Gas station without pumps

2012 February 5

Gravitational potential energy

Filed under: home school — gasstationwithoutpumps @ 11:55
Tags: ,

We tried doing a lab on gravitational potential energy yesterday, but it did not go very well.

The idea of the lab was simple: roll a cart down a ramp from a measured height, then determine its velocity at the bottom of the ramp.  Theoretical computations that we did indicated that we should have v^2 = 2 g h, where v is the speed after dropping a height of h.

The big problem was determining the speed at the bottom.  I had set up a Maxbotix ultrasonic rangefinder connected to an Arduino, but we could not get reliable, repeatable measurements from it. I’ve experimented with ultrasonic rangefinders before (both the Maxbotix and the Ping))) sensors), and found that they work ok for static things like walls (as long as you don’t mind a lot of noise in the distance measurement), but seem to be pretty useless for watching moving objects. We tried three different carts: an RC truck that I picked up for 60 cents at a thrift store, a $5 Disney Princess skateboard from the same thrift store, and the skateboard with a concrete block on it to increase the mass and make a sharper echo for the rangefinders.

After giving up on the ultrasonic rangefinders, we discussed two other approaches: getting out the video camera and using Tracker to determine velocity or just measuring the time the cart took to run a fixed distance using a stopwatch.  Neither of the students was enthusiastic about using Tracker, though I think we could have gotten decent measurements (with some trouble) that way, so we ended up with the other approach.

We set up a piece of plywood on the porch steps and measured the distance from the end of the ramp to a line on the sidewalk.  We rolled a skateboard with a brick on it down the ramp and timed how long it took from the end of the ramp to the finish line.  The data were pretty noisy (stop watches are not great for short times), and the friction was high (the skateboard slowed noticeably from the ramp to the finish line), so the results can’t be expected to follow theory very well. We measured height and distance in cm:

height  distance        time
N       N       N
30      242     1.56
30      242     1.69
30      242     1.55
30      242     1.69

48      242     1.18
48      242     1.25
48      242     1.24
48      242     1.19
48      242     1.05
48      242     1.13

I plotted the measured velocity and compared it to the theory:plot for gravitational energy experiment

Although this experiment was a bit of a failure at demonstrating conversion of potential to kinetic energy, I think it could be rescued with two things: a good way to measure velocity easily and a lower friction cart (preferably a smaller one). A “hot wheels” track might be good—especially since the ramp shape could be easily varied, but the thrift store did not have any.

The problem of velocity measurement remains. The ultrasonic rangefinder has twice now been too unreliable to be useful, and using the video camera and extracting the data from the video is too slow and off-line (neither of the students has followed through on post-lab analysis for any of the labs where we collected the data by video).

An optical timing trap might be a good way to go, though I’d need to set up something larger than the 1cm gaps of the photointerrupter I used in the pendulum lab.  I’ll need to get a couple of photocells, modulate a light beam, and make filters to detect the modulation.  That seems like a lot of trouble—maybe I could hack a couple of the commercial light-beam sensors used for things like automatic garage doors and gates.

6 Comments »

  1. If you are only demonstrating physics, I’d suggest a solenoid based gate at the top, with a simple switch at the bottom. If you don’t mind things coming to a dead stop at the end, you can use the kinetic energy to close s switch or even push a paperclip to close a circuit. I haven’t played with interrupt driven arduino (http://arduino.cc/en/Reference/AttachInterrupt) setups yet, but I would imagine it would give you the consistency you want.

    Comment by Matthew Tippett — 2012 February 5 @ 14:55 | Reply

    • I wasn’t timing from the top of the ramp to the bottom, but trying to measure velocity at the bottom.
      A pair of switches could work (if I could hit them consistently).

      I don’t need to be interrupt driven on the Arduino to get good timing. One of the best ways to measure time on the Arduino is with pulseIn, and for that all I’d need externally is an SR latch set and reset by the pair of switches.

      Comment by gasstationwithoutpumps — 2012 February 5 @ 17:23 | Reply

  2. This might be a gross assumption, but if you assume that the skateboard decelerates constantly, then could you measure the distance it travels beyond the bottom of the ramp and the amount of time it takes. Then v=2d/t. This would reduce the error in the time measurements — but of course that wouldn’t matter if the assumption is incorrect.

    Comment by Ron G. — 2012 February 5 @ 19:27 | Reply

    • I was thinking of using a uniform deceleration model, but the sidewalk was not uniform enough for long enough to justify that. (Most of the time the skateboard ran into the grass before stopping.)

      So far, Matthew Tippett’s idea of using a pair of switches a known distance apart seems like the simplest solution. I might try that for next week. We’re going to want to try potential energy of springs also, so it would be good to have a way to measure speeds for that also.

      Comment by gasstationwithoutpumps — 2012 February 5 @ 22:10 | Reply

  3. I don’t know how your range finder works, but we have some similar sensors that go with graphing calculators, and I was able to get pretty good readings from them for a truck-down-a-ramp type problem by taping a cardboard box to the truck (to make the object it’s supposed to be sensing big enough to consistently get a reading from the object I wanted, rather than from some other random thing in the room).

    Comment by LSquared — 2012 February 8 @ 10:13 | Reply

    • Both the maxbotix and the Ping))) sensor work essentially the same as other ultrasonic rangefinders: they send out an ultrasonic pulse then listen for the echo. For both, I’m using the pulse-width output (the Maxbotix has other options), which turns the output on when the ultrasonic pulse is sent and off when the echo is heard. The problem is that I get very variable readings—even when using a large, hard target like a concrete block. The sensors seem ok for walls, but not very good for smaller targets. There may be ultrasonic rangefinders that are better designed for smaller targets, or that provide more consistent detection of the echo.

      Comment by gasstationwithoutpumps — 2012 February 8 @ 10:32 | Reply


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