## Work done by a Variable Force – Class 11 | Chapter – 6 | Physics Short Notes Series PDF for NEET & JEE

Work done by a Variable Force: When a force is applied to an object and the object moves, work is said to be done by the force. The amount of work done by a constant force can be calculated by multiplying the magnitude of the force by the distance moved in the direction of the force. However, when the force acting on an object is variable, the work done is calculated by integrating the force with respect to the displacement.

The work done by a variable force can be positive, negative or zero, depending on the direction and magnitude of the force and the direction of the displacement. A positive work means that the force has done work on the object, increasing its energy. A negative work means that the force has removed energy from the object, decreasing its energy. Zero work means that there is no change in the object’s energy.

## Work done by a Variable Force

Here is the general formula for work done by a variable force:

W = ∫F(x) dx

Where,

• W is the work done by the force,
• F(x) is the force at a given position x, and
• dx is the displacement in the direction of the force.

To apply this formula, you need to know the function that describes the force as a function of position. Once you have this function, you can integrate it over the distance moved to calculate the work done.

For example, if you are pushing a box with a force that varies with position, you need to know the force function as a function of the position of the box. Then you can integrate the force function over the distance that the box moves to determine the work done by the force.

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