Q#12 (Past Exam Paper – March 2016 Paper 12 Q2)
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
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
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