Finding a spring constant in five seconds

In my general physics section, we’re studying springs: force of a spring, energy of a spring, and the mass-on-a-spring as an example of simple harmonic motion. Laboratory exercises with springs are useful and fun, especially because it’s easy to get good, reliable data. Before I introduced springs formally in class, I assigned a lab exercise in which they determined the spring constant of a spring. The experiment I assigned is detailed here via collegeboard.com.

Today we began a different experiment involving the spring in simple harmonic motion. Thing is, in order to use the equation

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each lab group has to know the spring constant of their spring. Usually they know k because they use the same spring from the first experiment. But, I forgot to have them label their springs for later use. I was too caught up in the physics tournament and lab cleanup, I guess.

I asked the students to make a “quick and dirty” measurement of k just using a few weights and a measurement of how far those weights extended the spring. But I don’t yet trust my general students to do quick and accurate lab work. Estimates of k were varying by 40% within the same lab group on the same spring! What to do?

Fortunately, I had the force probe and motion detector hooked up from my in-class demonstration of the force of a spring. The setup is in the picture to the right, though I admit the picture isn't so clear. Some mass hangs from the spring, which is attached to the force probe. The motion detector sits on the table beneath the mass. The mass is allowed to vibrate, and logger pro takes force vs. distance data.

It takes only about 5 seconds to acquire a graph like the one you see in the screen shot. Press the “slope” button at the top of the screen, and you get the slope of the force vs. displacement graph – voila, the spring constant!

I’ll leave it as an exercise to the reader why the graph has a negative slope. Feel free to post a comment with the answer.