Bio mechanic force/moment problem sets

[acdree]

Homework Statement

Hi everyone, I have 2 questions that I think are relatively easy but are frustrating in that I just can't seem to get an answer

1st -- If a lateral-to-medial load is applied to the foot, a counteracting moment is produced at the knee joint in a lateral-medial plane, which stretches the lateral collateral ligament and
the cruciate ligaments. Estimate the moment produced by cruciate ligaments to that
produced by the lateral collateral ligament. Use the force-deflection characteristics of the
ligaments in your solution.

Homework Equations

(F = kΔx and M = Fd); assume that ligaments act as springs

The Attempt at a Solution

The free-body diagram is in the attachment. Fc is the force produced by the collateral ligament, Fl is the force produced by the lateral ligament and dc and dl are the corresponding distances of both forces from the load N. I really don't know how to do this question. I wrote out the equilibrium moment equation but then I get stuck. I don't know how to continue or if my free-body diagram is even right.

Homework Statement

2nd -- An athlete lifts a weight of 80N from position A to position D which makes an angle of 180 degrees. The weight of athlete’s arm (from shoulder to fingers) is 20N. Arm will move with no bent in the wrist and elbow joints over angle θ. Note that the reference point O is on the shoulder joint. The arm weight 20N act at x=0, y=0 halfway of the arm total length of 60cm.

(a) Determine the quasi-static moment equation corresponding to the arm bicep muscle as
a function of flexion angle θ. At the arm bicep muscle, consider moment Tm and force
vectors (along x and y).

(B) Determine angles at what the lowest and the highest moments on the bicep muscle
are achieved.

Homework Equations

(ƩM = 0)

The Attempt at a Solution

The free-body diagram is in the 2nd attachment. I got an equilibrium moment equation of: M_o = 20(0.3 cosθ) + 80(0.6 cosθ)
dM_o/dθ = 0
= -20(0.3 sinθ) - 80(0.6 sinθ)
θ = 0 and 180 deg.

The problem here is just of uncertainty; don't know if I am right or not


Any help would be greatly appreciated. Thank you for time.

 

[acdree]

Sorry everyone there is a mistake in the information given for problem number 1 about the ligament forces. The lateral-medial load is a sideways force therefore 'N' in the free-body diagram attachment is not the load (Really don't know what it is, that is just what the professor provided us with)