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 2.00 kg weight in his hand. This weight is 60.0 cm from the shoulder joint. His forearm (including his hand) has a mass of 2.46 kg and is 34.0 cm long; its center of mass is 43.0 cm from the shoulder joint, measured along the arm. His upper arm is 26.0 cm long and has a mass of 2.65 kg ; its center of mass is 13.0 cm from the shoulder joint. The deltoid muscle is attached to the humerus 15.0 cm from the shoulder joint and makes a 14.0 angle with the humerus. (See part (b) of the figure.)

Explanation / Answer

Torque = F X r (perpendicular distance)
Force = T X sin 14

Perpendicular distance r = Horizontal distance from the shoulder joint to the
Perpendicular distance = 15 cm = 0.15 m
Clockwise torque = T X sin 14 X 0.15

The counter clockwise torque is caused by the 3 weights.
Weight of upper arm = 2.65 X 9.8 = 25.97 N,

Perpendicular distance = 13 cm = 0.13 m
Counter clockwise torque = 25.97 X 0.13=3.37

Weight of forearm = 2.46 X 9.8 = 24.104 N,

Perpendicular distance = 43 cm = 0.43 m
Counter clockwise torque = 24.104 X 0.43 =10.36

Weight of object in the hand = 2.0 X 9.8 = 19.6 N

Perpendicular distance = 0.6 m
Counter clockwise torque = 19.6 X 0.6 =11.76

Total counter clockwise torque = 3.37+10.36+11.76
Clockwise torque = Total counter clockwise torque
T * sin 14 * 0.15 = 3.37+10.36+11.76
T = (25.49) ÷ (sin 14 X0.15)
T 702 N

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