Question

A crate is pulled by a force of 628 N628 \mathrm{~N} across the floor by a worker using a rope making an angle of 46.046.0^{\circ} with the floor. How much work does the force on the rope do, if the crate is pulled 15.0 m15.0 \mathrm{~m}.

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Work done by force which is not in direction of motion to move body for distance s is expressed by equation:

W=Fcosθs=628 Ncos46.015.0 m=6540 J\begin{align*} W &= F \cdot \cos{\theta} \cdot s \tag{only horizontal component of force do the work}\\ &= 628\ \mathrm{N} \cdot \cos{46.0^{\circ}} \cdot 15.0\ \mathrm{m} \tag{Unit is joule: $N\cdot m = J$ }\\ &=\boxed{6540\ \mathrm{J}}\\ \end{align*}

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