Chain Hoist
Chain Hoist
Vector Addition of Forces (Statics)?
A beam is to be hoisted using two chains.If the resultant force is to be 600N, directed along the positive y axis, determine the magnitudes of forces F_A and F_B acting on each chainand the orientation delta of F_B so that the magnitude of F_B is a minimum. F_A acts at 30°from the y axis.
Let the angle between the chain( forces F(a) and F(b) ) and the vertical are angle A and angle B respectively.
From the givens :
A = 30 degrees
F(a) cos 30 + F (b) cos B = 600 ------------------------eq (1)
from the above equation, for F(b) to be minimum, cos B should be maximum. But the cosine is maximum when angle equalls zero, then B = 90 with vertical = horizontal.
Summing force into vertical direction.
F(a) cos 30 + 0 = 600 ,
then F(a) = 692.8 N
Summing force into horizontal direction.
F(a) sin 30 - F (b) sin 90 = 0 ( act in opposite direction)
then F(b) = 346.4 N
Good Luck
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