# Monkey and the Hunter Conceptual Explanation

Back in mid-November, I posted to my 180 blog about the classic monkey and hunter demonstration. In that post I referenced a conceptual explanation as to why the hunter should aim directly at the monkey. Andy asked me to share the conceptual explanation and I’m finally taking time to do so.

For many years the best conceptual explanation I could offer was based on that of a student who came up with the following after seeing the demonstration. Imagine there is no gravity. The angle is such that in the time it takes the projectile to move horizontally, it will move the necessary vertical distance to hit the monkey. The effect of adding back gravity just adds the $\frac{1}{2} a t^{2}$ part of the equation which is the same for the monkey and the projectile.

This year, I developed an alternative conceptual explanation. Put yourself in the frame of reference of the monkey. The difference in the vertical component of the velocity between the monkey and the projectile is the same and will remain the same due to the acceleration of gravity. Therefore, the projectile has a constant velocity and, if aimed directly at the monkey, will move in a straight line toward the monkey.

I received a GoPro for Christmas and plan to use it to film this demonstration from the perspective of the monkey.

# The Preconception Eliciting Tennis Ball

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!

# Halloween Physics

There is a tradition at my school of physics and chemistry classes having a day of science-related demos on Halloween (or the closest school day). We share and discuss a wide variety of demonstrations with the students that relate to topics they have already studied, topics they will be studying, or just cool stuff that, for whatever reason, we won’t study.

One of my favorite demonstrations involves a PVC pipe, a ping pong ball, a soda can, and a vacuum pump. The ping pong ball is inserted into the PVC pipe and both ends of the PVC pipe are sealed with mylar (the shiny material of some helium balloons) and PVC couplings. The vacuum pump then evacuates the PVC pipe. Once evacuated as much as possible, a knife tip breaks the seal at one end of the PVC pipe and the ping pong ball is pushed out the other end at an incredible high speed. Last year, we captured the result with a high-speed video camera (1000 fps):

This demo provides a great shared experience to later relate to almost any area of mechanics. I can use it as an example for the work-energy theorem with my regular physics class, fluids with my advanced physics class, or challenge the AP C class to solve for the force on the ping pong ball given the pressure applied to the hemisphere. Plus, we now have a whole collection of decimated soda cans on display!