User's Manual
®
Model No. ME-9452 Experiment 9: Conservation of Energy
29
Experiment 9: Conservation of Energy
Purpose
In this experiment, you will determine the spring constant of a compression spring
and use the spring to launch a cart up an incline. You will compare the potential
energy initially stored in the spring to the maximum gravitational potential energy
achieved by the cart.
Theory
The spring constant of a spring is
(eq. 1)
where F
x
is the force applied to the spring and x is the distance by with it is com-
pressed.
The potential energy stored in a spring is
(eq. 2)
The change in gravitational potential energy of a cart moving up an inclined track is
(eq. 3)
where m is the mass of the cart, g = 9.8 m/s
2
, s is the distance traveled along the
track (in the uphill direction), and is the track’s angle of incline.
Required Equipment from Dynamics System
Track with Feet and End Stops
Cart
Pivot Clamp
Spring Cart Launcher (with a spring and release pin)
Super Pulley with Clamp
Other Required Equipment Suggested Model Number
Base and support rod ME-9355
Mass hanger and mass set ME-9348
Graph paper
String (40 cm)
k
F
x
x
------
=
Spring constant
U
spring
1
2
---
kx
2
=
Potential energy stored in
a spring
U
gravity
mgs sin=
Potential energy of a cart
on an inclined track