Hooke’s Law Formal Lab
Theory: Hooke’s Law states “the amount that a spring stretches or compresses is directly proportional to the
magnitude of the applied force. Basically, there is a relationship between how much you pull on a spring and
how far it will stretch. But, you probably could have figured that out on your own. In mathematical terms,
Hooke’s Law looks like this…Fs = kx.
In the equation, F is the force applied to the spring, x is the distance that the spring stretches or compresses from
its resting position in response to the force, and k is the spring constant. The unit for the spring constant is
Newtons per meter (N/m). The spring constant tells us how “strong” or “weak” the spring is. A higher spring
constant tells us that the spring is “strong” and that it will require a greater force to stretch or compress the
spring a specific distance. A “weak” spring, one with a low spring constant, requires a smaller force to stretch
or compress the spring the same distance.
The force may be calculated by realizing that the spring is stretched by the weight of the hanging mass. At
equilibrium, the weight of the hanging mass balances the spring’s restoring force. The force of the spring Fs =
Fg.
Objective: Find the spring constant for two different springs and use this information to determine the mass of
an unknown object.
Procedure:
1. Obtain a Hooke’s Law apparatus and adjust the ruler so that the zero lines up with the pointer of the
empty mass holder (if you cannot do this due to the length of the spring, remember that the
displacement of the spring is just the change in the spring’s position from before and after the mass is
added).
2. Hang a mass on the mass holder. With your eye level to the bottom of the spring, read the new position
of the bottom of the spring. Record the change in position. Note: The units of the ruler are in
centimeters, so you will have to convert. If the spring is very stiff, you may have to change the
recommended starting mass, and be creative about how much additional mass you will add, in
order to measure the stretch of the spring.
3. Repeat step 2 by adding masses to the spring until you have at least five readings.
4. Remove all of your mass and place the unknown mass onto the end of the spring. Record the
displacement of the spring with the unknown mass.
Free Body Diagram and Diagram of the Experimental Setup: Draw a diagram of the experimental set up,
and draw a free body diagram for the mass hanging from the spring. Include any formulas you use along with
the free body diagram in your theory section.
Data: Create a data table for each of the springs tested. Include columns for the mass added in grams, mass in
kilograms, distance stretched in meters, applied force in newtons, and calculated value of the spring constant.
Graph: Create 2 graphs, one for each spring, of applied force vs. displacement. You have the option of
making only one graph and placing both sets of data on the one graph. On the graphs, add a trendline and find
the slope of the trendline. If the equation involved in the graph is F = kx and the equation of a line is y = mx +
b, what is represented by the slope of the graph?
Analysis &Calculations: Analyze the graph, discuss its shape and write down the values of the spring
constant that you find from the graphs. Show one conversion from grams to kilograms, one conversion from
centimeters to meters, one applied force calculation, and two calculations of the unknown mass using the spring
constant values that you have found for each spring. Also do a percent error calculation; the theoretical value
for the unknown mass will be supplied by your teacher.
Conclusion: Write up a conclusion to the experiment. Sum up the results and look for possible sources of
error. Do not just say human error- be specific! And don’t say calculation error- fix it if you made a mistake.