A waiter holds two plates of food in one hand. His forearm has a mass of 2.2 kg

Question

A waiter holds two plates of food in one hand. His forearm has a mass of 2.2 kg and the center of mass of his forearm is located 13 cm from his elbow joint. The center mass of the two plates is located 37cm from his elbow joint and the total mass of the two plates is 1.1 kg. His Bicep is attached to the bones of his forearm 3.5 cm from his elbow joint.

A) what is the torque produced by the mass of the two plates?

B)what is the torque produced by the mass of the waiters forearm?

c)what force must be exerted by the waiters biceps muscle to ensure that the plates and forearm are motionless?

Please show me step by step how you got the answer :)

Explanation / Answer

Mass of the two plates = 1.1 kg

Location of plates from elbow = 37 cm = 0.37 m

Mass of forearm = 2.2 kg

Location of center of mass of of forearm = 13 cm = 0.13 m

Locatoion of biceps = 3.5 cm = 0.035 m

(A.) Torque produced by plates = 1.1×g×0.37 = 3.99 Nm where g = 9.8 m/s2

(B.) Torque pproduced by forearm = 2.2×g×0.13 = 2.8 Nm

(C ) let the force of biceps be F .

The net torque on elbow must be zero for equilibrium.

Hence F×(0.035) = 3.99 + 2.8

Or F = 194 N

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