Hookes’Law for Springs
Equipment: Springs, graph paper, and various masses
ABSTRACT: The purpose of this activity is to show that the distortion produced in an elastic
body (a spring in this case) is proportional to the distorting force which acts to produce that
distortion; as long as the elastic limit is not exceeded. That is - the distance the spring stretches
depends on the amount of weight we add; the more weight added, the more stretch produced. As
weight (a mass in gravity) is added to the spring, pulling it down; the spring will stretch more
and more. Therefore, we say that the stress applied is related to the strain produced. In this way
the elasticity of the spring can be measured as the spring constant for that spring. By graphing
the elongation (strain effect produced in the spring) versus the weight of the mass in gravity
producing it (the stress force) we will reveal Hooke’s Law of Springs, a direct relationship
between stretch and strain which describes the operation of springs and spring scales.
Procedure: Hang the spring from a “stand”. Use a ruler to measure it’s length before you add
any weights. Do not shake the table during measurements. Each team member should assist in
the gathering of data.
PLEASE DO NOT EXCEED THE ELASTIC LIMIT OF THE SPRING.
Using a variety of weights provided carefully load and measure the elongation produced for your
spring. Record all the data in the table provided. Take as many measurements as possible. For the
mass, first convert grams into kilograms (how?) and then determine the weight using weight =
mg (with g = 9.8m/s2). Label the weight in NEWTONS and record it in the data table. For the
elongation, convert the length in centimeters into meters. Record this in the data table as well.
Analyze the Data: Make a graph of your measurements by plotting the elongation (length
stretched) versus the weight. Lay out the elongation axis with respect to the range of the results.
Do the same for the weight axis. Ignore any points clearly in error. Draw a “best-fit” straight line
thru the points in that region of the graph that seems to show elongation as a direct function of
the weight. The spring constant K is the slope of this straight line (the force or weight divided by
the elongation). Determine the slope (the spring constant) for each interval of the useful data.
Record this in the data table as well. Take the average of the determined slopes (the spring
constants) and include this in the lab report. Determine the slope of the best-fit line as well.
Show these calculations in your lab report.
The slope of a line can be determined by locating any two points on that line and determining the
difference of the two terms in the vertical divided by the difference of the two terms in the
horizontal. This can also be done with any two points on the best-fit line, that is, the rise divided
by the run.
QUESTIONS:
1. What spring constant does your data suggest? Report the results from the slope of the graph
as well as the average of the slopes (spring constants) as calculated from the data. State your
spring constant for the spring in Newton/meter. Describe the meaning of this measured
number. Explain how this represents elasticity. How does the spring constant illustrate this?
2. We interpolate when we draw a best-fit line. We measure data and plot points but represent
this relationship as a line. Interpret the meaning of the best-fit line in this case. Write an
equation that expresses the observed behavior. When we draw a line past the data points
measured we call that extrapolation. Why is this not advised in this case? Can we predict how
this spring will respond beyond the data actually measured? Explain why not (in light of the
elastic limit)
3. The cables of a suspension bridge are elastic. Explain why so. Give reasons why the bridge
must be elastic. What is the elastic limit?
What reason is there for us to avoid this elastic limit?
4. Hooke's law is a direct relationship. Explain what this means.
Mass (grams) Mass (kg) Weight (N) D x (cm) D x (m)
