The deltoid muscle is the main muscle that allows you to raise your arm or even

Question

The deltoid muscle is the main muscle that allows you to raise your arm or even hold it out. It is connected to the humerus of the upper arm. (See part (a) of the figure (Figure 1).) The person shown is holding his arm out horizontally with a 2.51kg weight in his hand. This weight is 58.4cm from the shoulder joint. His forearm (including his hand) has a mass of 2.34kg and is 34.1 cm long: its center of mass is 42.2cm from the shoulder joint, measured along the arm. His upper arm is 25cm long and has a mass of 2.6kg its center of mass is 12.4cm from the shoulder joint. The deltoid muscle is attached to the humerus 13.9cm from the shoulder joint and makes a 14 degree angle with the humerus. (See part (b) of the figure.) Part A What is the tension in the deltoid muscle? T= 850 N Part B If the person was using wrist wieghts instead of one in his hand. what would be the tension in the deltoid muscle then? Let the new position of the weights be 49.38 cm from the shoulder joint. T= N

Explanation / Answer

Basically, it is all a matter of torques or force momenta defined as tau = r x F, where r and F are to be intended as vectors and x is the cross product so that |tau| = |r||F|sin theta, where theta is the angle between r and F. In this case, F is the weight force mg. To reach equilibrium, that is no net rotation, the torque due to the wight must be equal and opposite to the torque exerted by the muscle. Thus, one has to equate both torques and solving for the tension, which is the force entering the torque of the muscle.

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