Two movable pulleys: 30 kg, 4 rope segments

A pulley block with 2 movable pulleys lifts a 30 kg load at a steady speed; 4 rope segments support the load, and the load rises 1 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 = 30×10 = 300 N
   Find the weight of the object being lifted first
2. F = G/n = 300/4 = 75 N
   n rope segments share the load, so each needs only G/n (n = 4 ✓)
3. s = n·h = 4×1 = 4 m
   Less force means more distance: the rope end moves n times the lift height (work is not saved ✓)

Why it works

When n rope segments share the load, the minimum pull is the weight divided by n, while the rope end moves n times as far as the load rises. Saving force costs distance, so the work done is unchanged.

Common mistakes

• Dividing the weight by 2 instead of by the 4 rope segments.
• Forgetting that the rope end moves farther than the load rises.

Related

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