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EXPERIMENT
11
The Spring
Hooke’s Law and Oscillations
Objectives
•
To investigate how a spring behaves when it is stretched under the influence of an
external force.
To verify that this behavior is accurately described by Hooke’s Law.
•
Measure the spring constant, k in two independent ways
Apparatus
A spring, photogate system, and masses will be used.
Theory
Hooke's Law
An ideal spring is remarkable in the sense that it is a system where the generated force is
linearly dependent
on how far it is stretched.
Hooke's law describes this behavior, and we
would like to verify this in lab today.
In order to extend a spring by an amount
Δ
x from its
previous position, one needs a
force
F which is determined by F = k
Δ
x.
Hooke’s Law states
that:
F
S
= k
Δ
x
(1)
Here k is the
spring constant
which is a quality particular to each spring and
Δ
x is the
distance the spring is stretched or compressed.
The force F
S
is a restorative force and its
direction is opposite to the direction of the spring’s displacement
Δ
x.
To verify Hooke’s Law, we must show that the spring force F
S
and the distance the spring is
stretched
Δ
x are proportional to each other (that just means linearly dependant on each
other), and that the constant of proportionality is k.
In our case the external force is provided by attaching a mass m to the end of the spring.
The
mass will of course be acted upon by gravity, so the force exerted downward on the spring
will be F
g
= mg.
See Figure 1.
Consider the forces exerted on the attached mass. The force
of gravity (mg) is pointing downward.
The force exerted by the spring (k
Δ
x) is pulling
upwards. When the mass is attached to the spring, the spring will stretch until it reaches the
point where the two forces are equal but pointing in opposite directions
:
F
s
– F
g
= 0
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or
mg = k
Δ
x
(2)
This point where the forces balance each other out is known as the
equilibrium point
.
The
spring + mass system can stay at the equilibrium point indefinitely as long as no additional
external forces come to be exerted on it. The relationship in (2) allows us to determine the
spring constant k when m, g, and
Δ
x are known or can be measured.
This is one way in
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 Summer '08
 J.T.
 Physics, Force

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