derivation of work done by a variable force
Answers
The work done by a constant force of magnitude F, as we know, that displaces an object by Δx can be given asL:
W = F.Δx
In the case of a variable force, work is calculated with the help of integration. For example, in the case of a spring, the force acting upon any object attached to a horizontal spring can be given as:
Fs = -kx
Where,
k is the spring constant
x is the displacement of the object attached
Hope it helps...
Answer:
It is interesting to know that the forces we encounter every day are mostly variable in nature which is defined as a variable force. A force is said to perform work on a system if there is displacement in the system upon application of the force in the direction of the force. In the case of a variable force, integration is necessary to calculate the work done.
The work done by a constant force of magnitude F, as we know, that displaces an object by Δx can be given asL:
W = F.Δx
In the case of a variable force, work is calculated with the help of integration. For example, in the case of a spring, the force acting upon any object attached to a horizontal spring can be given as:
Fs = -kx
Where,
k is the spring constant
x is the displacement of the object attached
We can see that this force is proportional to the displacement of the object from the equilibrium position, hence the force acting at each instant during the compression and extension of the spring will be different. Thus, the infinitesimally small contributions of work done during each instant are to be counted in order to calculate the total work done.
The integral is evaluated as:
work done by variable force