A crane has an arm to which is attached a frictionless pulley. A cable passes over the pulley and supports a load of 10 kN as shown.

Question 12

A crane has an arm to which is attached a frictionless pulley. A cable passes over the pulley and supports a load of 10 kN as shown.

The crane arm exerts a force F on the pulley.

What is the value of F ?

A 5.0 kN                      B 8.7 kN                      C 10 kN                       D 17 kN

Reference: Past Exam Paper – March 2016 Paper 12 Q2

Solution:

Answer: D.

The force of 10 kN in the cable and the load of 10 kN both have a component along the crane arm.

The force F exerted by the crane arm on the pulley is the sum of these 2 components.

Component of force in cable along the crane arm = 10 cos 30°

Component of load along the crane arm = 10 cos 30°

Considering the forces on the pulley,

F = 10 cos 30° + 10 cos 30°

Force F = 17.32 kN = 17 kN