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.
by Stressmaker 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.
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.
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.
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:
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:
[#embed: https://sheet.zoho.com/publish/rhettallain/hammer-calc]
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).
