A physical therapist wants her patient to rehabilitate his injured elbow by layi

Question

A physical therapist wants her patient to rehabilitate his injured elbow by laying his arm flat on a table, and then lifting a 2.1 kg mass by bending his elbow. In this situation, the weight is 33 cm from his elbow. He calls her back, complaining that it hurts him to grasp the weight. He asks if he can strap a bigger weight onto his arm, only 17 cm from his elbow. How much mass should she tell him to use so that he will be exerting the same torque? (He is raising his forearm itself, as well as the weight.)

Explanation / Answer

As the same torque is reqired for the same workout, and in the given case,
torque = r x F
F = mg ( m is mass of the object, g is acceleration due to gravity and r is distance of the mass from the elbow)
so, T = rmg ( assuming small angles)

for two cases
r1*m1 = r2*m2
r1 = 33 cm
m1 = 2.1 kg
r2 = 17 cm
m2 = r1*m1/r2 = 4.076 kg

so he should strap 4.076 at 17 cm from elbow for same workout

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