When you lift an object by moving only your forearm, the main lifting muscle in

Question

When you lift an object by moving only your forearm, the main lifting muscle in your arm is the biceps. Suppose the mass of a forearm is 1.50 kg . If the biceps is connected to the forearm a distance dbiceps = 3.50 cmfrom the elbow, how much force Fbiceps must the biceps exert to hold a 850 g ball at the end of the forearm at distance dball = 31.0 cm from the elbow, with the forearm parallel to the floor? How much force Felbowmust the elbow exert? (Figure 1)

Part J

Although it is uncommon, orthopedic surgeons have seen patients who have torn their biceps tendon when forces of greater than 390 N have been exerted on the tendon with the arm bent at the elbow so that the forearm is parallel to the ground. What is the minimum mass of a ball Mball such a patient might have held to cause the biceps tendon to tear?

Explanation / Answer

While holding the ball, net torque about Elbow must be zero.
Torque due to weight of ball and weight of forearm, are in one direction and torque due to force of biceps in opposite direction.
Torque due to weight of ball = weight of ball x length of forearm = mg l = 0.85 *9.8* 0.31 = 2.6 Nm
Torque due to weight of forearm = weigth of forearm x length of forearm /2 ( assuming uniform distribution of mass of forearm)
= 1.5*9.8*0.31/2 = 2.3 Nm
Total torque due to weight of ball and forearm = 4.9 Nm = torque of biceps force = F(biceps) x distance
= F(biceps) * 0.035
F(biceps ) = 140 N

J) for force of 390 N, torque due to force of bicep = 390*0.035 = 13.65 Nm
Torque due to weight held = torque of biceps force - due to weight of forearm = 13.65 - 2.3 = 11.35 Nm
torque due to weight held = mg l
m = torque / gl = 11.35 / 9.8*0.31 = 3.73 kg

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