Question

A massless frictionless pulley is held up by a single rope from the ceiling. Two 100 N weight hang from the sides of the pulley (balanced). Sketch a free-body diagram of the pulley, and determine the tension in the ropes.

Answer 1

Task:

A massless frictionless pulley is held up by a single rope from the ceiling. Two 100 N weight hang from the sides of the pulley (balanced). Sketch a free-body diagram of the pulley, and determine the tension in the ropes.

Solution:

Due to Newton's second law:

$$m a = T - P \text{ (for the right side)}$$ $$- m a = T - P \text{ (for the left side)}$$

Solve the system of equations:

$$m a - m a = T + T - P - P$$ $$0 = 2 T - 2 P$$ $$T = P = 100 \, \text{N}$$

Answer:

$$T = 100 \, \text{N}$$