The figure shows an outstretched arm (0.61 m in length) that is parallel to the

Question

The figure shows an outstretched arm (0.61 m in length) that is parallel to the floor. The arm is pulling downward against the ring attached to the pulley system, in order to hold the 98-N weight stationary. To pull the arm downward, the latissimus dorsi muscle applies the force in the figure, at a point that is 0.069 m from the shoulder joint and oriented at an angle of 29?. The arm has a weight of 41 N and a center of gravity (cg) that is located 0.28 m from the shoulder joint. Find the magnitude of .

Explanation / Answer

The magnitude of each individual torque is the magnitude of the force timesthe corresponding lever arm. The forces and their lever arms are as follows:

Force   Lever Arm

98 N 0.61 m

47 N 0.28

M (0.069 m) sin 29°

Each torque is positive if it causes a counterclockwise rotation and negative if it causes aclockwise rotation about the axis. Thus, since the net torque must be zero, we see that

( 98 N )( 0.61 m ) ( 47 N )( 0.28 m ) M [( 0.069 m ) sin 29°] = 0

Solving for M gives

M = 1400 N

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