The load has a mass of 15 kg and is lifted by the pulley system shown. Determine the force F in the cord as a function of the angle θ. Plot the function of force F versus the angle θ for 0 ≤ θ ≤ 90°.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.
Solution:
We will first draw a free body diagram like so:
It is important to note that because we are assuming the pulleys to be frictionless, the tension throughout the cord is constant.
Let us write an equation of equilibrium for the y-axis forces.
+\uparrow \sum \text{F}_\text{y}\,=\,0
F\text{cos}\theta\,+\,F\text{cos}\theta\,-\,147.15\,=\,0
F\text{cos}\theta\,+\,F\text{cos}\theta\,-\,147.15\,=\,0
(Isolate for F)
F\,=\,\dfrac{73.575}{\text{cos}\theta}
We can now graph this function like so:
