PASCO ME-9430 Dynamics Cart with Mass - Manual (Page 15)

012-04840E Dynamics Cart
11
®
Experiment 4: Cart Calibration
(Measuring the Spring Constant)
Pan for holding masses
Note the initial position
of the plunger.
15 cm ruler attached to
cart
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
d
t
v
o
= 2 (EQN-4)
mv
0
2 = kx
0
2 (EQN-2)
2
1
EQUIPMENT NEEDED:
– Dynamics Cart (ME-9430) – 500 g mass
– Mass set (SE-8704) – Stopwatch (SE-8702)
– Pan for holding masses – 15 cm/6 in ruler (SE-8730)
– Balance (SE-8723 or equiv.)
Purpose
The Dynamics Cart has a spring plunger, which can be used to produce relatively elastic
collisions and provide a reproducible launch velocity.
Theory
For this and following experiments, you will 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 vs. x is plotted on graph paper,
the spring constant is given by the slope of the graph as:
k =
∆F/∆x (EQN-1)
Once k is known, you can 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 checked experimentally by measuring the total rolling distance
d on a horizontal surface and the corresponding time t for given launch conditions. This leads to:
m
k
v
o
= x
o

(EQN-3)
1
2
(Here it is assumed that the acceleration of the 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.