The maximum mass m that a person can hold in a hand when the arm is positioned with a 105∘ angle at the elbow as shown in (Figure 1) is 21kg . Assume the forearm and hand have a total mass of 2.0 kg with a CG that is 15 cm from the elbow, and that the biceps muscle attaches 5.0 cm from the elbow.
let r1 = 35cm = 0.35m
r2 = 5cm = 0.05m
r3 = 15cm = 0.15m
M = 2kg
m = 21kg
Take counter clockwise positive, then clockwise is negative. The forces from the bone on the rotation point (elbow) are ignored because the distance between the force and the rotation point is 0 so it will be easier to calculate the max force by the muscle.
F*r2*sin105° – Mg*r3*sin90° -mg*r1*sin90° = 0
F*r2*sin105° – Mg*r3 – mg*r1 = 0
(Sin90° = 0)
F = (Mg*r3 + mg*r1)/(r2*sin105°)
= (2*9.8*0.15 + 21*9.8*0.35)/(0.05*sin105°)
=(2.94 + 72.03)/0.0483
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