The world-champion head-butter Angus Macbangus can accelerate himself from rest

Question

The world-champion head-butter Angus Macbangus can accelerate himself from rest to head-butting speed of 8.5m/s. Since the upper body is involved in a properly executed head-butt, the effective mass of the head is 24kg. Label the direction the head moves as (i). Assume linear motion at the moment of impact. If Angus reaches 'butting speed' in 0.5 seconds, what power must his muscles produce? If Angus head-butts an opponent in the face and his head comes to rest in a time of 0.15 seconds, what is the magnitude and direction of the force that the opponent's face experiences?

Explanation / Answer

part a )

P = W/t

W = change in kinetic energy

W = 1/2 * m * v^2 = 1/2 * 24 * (8.5)^2

W = 867 J

P = 867/0.5 = 1734 W

part b )

F*t = change in momentum

F*t = m(vf - vi)

F*t = 24 ( 0 - 8.5)

F*0.15 = -204

F = -1360 N ( -i ) direction

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