Sunday, July 24, 2022

Is a tape measure a constant force spring?

I recently came across a video of tape measures "racing" along a board of wood as they retract. Who doesn't love extending the tape as far as you can and recklessly letting it fly in? It obviously accelerates dramatically. Like any physics-minded person I got to wondering if the force is constant. How might we assess?

I'm home for the summer, a summer I desperately needed, and away from some of my usual tools. No probeware. No students to help. First I put a small bucket with a handle on a food scale from our kitchen. I extended the tape measure and used it to pull up on the scale. The force was somewhat constant, but not as steady as I would like. A force probe would have been handy to average many data points and see the force graphically.

Perhaps it would be simpler to measure acceleration, rather than measuring force directly. We could replicate the original video. But what about friction? I've also noticed that tape measures sometimes stick when used in this position. What if we pulled a cart of known mass and analyzed the video? The toy cars at my disposal were all too light—or had too much friction—to provide a motion that was slow enough and consistent enough to satisfyingly measure with the tools on hand.

But there it was staring me in the face: the air hockey table. I put the tape measure on its side, so that the weight of the extended tape doesn't cause it to rub as much against the tape (tape retracts more smoothly). Lego base plate floats beautifully on table. A few Lego bricks are placed on one end of the plate to hold the hook of the tape measure during retraction.