The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
W = ΔKE
Where W represents the work done on the object and ΔKE represents the change in kinetic energy.
The theorem assumes that the force acting on the object is constant throughout the entire displacement. In other words, it assumes that the force and the displacement are collinear and constant in magnitude and direction.
When the force acting on an object is non-constant, the work done cannot be simply calculated using the equation W = Fd, where F is the force and d is the displacement. This is because the force can vary at different points along the path of the displacement.
In such cases, the work done must be evaluated using integration. By breaking down the displacement into infinitesimally small intervals and calculating the work done over each interval, you can find the total work done by summing up these small contributions. The integral form of the work-energy theorem is:
W = ∫ F · dx
Where F represents the varying force and dx represents an infinitesimally small displacement.
By integrating the force with respect to displacement, you can determine the work done accurately even when the force is non-constant.