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

ID: 1369488 • Letter: W

Question

While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contracting the muscles in the back of the upper leg. Find the magnitude of the angular acceleration produced given the mass lifted is 10.5 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900 kg·m2, the muscle force is 1490 N, and its effective perpendicular lever arm is 3.40 cm.

How much work is done if the leg rotates through an angle of 25.0° with a constant force exerted by the muscle?

Explanation / Answer


net torque = I*alfa


F*l1 + m*g*l2 = I*alfa


1490*0.034 + 10.5*9.8*0.28 = 0.9*alfa

alfa = 88.3 rad/s^2


(b)

from eqution of rotatory motion


wf^2 - wi^2 = 2*alfa*theta


theta = 25 degrees = 25*(pi/180) = 0.44 rad

Work = change in KE = 0.5*I(wf^2 wi^2)

wi = initial speed = 0

W = 0.5*I*wf^2 = 0.5*0.9*2*88.3*0.44


w = 35 J