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Multiple Pulleys

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Unit: Force and Newton's Laws

Prerequisites

Pulley Systems (with Rope Constraints)

Later Topics

None

Multi-Step Problem Preview

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Part 1

A mass m=92.85 kgm = 92.85\,\mathrm{kg} is suspended from two different pulley systems. In this problem, you will compare the force required to lift the mass using a single pulley versus a 2:1 pulley system. The acceleration due to gravity is g=9.81 m/s2g = 9.81\,\mathrm{m/s^2}. Assume the pulleys are ideal (frictionless and massless).

image

Select the correct free-body diagram for the mass in the single pulley system on the left.

Correct!

Solution:

Solution

For a mass suspended in a single pulley system in equilibrium, only two forces act on the mass:

  1. Weight W⃗\vec{W}: Acts downward with magnitude W=m⋅g=92.85⋅9.81=910.86 NW = m \cdot g = 92.85 \cdot 9.81 = 910.86\,\mathrm{N}

  2. Tension T⃗\vec{T}: Acts upward through the rope attached to the mass

Since the mass is in equilibrium (not accelerating), these forces must be equal in magnitude and opposite in direction. The free-body diagram shows the weight vector pointing downward and the tension vector pointing upward, both with equal magnitudes.

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