Experiments
Plunger Cart
012-14781A
13
Experiment 4: Cart Calibration (Measuring the Spring Constant)
Purpose
The Plunger Cart has a spring plunger, which can be used for producing relatively elastic collisions
and providing a reproducible launch velocity.
Theory
For this and the following experiments, it will be necessary to find the spring constant k of the cart’s
spring plunger. As compressional forces F are applied to the spring, the spring will compress a
distance x, which is measured with respect to its uncompressed equilibrium position. If F is plotted
versus x on graph paper, the spring constant is given by the slope of the graph as:
Once k is known, it is possible to predict the launch velocity v
o
by using conservation of energy,
since the elastic potential energy stored in the spring is converted into kinetic energy at the time of
launch. The launch velocity can be found from:
which leads to:
This predicted launch velocity can be experimentally checked by measuring the total rolling distance
d on a horizontal surface and the corresponding time t for given launch conditions. This leads to:
It is assumed that the acceleration of the Plunger Cart is constant, so that the initial velocity of the
cart at the moment of launch is twice the average velocity of the cart over its whole run.
Equipment Needed
Plunger Cart
Stopwatch
Mass Set
Balance
Pan for holding masses
Metric Ruler
Metric Measuring Tape
F
k
x
Eqn. 1
2
2
0
0
1
1
mv
kx
2
2
Eqn. 2
Eqn. 3
0
0
k
v
x
m
0
d
v
2
t
Eqn. 4