Dot Physics

Maybe this isn’t the best video to analyze, but it sure is funny. I am not sure why it is so funny – maybe you should just watch it first.

I don’t really know why these guys are putting explosive on sledge hammers. Sure it looks fun, but I think I would pass. Anyway, here is the part I was curious about.

i-359dd38de6c91c3bf41e66a3eb583f05-sledgehammer_.jpg

Did the exploding hammer lift him off the ground, or did he jump as a reaction to the explosion. It kind of looks like he was lifted, but I am not sure that is possible. Video analysis to the rescue. (using Tracker Video) So, I assumed the sledge hammer was 1 meter long (if not true, it is close enough to being true). I used that to scale the video. I tried to look at the velocity of the heavy part of the hammer after the explosion, but I could only get two frames of data. That is enough for a speed. Here is the y-position of the hammer with a linear fit.

i-45372eae15870a97dacabea49a55231e-data_tool_1_2.jpg

This gives the hammer a velocity (in the y-direction) of 10 m/s. What about the handle end of the hammer? That is in the video a little longer. Here is a plot of it’s y-motion.

i-c1fb415c826a0d72a1831f6abd3c0144-data_tool_2_1.jpg

This gives a velocity of 7 m/s. So, 7-10 m/s seems to be the speed of the hammer while the guy is holding it. How much energy did it have after the explosion? It would probably going even faster than that, but not too much. I have no idea how fast the hammer was going have he let go, but I can still do some simple calculations.

Did the hammer have enough energy to lift the guy up? If I break this into a before and after case, before the hammer is moving with some speed. After the interaction, the hammer is still moving up, and the guy has increase in gravitational potential energy (and so has the hammer). This would give a conservation of energy equation as:

i-d0c45ceabd7cc4adf703fc5669537b10-energy_hammer_cons.jpg

So, here are my starting values (estimates)

  • Mass of sledge hammer = 5 kg
  • Mass of guy = 65 kg
  • Initial velocity of hammer = 8 m/s
  • Final velocity of hammer = 4 m/s
  • Final height of hammer = 1 m
  • Final height of guy = 0.15 m

Well, that last one was a measurement and I am going to calculate what the estimates give me to compare. Solving the above energy equation for height of the guy:

i-403be797ff445b05d149337d89624df4-h_guy_calc.jpg

Well, with my estimations, I get 11 cm. So, I guess it could lift him up. I am glad because it didn’t really look like he jumped. Plus, it makes the whole video funnier (also that it does not seem like anyone got hurt – that would make it un-funny).

Comments

  1. #1 CCPhysicist
    June 24, 2009

    No, he did not jump. He (like the observer in the left foreground) was crouching in expectation of a large explosion and holding onto the sledge like anyone would when swinging it. It not only lifted him up, it pulled him out of that crouch. As I posted on my blog, the question really is “How high would he have gone if he had not let go of the hammer?”!

    I think your velocity estimate is low because the hammer is interacting with him and gravity, slowing it down, during the time you observed. It could not be due to his own muscles: compare the time it took for him to swing it down (with gravity helping) into that crouch to the time it took to go the other way.

    A sequence of stills from your frame analysis should make that clear. Why not post that? And can anyone with knowledge of plastic explosives estimate how much he taped on that hammer?

  2. #2 CCPhysicist
    June 24, 2009

    Oh, yeah, the handle is longer than a meter. Looks to me like it is at least 4 feet, since it seems like it would reach his shoulder.

  3. #3 Rhett
    June 24, 2009

    Dr Pion, I agree that this analysis could be off. To tell you the truth, I really didn’t try to hard to find a good scale, close was good enough. Actually, I laughed so hard watching this video, I wanted an excuse for posting it.