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Work Done as Dot Product

A man pulls 4...

Question

A man pulls 40 kg crate through 20 m across a level floor with a rope which makes 30 with the horizontal. He exerts a force of 150 N on the rope. Find the work done.

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Solution

The horizontal component of the force $F_{h} = F cos 30 = 150 \times \frac{\sqrt{3}}{2} = 75 \sqrt{3} N$
As force due to gravity is downward so the work done causes by only horizontal force.
Work done $W = F_{h} d = 75 \sqrt{3} \times 20 = 1500 \sqrt{3} J$

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