Elena, a black belt in tae kwon do, is experienced in breaking boards with her f

Question

Elena, a black belt in tae kwon do, is experienced in breaking boards with her fist. A high-speed video indicates that her forearm is moving with a rotational speed of 43 rad/s when it reaches the board. The board breaks in 0.0040 s and her arm is moving at 21 rad/s just after breaking the board. Her fist is 0.32 m from her elbow joint and the rotational inertia of her forearm is 0.050 kgm2.

Part A

Determine the magnitude of the average force that the board exerts on her fist while breaking the board (equal in magnitude to the force that her fist exerts on the board). Ignore the gravitational force that Earth exerts on her arm and the force that her triceps muscle exerts on her arm during the break.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

|a|= (w2-w1)/ t = (21-43)/0.0040 = 5500 rad/s^2

For F use equation,

Torque = I*alpha = F*R

F= ( I*alpha )/ R = (0.050*5500)/0.32 = 859.4 N = 860.0 N

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