The load has a mass of 15 kg


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°.

The load has a mass of 15 kg

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:

The load has a mass of 15 kg

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

(Isolate for F)

F\,=\,\dfrac{73.575}{\text{cos}\theta}

 

We can now graph this function like so:

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.

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 3, question 3-40.

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