PASCO ME-6950 PAScar with Mass - Manual (Page 12)

012-07361B PAScar with Mass
11
Experiment 4: Cart Calibration
(Measuring the Spring Constant)
Pan for holding
masses
15 cm ruler attached
to car
1
Figure 4.1
2 3
1/2 total added mass
Total added mass
Note the final
position of the end
of the plunger.
Spring plunger
v
o
= 2
mv
0
2 = kx
0
2
EQUIPMENT NEEDED:
– PAScar (ME-6950) – 250g mass
– Mass set (SE-8704) – Stopwatch (SE-8702)
– Pan for holding masses
– Balance (SE-8723 or equiv.)
Purpose
The PAScar 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 car’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:
k =
∆F/∆x
v
o
= x
o

Note the initial position
of the plunger.
2
1 1
2
(EQN-1):
(EQN-2):
(EQN-3):
(EQN-4):
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:
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:
which leads to:
It is assumed that the acceleration of the car is constant, so that the initial velocity of the car at the
moment of launch is twice the average velocity of the car over its whole run.
d
t
m
k