Today me and my son spent some nice time outdoors. When I was slinging balls for our dog Smyk, he took a few pictures of me. One of the photos is great, the boy has caught the dog-ball just after the release. Thus I had an opportunity to make some interesting calculations.
The camera set the shutter at 1/320 s (I believe it is a very accurate setting). In this time the ball was drawing the light trail on the picture. So only thing I need to calculate the velocity, was the length of the ball relocation in this time. It was very easy to calculate it from the picture.
I precisely measured (mm) the length and width of the trail on the zoomed picture on the screen. Then I was able to calculate the ratio:
length/width = 82/27 = 3.04
Since the width = the ball diameter = 0.068 m, there was no problem to calculate the length of the trail:
length = 3.04 * 0.068 m = 0.21 m
In order to get the length of the ball movement:
s = length - ball diameter = 0.21 m - 0.068 m = 0.142 m
Finally, the dogball velocity is
v = s/shutter speed = 0.0142 m/(1/320 s) =
45.44 m/sv = 164 km/h = 149 foot/second = 102 mphSo, the kinetic energy of the movement is
E = mv^2/2 = 0.04 kg * (45.44 m)^2 =
41 joules = 30 foot pound-force I'm curious, how it could be felt by our heads
Consider, the real velocity could be a bit bigger, because of a possible 'diagonal' camera position relative to the trajectory. Anyway, the result is surprising considering, that it was just easy slinging for fun with the dog, using a big soft and light weighted (ca. 40 g) squealing ball, and the relatively short sling. Even, I don't remember if that shot was a good one.
The next interesting thing on the picture is, that you can see the spiral trails of the color dimples from the ball.
It looks like in this case the ball had the "point-first" fly ??? At my guess, the ball is doing ca. 1/8 (or more) of the full rotation, in the time 1/320 s. It gives:
(1/8)/(1/320) = 320/8 =
40 rotations per second = 2400 r/minute !? Damn! It is faster then usually electrical engines do. Or maybe I'm wrong in the calculations.
Just enough the numbers. For the end, here is the picture of the Smyk among the fresh spring grass, just after a refreshing bathing. He deserved it for helping during the experiment.
Jurek