PHYSICS 101 Laboratory
Hooke's Law – II
Series and Parallel Springs
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Introduction:
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In this experiment we are going to investigate a property of "elastic" material which is known as
Hooke's Law.
Equipment needed:
Springs, weights, meter stick, support stand, hanger arm for support stand
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A frequently observed property of solids is the ability of an object to return to an original shape after being
deformed by some applied force simply by removing the force. This property is called elasticity. For example, we
know that when a weight is hung on a spring (which means a force is applied) the spring stretches. If we add more
weight, but not too much, the spring stretches more and when the weights are removed the spring returns to its original
length. If the amount of stretch of the spring is directly proportional to the amount of applied force then the spring is
said to obey Hooke's Law. This law is often stated in terms of the restoring force exerted by the distorted object and
the original change in dimension caused to the object. Thus we can write an expression for the law as
F = –kΔx
(Hooke's Law)
where F is the restoring force, Δx is the change in length of the object and k is called the "spring constant" and is
determined by properties of the "spring." The minus sign comes because the force is the restoring force of the elastic
object, which is always in the opposite direction of the original change in dimension.
I.
First, you are going to find the spring constant for two individual springs. The springs you are using are ordinary
springs such as you could buy from the local hardware store. This notwithstanding, you must treat the springs with
some care. Do not add more weights to the spring than asked for in the experiment. Don't jerk the spring down and
over extend it's length. In other words, treat the springs gently.
A. Attach two springs to a support stand using the special support arm. For each spring, it is best to anchor a
holder, such as a paperclip, directly to the support arm (use the two outer attach points) and attach the spring to
the holder. Attach a 100-gm "weight" to the end of each spring to give the springs some initial "stretch." Use a
meter stick to measure the "height" of a reference point. Take care to select a true reference point, such as the
top of the weight, for each of the spring/weight arrangements. This becomes the "zero" reference point. The
amount of original added weight and resulting stretch are not important, they simply establish the original
equilibrium position. Record the value for the reference heights in Table 1 below. Note that we need to be very
careful with units.
B. Add a 100-gm mass to each of the springs. Note the height of the reference point for each of the springs and
record the appropriate values in Table 1.
C. From the recorded data, determine the remaining values for Table 1. Note that in the table "Force(N)"
denotes the total force while ΔX denotes the total displacement from Start Reference height.
Table 1
Spring - 1
Mass(kg)
Force(N)
Start
Reference
With added
mass
0
height(m)
Spring - 2
ΔX(m)
height(m)
0
ΔX(m)
0
k=
k=
1
PHYSICS 101 Laboratory
Hooke's Law -- II
II.
Now, we are going to find the spring constant for springs combined in different ways. One way is called
"series" where two springs would be hooked together end-to-end to form a single, longer spring. The other way is
called "parallel" where two springs are used side-by-side.
A.
SERIES
1.
Think about two identical springs hooked together end-to-end making one longer spring. This means that
the spring constant of each of the original springs is the same value, k1. Predict, on your own (this means
without discussion with others) what you think the spring constant might be for the combination.
MY PREDICTION (don't forget, you are predicting the spring constant, not the stretch), and WHY!
2.
Now, acting as a group, make the same prediction.
GROUP'S PREDICTION and WHY.
3.
Now, guess what! You will determine from experiment if any of the predictions are correct. Connect your
two springs end to end, attach your "ballast weight," record the reference height and then add a mass of 100-gm to
determine the spring constant k.
4.
Comment on your results. State your comments in light of the following questions. Were your (or group's)
predictions correct? If not, what are the mistakes in reasoning? Can you extrapolate to three springs (or a single
spring three times as long) or to a spring half as long as your original? To two springs with different k values? Do
so in each case.
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PHYSICS 101 Laboratory
B.
Hooke's Law
PARELLEL
1.
Think about two identical springs hooked together side-by-side so as to act as "one" spring. Again, this
means that the spring constant of each of the individual springs is the same value, k1. Predict, on your own (this
means without discussion with others) what you think the spring constant might be for the combination.
MY PREDICTION and WHY (again, don't forget, you are predicting the spring constant, not the stretch).
2.
Now, acting as a group, make the same prediction.
GROUP'S PREDICTION and WHY.
3.
Using the two springs, conduct a parallel spring measurement. Let exercise A3 for the series case guide
you, but in this case use a mass of 400-gm.
4.
Comment on your results. State your comments in light of the following questions. Were your predictions
(or group's) correct? If not, what are the mistakes in reasoning? Can you extrapolate to three identical springs?
Perhaps to two springs but each with different k values? Do so in both cases.
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