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Question

# (a) What happens to the work done when the dispacement of body is at right angles to the direction of force acting on it? Explain your answer. (b) A force of 50 N acts on a body and moves it a distance of 4 m on horizontal surface. Calculate the work done if the direction of force is at an angle of 60° to the horizontal surface.

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Solution

## (a) When the force is perpendicular to the direction of motion, the work done in such cases is zero. We have a relation as, W = FS cos θ Where, (W) - Work done (F) - Force (S) - Displacement (θ) - Angle between force and distance When the force is perpendicular to the direction of motion, cos 90° = 0, and hence the work done is also zero. Example - The work done by the earth on a satellite moving in a circular orbit around it is zero because gravitational force of attraction and displacement of sattelite at any instant are perpendicular to each other. (b) We have a situation in which, work is done by force acting obliquely. Force, (F) = 50 N Distance travelled by the body, (S) = 4 m Angle between force and direction of distance, (θ) = 60° We have a relation as, W = (F)(S) cos θ So, $W=\left(50\right)\left(4\right)\mathrm{cos}60°\phantom{\rule{0ex}{0ex}}=200\left(\frac{1}{2}\right)\mathrm{J}\phantom{\rule{0ex}{0ex}}=\overline{)100\mathrm{J}}$ So, the work done is 100 J.

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