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 3.50 kg weight in his hand. This weight is 60.0 cm from the shoulder joint. His forearm (including his hand) has a mass of 2.42 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 2.59 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.)

Part A

What is the tension in the deltoid muscle?

Explanation / Answer

Let the tension in the deltoid muscle be t.
Now,Since the system is in equilibrium,so we need to find out torque for given masses
and then equate them to zero.
W know that,torque = force * distance to pivot point
Now,torque due to given Weight is:T1= 3.5*9.8*0.6= 20.58 N-m.
torque due to Forearm is: T2 = 2.42*9.8*0.43 = 10.198 N-m.
torque due to Upper arm is: T3 = 2.59*9.8*0.13= 3.299 N-m
torque due to Muscle is: T4 = t* 0.15 *sin(14 degree)=0.036t   
(Here g in all the cases has been taken as 9.8m/s^2)
Now, since they are in equilibrium,
So,T4 = T1 + T2 + T3
=> 0.036t= 34.077
=> t= 946.58 N
Hense, this is the reqired tension.

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