Hearted Youtube comments on The Slow Mo Guys (@theslowmoguys) channel.
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I'm curious as to the amount of energy transferred to his head in the second shot. Did you guys happen to weigh the ball when it had the water, or could you tell me what % of the ball was filled?
From how it was floating on the water it looked to be 1/2 or maybe 5/8 filled, but that could be misleading. Air compresses with increasing pressure, whereas the liquid water doesn't really compress (noticeably, anyway). This means that the buoyancy of the ball depends on the pressure within, a variable that we don't know. So I'm going to start with
Assumptions: The ball is a size 5 (22.5 cm diameter, 425 g empty), and filled 5/8 full with water (3/8 air) by volume, at a total pressure of 13 PSI (0.885 atm). Also, going from Gav's comment; ''it's like bloody 30 degrees out here, 35 degrees'', we'll say 30 C.
The volume inside the ball = 5964 cm^3
Volume_water = (5/8)*5964 = 3727 cm^3
Volume_air = (3/8)*5964 = 2237 cm^3
So the total mass of the ball is
M_air + M_water + M_ball = M_total
2237cm^3*(0.001225g/cm^3) + 3727cm^3*(1g/cm^3) + 425g = M_total
M_total = 4155 g or ~4.16 kg
I downloaded the video and went through frame by frame to track the movement of the ball, and for the second throw, it seemed to be traveling at about 5.1 meters per second. You can also notice that after hitting Dan's head, the ball proceeds to fall nearly straight down, meaning all the kinetic energy of the ball was transferred to Dan's body.
So, total kinetic energy = KE_total = (1/2)mv^2
=(1/2)(4.16kg)(5.1 m/s)^2 = 54 kgm^2/s^2 or 54 Joules of energy!
Let me know if anyone has any other insights, or if I made mistakes/assumptions that should be corrected.
=) that was fun.
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