Hooke’s Law Lab (with Inquiry extension)
Purpose: To understand Hooke’s Law and to determine whether a given elastic
material does or does not obey Hooke’s Law.
Background Information: Most solid bodies, even buildings and bridges and even
the Earth itself, are somewhat elastic. That is, if you push them, they will sway back
and forth. Stop pushing, and the swaying will subside until eventually the object will
come to rest in its equilibrium position. The harder you push (or pull) on the thing,
the greater will be the amplitude of the resulting swing. Playground swings are
excellent examples of this; to get going really high, you need a good hard push to get
there; when you stop pushing/pulling, the swing begins to loose amplitude with
each cycle, until it rests at its equilibrium position. Robert Hooke discovered the
mathematics behind this phenomenon and published it in 1678. The law states,
essentially, that “the force applied is proportional to the resulting displacement” and
Hooke’s law looks like this:
F = -kx
Where F stands for the restoring force (the force that is applied by the elastic
material, against the applied force such as a weight on a spring), k is what’s known
as the spring constant (really stiff springs like shock absorbers have high spring
constants, and delicate watch springs have tiny spring constants), and x is the
amplitude, or the amount of displacement from the equilibrium position.
The role of the negative value is to show that the restoring force exerted by the spring
and the displacement are in opposite directions. That is, if you put a mass on a spring
and pull it down past the equilibrium position, and release it, the spring (which
provides the restoring force) pulls up and the weight moves up. Once the weight
goes past the equilibrium position, the spring becomes compressed, and the
displacement position is now up above the equilibrium point; in response, the
spring pulls down on the weight until the weight stops travelling upward and
moves down toward the equilibrium position. Hence, you can see that the spring is
always forcing the weight towards the equilibrium position. If the weight is
displaced above the equilibrium position, the spring will pull it downward; if the
weight is below the equilibrium position, the spring will pull it upwards.
The astute student will have noticed that Hooke’s law is written in the form of a line
equation (y = mx + b). In this case, restorative force is on the y axis, displacement is
on the x axis, and the slope of the line is the spring constant. There is no y-intercept
in this equation, but there might for the line that appears on your graph, depending
on the data that you graph.
Not all elastic materials are Hooke-type materials, and even those that are will only
obey Hooke’s Law within certain limits. If you pull too hard on a spring, it will
become deformed, the coils will not go back together, and it will no longer obey
Hooke’s Law.
Here’s an overview of what you will be doing and what you need to turn in:
1. Graph a given set of data
2. Answer questions about the graph you generated
3. Conduct your own investigation to answer a research question and write a
lab report.
You will turn in everything together as one paper. Title your lab report “Hooke’s
Law Lab” and be sure to title each section with the step number and name so that I
know what I am looking at.
Step 1: Graph given data
Here is data from an experiment with a spring that does obey Hooke’s Law.
Somebody put different masses on a spring and let the spring extend downward
until the applied weight was equal to the restoring force of the spring and the
weight hung motionless. So, although the spring’s restoring force is not something
that can be directly measured, it can be determined from the mass that is hanging
from the spring; it is equal to the weight that is attached to the spring.
Image courtesy of Wikipedia, http://en.wikipedia.org/wiki/Hooke's_law
Here is the data generated in the experiment:
Weight vs Stretch Distance in a Spring
Stretch Distance (m)
Weight applied to spring(N)
0.0
0.0
0.30
1.9
0.60
3.7
0.90
6.3
1.2
7.8
Data courtesy of Physics Principles and Problems, McGraw Hill, 2013
 Graph the data so that your line equation correctly matches the form
showed in Hooke’s Law Equation. Draw in a best-fit line to match the data.
Step 2: Analyze the Graph
Below your graph, answer the following questions:
1. Write the line equation for this specific graph. Do not write “y = mx + b,”
that’s a general equation. Instead, fill in the generic values given in the
equation with the specific things those values stand for in this graph. Instead
of “y,” write what is represented on the y axis. Instead of “x,” write what is
2.
3.
4.
5.
represented on the x axis. Instead of “m,” write what the slope represents. In
this case, the slope represents something about the nature of the spring.
What is the spring constant of this spring? To find the answer: Compare
the line equation that you wrote above to the equation for Hooke’s law to
determine what aspect of the graph you need to determine.
The y-intercept of your graph should be zero. What does a zero yintercept mean in terms of the experiment, why does this make sense?
As you can see, both force and distance are present on this graph. Remember
that Fd = Work. In this case, gravity does work to pull the mass down, and
that energy is stored in the spring as potential energy. You can determine the
amount of elastic potential energy stored in the spring by finding the area
under the curve (which in this case is a straight line, if you drew your graph
correctly). How much potential energy is stored in the spring when the
weight applied = 5 N?
Rewrite the geometric equation you used to solve #4 to reflect the
physics of the potential energy stored in a spring. Do this the same way
that you rewrote the generic line equation to fit this particular graph. Instead
of writing “area of a triangle,” for example, you will write “elastic potential
energy,” etc.
Step 3: Investigate
In this portion of the activity, I will give you an elastic material and you will
determine whether or not it obeys Hooke’s Law.
In your lab report, be sure to include:
 your research question
 a data table
 a graph
 answer the research question (please justify/explain your answer, don’t just
say “yes it obeys Hooke’s Law” or “no it doesn’t obey Hooke’s Law.”)