11.22 You are doing exercises on a Nautilus machine in a gym to strengthen your

Question

11.22 You are doing exercises on a Nautilus machine in a gym to strengthen your deltoid (shoulder) muscles. Your arms are raised vertically and can pivot around the shoulder joint, and you grasp the cable of the machine in your hand 64.0cm from your shoulder joint. The deltoid muscle is attached to the humerus 15.0cm from the shoulder joint and makes a 12.0deg angle with that bone. (See the figure below (Figure 1) .)

A:If you have set the tension in the cable of the machine to 36.0N on each arm, what is the tension in each deltoid muscle if you simply hold your outstretched arms in place?

Explanation / Answer

The torques applied from the cable and from the muscle must equal each other, to hold steady.
Angle of cable from horizontal = (125 - 90) = 35 deg.
Horizontal force component applied from cable = (cos 35) x 36, = 29.48N.
This is applied at 0.64m. from the shoulder joint (the fulcrum or centre of rotation).
Torque = (0.64 x 29.48) = 18.8672N/m.
To hold steady, the muscle must supply equal torque.
The horizontal component of the torque 0.15m. from the fulcrum is the 18.8672N/m., so the horizontal force component needed = (18.8672/0.15) = 125.78N.
The muscle force is applied at an angle of 12 degrees from vertical.
Muscle tension required = 125.78/(sin 12) = 604.97N.

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