While exercising in a fitness center, a man lies face down on a bench and lifts

Question

While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900 kg m^2, the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. How much work is done if the leg rotates through an angle of 20.0 degree with a constant force exerted by the muscle?

Explanation / Answer

net torque = 1500N * 0.03m - 10kg * 9.8m/s² * 0.28m
= 17.56 N·m

total I = 0.9kg·m² + 10kg*(0.28m)² = 1.684 kg·m²

= I
17.56 N·m = 1.684kg·m² *
= 10.43 rad/s²

EDIT: To find the work done, use the rotational equivalent of F*d:
work = * = 17.56N·m * /9 = 6.12 J

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