both of the blank columns in the table
with calculated values of your quantities, including
units.

2009 AP B Free Response #1 Lab
(d) Using your best-fit line,
(c) On the axes below, plot your data and draw a best-fit straight calculate the numerical value
line. Label the axes and indicate the scale.
of the spring constant.
kx 2 1
h

2g m
kx 2
slope 
2g
2g(slope)
k
x2
2  9.8  0.004
k
0.02 2
k  196 N /m
(e) Describe a procedure for measuring the height h in the experiment, given that the toy is
only momentarily at that maximum height. (place meter stick behind it and notice initial and
final heights, h = hf – hi , a video helps but isn’t necessary)