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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.