Three movable pulleys: 18 kg, 6 segments

A pulley block with 3 movable pulleys lifts an 18 kg load at a steady speed; 6 rope segments support the load, and the load rises 0.5 m. Find the minimum pulling force and the distance the rope end moves. (Take g = 10 N/kg.)

Step-by-step

1. Weight G = mg = 18×10 = 180 N
   Find the weight of the object being lifted first
2. F = G/n = 180/6 = 30 N
   n rope segments share the load, so each needs only G/n (n = 6 ✓)
3. s = n·h = 6×0.5 = 3 m
   Less force means more distance: the rope end moves n times the lift height (work is not saved ✓)

Why it works

With n rope segments supporting the load, the minimum pull is the weight divided by n and the rope end moves n times the load's rise. Work in equals work out when friction and pulley weight are ignored.

Common mistakes

• Using 3 rope segments (the number of pulleys) instead of 6.
• Multiplying the weight by 6 instead of dividing it.

Related

pulley-two-movable-rope-distance pulley-one-movable-minimum-force n-phy-pulley-two-1