Work Done by Variable Force

Work is defined as the measurement of an object’s energy when it is moved from its original location caused by the actions of an external force. In science, work is defined as the product of force and the displacement produced by that force. In the case of a constant force, it is the scalar product of the force applied and the displacement induced by this force. Work is a scalar variable despite the fact that both displacement and force are vector values. We commonly need to calculate the amount of effort done by a moving item. A variable force is one in which the force exerted on a body changes in response to changes in time.

What is work?

Work is a vital process in our daily lives and in science. There are several examples of work done in our daily lives. For example, an ox carrying a plough across a field, a guy lugging a trolley at a supermarket, a teenager placing his gym bag over his shoulders, and many more. The work done can be facilitated using a constant force or a variable force.

Constant Force

A work completed by the application of force on it may be separated into two types: work from a constant force and work from a variable force. The amplitude and direction adopted of the force stay intact in the first kind. Work (W) is equal to force applied (F) multiplied by displacement in this situation. Hence W = F ✕ X

Here, W = Work, F = force applied, X = displacement.

Variable Force

The work accomplished with the exertion of a variable force on the work is a little more complicated. The amplitude and direction path of force can vary at any point throughout the task in this circumstance. The majority of the labour we do in our everyday lives is an instance of Work Done by Variable Force applications. Work Done by Variable Force calculation is a difficult process that necessitates integration. To have a better grasp of the work done by variable force, consider the operation of a spring.

Hooke’s Law

Hooke’s Law asserts that the spring force for just a compression or stretched spring is equivalent to the force for the spring’s extension or compression. This spring force, however, is directed in the opposite direction in relation to this expansion.

The  force exerted  on the spring versus displacement for an unstretched spring when displacement is zero. The elastic potential energy of an extended spring is denoted by the symbol Us. This spring force-displacement plot may be used to calculate force using Hooke’s Law. Thus, Work Done by Variable Force can be computed.

Fs = -𝒌𝒙,

Thus, Ws = Fs x 𝒗d𝒕

Integration and formula for work done by variable force

However, to obtain precise results while working with a variable force, integration must be used. Therefore,

W₈ = ₀∫^t F_s.𝒗d𝒕

W₈ = ₀∫^t – 𝒌𝒙𝒗_𝒙d𝒕

W₈ = _x0∫^x – 𝒌𝒙d𝒙

W₈ = -1/2 𝒌Δ𝒙2

As a result, using the method described above, one may readily calculate the jobs performed by varying force.

Unit of work

The joule is the SI unit of labour (J). 1 Joule is defined as the work done by a force of one newton in moving a particle over one unit distance (1 unit metre) in the force’s direction. In any problem, a work formula is used to determine work done, force, or displacement. It is denoted by the symbol Nm, which stands for Newton metre.

Different types of work:

1. Positive Work: When an item is moved by a force operating in its direction, this is referred to as positive work. This form of labour is exemplified by the motion of an item falling towards the earth, where the object’s displacement is in the direction of gravity.
2. Negative Work: When the force and displacement are in opposing directions, work is termed negative. If an item is hurled upwards, its displacement will be upwards, whereas the force due to gravity will be downwards.
3. Zero Work: When the directions of force in relation to displacement directions are perpendicular, the force on the object does not perform. When we push hard against even a wall, the force we exert on the wall does not create work since the wall’s displacement in this instance is d = 0.

Conclusion

In the above chapter, we have discussed the definition, SI unit, formula, and examples of the work done by a variable force, constant force & variable force. We have also read about the different types of work. The positive and negative work is also an example of the work. When the force exerted on a body fluctuates with reference to changes over time, this is referred to as a variable force. A body’s motion is not equally accelerated when subjected to varied force. Variable force is defined as a force that changes direction and amplitude as a body is moving. Magnetic force, spring force, and electrostatic force are examples of variable forces. The forces we experience in our daily lives are largely changeable forces. By splitting displacement into tiny intervals, work done by a variable force is computed.