A negative work is done when an applied force F and the corresponding

A negative work is done when an applied force F and the corresponding displacement S are

[amp_mcq option1=”perpendicular to each other.” option2=”parallel to each other.” option3=”anti-parallel to each other.” option4=”equal in magnitude.” correct=”option3″]

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UPSC NDA-2 – 2021

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A negative work is done when an applied force F and the corresponding displacement S are anti-parallel to each other.

The work done (W) by a constant force (F) when an object undergoes a displacement (S) is given by the dot product of the force and displacement vectors: $W = \vec{F} \cdot \vec{S} = |\vec{F}| |\vec{S}| \cos\theta$, where $\theta$ is the angle between the force and displacement vectors. Work done is positive when the force and displacement are in the same general direction ($0^\circ \le \theta < 90^\circ$), zero when they are perpendicular ($\theta = 90^\circ$), and negative when they are in opposite directions ($90^\circ < \theta \le 180^\circ$). When the force and displacement are anti-parallel ($\theta = 180^\circ$), $\cos\theta = -1$, and the work done is maximum negative: $W = -FS$.

Examples of negative work include the work done by friction when an object moves (friction acts opposite to motion), or the work done by gravity when an object is lifted upwards (gravity acts downwards while displacement is upwards).

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