After investigating the motion of a falling object, I ask my students to draw position vs. time, velocity vs. time, and acceleration vs. time graphs of a ball that is thrown upward and then caught at the same height. As I walk around the room, most students have the position vs. time graph correct but struggle with the velocity vs. time and the acceleration vs. time graphs. For those students that struggle, the most common sketch of the velocity vs. time graph is a ‘V’ rather than a straight line with a negative slope. They then struggle to reconcile an acceleration vs. time graph with this V-shaped velocity vs. time graph.
I then model how I reason through these types of conceptual problems. I hold the tennis ball in my hand and ask, “Immediately after I release the ball, in which direction is it moving?” (They confidently say “up.”) I ask, “Immediately after I release the ball, is it moving fast or slow?” (They confidently say “fast.”) I then encourage them to plot that point on their velocity vs. time graph. I then ask while climbing on top of a lab stool, “As the ball travels upwards, how does its velocity change?” (They confidently say “it slows.”) While holding the ball near the ceiling, I ask, “When the ball is at its peak, what is its velocity?” (They confidently say “zero!”)
I now expose their preconception by immediately asking, “What is its acceleration?” (The answers are split between “9.8 m/s/s” and “zero!” depending on the class) I keep the ball near the ceiling and ask one of the students who enthusiastically answered “zero!”, “If its acceleration is zero and its velocity is zero, what would happen to the ball?” After some thought, the student realizes that the ball wouldn’t fall. I then release the ball and it sticks to the ceiling.
This demonstration appears to be sufficiently memorable due to its humor or unexpected outcome, that students can replace their preconception about the acceleration of an object at its peak. After some laughs, a reference to all the balls that are not suspended in midair over the tennis courts, and an xkcd comic, I continue demonstrating how I reason through the creation of velocity vs. time graphs. I ask the final part, “When the ball is about to be caught, in which direction is it moving?” and “Is it moving fast or slow?” I encourage them to plot this final point and then they have replaced the V-shaped graph with the proper velocity vs. time graph. The slope of their corrected velocity vs. time graph confirms that the acceleration of the ball must remain constant. The tennis ball spends the rest of the class period stuck to the blackboard.
We have a group of Physics teachers that meet at an area school monthly and share ideas. I learned this demo from a great Physics teacher at one of these meetings. He has practiced enough where he can throw the tennis ball and have it stick. He showed us how to modify a tennis ball:
Materials: Neodymium magnets, tennis ball, utility knife, hot glue gun.
Slice the tennis ball, squirt in a bunch of hot glue, and stick in the magnet.
Seal the slit in the tennis ball and let harden.
Stick the tennis ball on the ceiling!
I have a problem with a detail in this demonstration. A ball that is thrown into the air and then is allowed to fall back on its own power does indeed have gravitational acceleration the entire time of flight. However, if the ball is caught at any time, this is no longer the case. At the point at which the ball is caught, it does actually have no acceleration, because the forces acting on it are balanced (there is no net force). See F=ma.
The students who said that when the ball is caught and held at the apex, it has zero acceleration: they were right. The ball, in this case, will have 9.81 m/s/s acceleration when in motion, but not if it is stationary (when it is being held). That would also explain the students’ responses, increasing in confidence that the answer is zero acceleration the longer you hold the ball near the ceiling.
I hope that students appreciate that my holding of the tennis ball after tossing it up several times is a “stop motion effect” to aid in our discussion. However, perhaps they do not.
For next year, I may need to practice my toss to get the height just right without having to hold the ball!