The deltoid muscle connects the shoulder blade to the upper arm (humerus), and s

Question

The deltoid muscle connects the shoulder blade to the upper arm (humerus), and so contraction of the deltoid raises the arm (see figure below). The deltoid tendon connects the humerus 15.0 cm from the shoulder joint at an angle of 20.0° with the horizontal. Suppose the arm weighs 38.0 N and its center of gravity is 36.3 cm from the shoulder joint. A weight W is held in the outstretched hand 90.0 cm from the shoulder joint.

Find the tension in the deltoid tendon in terms of W. (Assume the tension is measured in newtons.)
T =  

Find the force the shoulder joint exerts on the humerus if W = 44.5 N. (Assume the +x direction is to the right.)

Why is this force so large even for such a small weight?

Explanation / Answer

let

tension in deltoid tendon is, T at x1=15 cm

arm weight w1=38 N at x2=36.3 cm

weight in the outstretched hand is W at x3=90 cm

a)

torque due to T, W1 and W at joint is,

T*sin(20)*x1 =(w1*x2) + (W*x3)

T*sin(20)*15 =(38*36.3) + (W*90)

T*sin(20)*15 = (1379.4 + (W*90))/(sin(20)*15)

T=(268.87+17.54*w)

b)

if w=44.5 N

shoulder joint exerts the force on the humerus is,

F=T*cos(22)

F=(268.87+17.54*w)

F=(268.87+17.54*44.5)

F=1049.4 N

this force is acting at joint and

at the same point torque due to W is must balance,

hence, force F should be large

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