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# $5$ Examples of negative work done.

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## Negative Work DoneWork done is defined as the force applied to displace a body from its original state.Work done is a scalar quantity.Force and displacement are vector quantities.We know that the dot product of two vectors gives a scalar quantity as its result.Therefore work done is the dot product of force and displacement.Unit of work and energy and equal and it is termed as joules or $J$.If $\stackrel{\to }{F}$ is the force applied and $\stackrel{\to }{S}$ is the displacement of the body, then the work done $W$ can be given as,$W=\stackrel{\to }{F}.\stackrel{\to }{S}$ $=F.S.\mathrm{cos}\theta$where, $\theta$ is the angle between the direction of force vector and displacement vector.Let $\theta =180°$$\therefore FS\mathrm{cos}180°=-FS=-W$Hence, if the angle is obtuse, work done is always negative.ExamplesThe work done by the buoyant force of water in the drowning of a ship.The work done by gravitational force when one climbs a tree.The work done by frictional force when pushing a block on a hard surface.The work done by gravity on a rocket goes perpendicularly upwards.The work done by us on pulling water from a well.

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