The net torque causes angular acceleration (Newton II), so we need to calculate

Question

The net torque causes angular acceleration (Newton II), so we need to calculate the net torque and set it equal to I. The force from the psoas major muscle contributes to the net torque, so we will be able to work it out.

Draw a free body diagram of the (leg+foot). There are three forces acting on it: one caused by gravity, one is the pull of the psoas major muscle (at 10 degrees to the leg) and one is the push of the hip socket against the ball joint at the top of the leg. The axis of rotation is the hip: write out an expression for the torque exerted by each of the three forces about that axis. Substitute into the rotational analog of Newton II and calculate the force exerted by the psoas major muscle. Enter your answer to 2 s.f. and check that the answer works out into newtons (N).
Is this a big force or a small force? How do you know, what can you compare it against?

Explanation / Answer

the following is the FBD of the leg

now, let weight of the leg be 15 kg ( average leg mass for an average adult)
then from force balance
Fsin(10) = mgcos(60)
Fcos(10) = N + mgsin(60)

also, length of leg = 1.5 m
distance of the point where the muscle eaatches with the leg = 0.3 m
hence
from torque balance
Fsin(10)*0.3 = mgcos(60)*1.5/2
F = 1059.253 N apx

weight of person of mass 95 kg = 931.95 N

hence the ofrce of the muscle is slightly greater than the weight of the person

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