|Photo credit: Robert Edwards|
I'm lucky to work at a school with four physics teachers. I'm good at a lot of stuff, but when I need help or ideas, three other experts are available in the other third-floor classrooms.
I knew I wanted to have my students measure the speed of a ball-on-a-string when dropped from various vertical heights. A motion detector can make the measurement, but it's difficult to set the detector at the right height, and even more difficult to train a ninth grader to filter out the meaningful speed from the 50 m/s reading the detector spits out when the mass rises above the detector's range.
My colleague Curtis told me to use a photogate. "That's difficult," I argued. "The ball is nearly as wide as the gate. If they don't set the photogate beam precisely at the center of the ball, they get a skewed reading, because the ball will have a different diameter intersecting the beam. And, incidentally, do you have any boy scout tricks for tying a string to a ball?"
"Nah," he said. "Use a cylindrical mass." Then no matter where the mass hits the photogate beam, it will always travel the same distance through the photogate. Woo-hoo! Solved!
It was a bit tricky to get the labquest programmed properly, but I figured it out -- use "motion" mode for the photogate with a distance equal to the diameter of the cylinder. (That's 2 cm for the cylinder pictured above.)
So, in class, I have students predict: If I double the vertical height from which the mass is dropped, what does that do to the mass's speed at the bottom? Do I double the speed? Quadruple the speed? Increase the speed by less than a factor of 2?
It takes a bit of work to determine that the speed should increase, but not double; good mathematicians see that the speed should be multiplied by the square root of 2.
The picture shows Logi measuring the vertical height from which he's going to drop the cylinder. The beauty of Curtis's setup is, the labquest just SPITS OUT a measurement of speed each time the cylinder goes through the photogate. There's no interpretation or calculation necessary, just a reading of a device. Woo-hoo!
And, boy, is this generally accurate. The students who are careful to measure vertical heights from the bottom of the cylinder consistently find that doubling the height of the drop increases the speed at the bottom... by a factor of about 1.4. And even those who are less careful still find a new speed that's greater than the original speed, but not doubled.