Please show with all working out. 3. A simple model, representing the forces act

Question

Please show with all working out.

3. A simple model, representing the forces acting in the human arm is represented in the figure below. The solid line represents the forearm, mg is the weight being carried by the arm (at the hand) and F is the force exerted by the biceps muscle. The forearm is 0.38 m long and the biceps are attached 0.05 m from the elbow P. The forearm has a mass of 1.8 kg and m is 5.0 kg. a. What is the value of the force F? (440 N) b. What force (magnitude and direction) is exerted on the forearm at the elbow joint P? (373 N directly downwards)

Explanation / Answer

a) sum torque around P

m g L sin (30) + mforearm g L/2 sin 30 - F x sin(30) = 0

m g L + m forearm g L/2 - Fx = 0

5*9.81*0.38 + 1.8*9.81*0.38/2 - F*0.05 = 0

F=440 N

b) sum forces in the y

P - 5*9.81 - 1.8*9.81 + 440 = 0

P = -373 N

so 373 N downwards

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