First slide

Work

Question

A body is thrown on a rough horizontal surface such that the frictional force is varying with distance as $f=(8x+5)N$ . Find the work done by friction on the body if it stops after travelling a distance of 10m _______

Difficult

Solution

$\begin{array}{l} W = \int \vec{f} \cdot \vec{ds} \\ = \int_{0}^{10} (8 x + 5) d x \\ W = - [8 \int_{0}^{10} x d x + 5 \int_{0}^{10} d x] \\ W = 8 \times [\frac{x^{2}}{2}] + 5 [x]_{0}^{10} \\ W = (4 \times 100) + (5 \times 10) = 450 J \end{array}$

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