Calculating force vectors – forces acting on pulleys or blocks
The net force F r on a point will bisect the angle made by the rope at that point such that :
F r = 2F a cos ( θ 2 )
Where :
F r
F a q is the resultant force acting on the anchor point is the force applied to the rope is the angle made by the rope across the point
In the worked examples given below , the pulley is assumed to have no friction ( perfectly efficient ) and the rope is loaded with a force of 1kN , with the opposite end tied off at an anchor .
F # = 2F $ cos ( θ 2 )
F # = 2 ( 1 ) cos ( 45 2 ) F # = 2cos22.5
F # = 2F $ cos ( θ 2 )
F # = 2 ( 1 ) cos ( 90 2 ) F # = 2cos45
F = 1 . 848
F = 1 . 414
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