The ping pong ball cannon is one of the demos that we perform for our Halloween Demo Day. As always, the question arose of just how fast the ping pong ball is traveling. Students began asking what else the ping pong ball could shoot through. When I shared that we were firing our ping pong ball cannon on Twitter, I received this reply:
This sounded like a challenge for Physics Club. I also wanted to film the ping pong ball with the high speed camera again in order to try and determine the velocity of the ping pong ball. While we were at it, we decided to have some fun:
The raw video footage was filmed at 1000 fps. The camera films the carnage indirectly via a mirror in order to be protected from the debris.
Here is the video used to determine the velocity of the ping pong ball. The ping pong ball is only visible for five frames and is pretty blurry, but it works. (Although our technology specialist commented that we really need a 10,000 fps camera; I’m keeping my fingers crossed!)
Here’s the graph of the ping pong ball’s horizontal position vs. time with the velocity calculated:
Based on the video analysis, the ping pong ball is traveling at 167.2 m/s or 374 mph.
I’ve used the ping pong ball cannon as a sample problem when studying the work-energy theorem:
Calculate the velocity of a 2.3 g ping pong ball as it leaves a 1.5â€ diameter air cannon that is 2 m long. Assume that we completely evacuate the air cannon and the force remains constant as the ball is expelled.
F = P A = (14.7 psi)(Ï€)(.75 in)2(4.45 N/lb) = 116 N W = F d = (116 N)(2 m) = 231 J KE = 1/2 m v2 = 1/2 (.0023 kg) v2 = 231 J v = 448 m/s = 1003 mph
So, in reality the ping pong ball is traveling much slower than the theoretical maximum value. I expect this is due to the limitations of our vacuum pump. While the ping pong ball does experience air resistance once it leaves the pipe, I was surprised how far it appeared to travel before slowing noticeably (which is reinforced by the video analysis).
Oh, and when we fired the ping pong ball into three empty soda cans, it passed through the first two cans and embedded a fragment of itself through the wall of the third!