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When a constant force F is applied on the box upon the smooth surface, at a certain point of application, it offers a displacement s.

Mathematically, it can express as W = F s cos Θ

(Image to be added soon)

Here,

Θ = the angle between F and s (displayed in the above image)

Here, F cos Θ plays an important role in the work done.

  • Role of Gravity in Work Done

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The work done by gravity is said to be negative if an object is moving in an upward direction. The expression for the statement is,

Wg = - m.g.h

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Note: Work done is positive when it is falling from certain heights.

  • Role of Friction in Work Done

A concept is always there in our mind that the force of friction results in a negative work. However, as per the observation, it is concluded that the work done by friction may be zero, positive, negative or zero according to the condition.

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  • Role of a Variable Force in Work Done

If there is a chance of any alteration or variation of magnitude and direction of a force in a three-dimensional space, the expression can be obtained as a function of the position vector F.

Consider that a force is present in 3 – D space. Also, assume that the force’s magnitude as well as direction changes for some reason.

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The coordinates are (x, y, z) for this force F.

We can write the work done formula as

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[overrightarrow{F}] . [overrightarrow{ds}] = dW