In the figure, a 21 kg block is held in place via a pulley system. The person\'s

Question

In the figure, a 21 kg block is held in place via a pulley system. The person's upper arm is vertical; the forearm makes angle e 34° with the horizontal. Forearm and hand together have a mass of 2.3 kg, with a center of mass at distance di 18 cm from the contact point of the forearm bone and the upper-arm bone (humerus). The triceps muscle pulls vertically upward on the forearm at distance d2 -2.9 cm behind that contact point. Distance d3 is 32 cm. Take the upward direction to be positive. What are the forces on the forearm from (a) the triceps muscle and (b) the humerus? Triceps com Humerus Block (a) Number Units (b) Number Units

Explanation / Answer

Given :-

mass of the block M = 21 kg

mass m = 2.3kg

d1 = 18cm = 0.18m

d2 = 2.9cm = 0.029m

d3 = 32cm = 0.32m

= 340

a)

since the block is in equlibrium the tension in the string is equatl to gravitational force   Mg on the block and is

directed upward we take counter clock wise as positive the balincing torque equation at contact is

-Ft d2 cos - mg d1 cos + Mg d3 cos = 0

Ft = ( Mgd3 - mgd1) / d2

Ft = [(21 x 9.81 x 0.32) - (2.3 x 9.81 x 0.18) / 0.029

Ft = 2133.28 N this force is upward

b)

Mg + Ft - Fh - mg = 0

Fh = mg - Ft - Mg

Fh = [(2.3 x 9.81) - 2133.28 - (21 x 9.81)

Fh = - 2316.60 N direction is downward.

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