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LAB 3: Work and Energy
INTRODUCTION:
In this lab, we will study the relationship between potential energy, kinetic
energy, and work. This lab has three parts. In each part, we will find the work done on an
object, by measuring how force and position vary over time. In part one, we will lift an
object straight up into the air at a constant speed. In part two, we will stretch a spring. In
part three, we will push a cart on a track in order to make it accelerate. These three mini
experiments will show us how work is related to energy.
THEORY:
Our experiment is based on the relationship between energy and work. Work is
measure of energy transfer. Work is found by the equation W = F
•
∆
d, where work is the
dot product of force and distance. There are two main kinds of energy used in this
experiment: kinetic and potential energy. Kinetic energy equals 1/2mv
2
and potential
energy equals mg
∆
h. These equations for energy come from E = mc
2
in some way. The
workenergy theorem states that W =
∆
PE +
∆
KE.
From this general equation for work and energy, we can find the work done by
gravity or a spring. Wg = Fg*
∆
d = mg
∆
d. This equation is identical to the equation for
gravitational potential energy: Ug = mg
∆
h. By their equations, gravitational potential
energy equals the work done by gravity.
For springs, Hooke’s Law says that F = k
∆
x, where k is the spring constant and
∆
x is the distance the string is compressed. Hooke’s Law is only valid for when force is
constant, however. From this equation, we can find the value of the spring constant. Also,
we can use this equation to find the equation for the work done by a spring. Work is the
area under the force curve; work is the integral of force. The antiderivative of Hooke’s
law gives Ws = ½ kx
2
. This is equivalent to elastic potential energy, because it measures
the amount of potential energy stored in the spring.
HYPOTHESIS:
I think that in part 1, for an object being lifted at a constant speed, force will be
constant. In part 2, a spring will have force that varies over time. In part 3, force will be
constant for something that has an initial velocity.
PROCEDURE:
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 Spring '06
 RogerTobin
 Energy, Force, Kinetic Energy, Potential Energy, Work

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