Work done by a variable force: two –dimensional case:
In two dimensions the force is having two components along x and
y directions respectively. Then the work done by the variable force in two dimensions can be given as:
Kinetic Energy and the Work-Energy Theorem:
The work-energy theorem states that the net work done by a force exerted on an object is given as the change in kinetic energy. The kinetic energy of
a particle of mass m moving with a velocity v
is given by,
Thus, the mathematical representation of work-energy theorem can
be given by,
where vi and vf are the initial and final velocities of the particle. In a more convenient manner the net work done can be written as:
It can be noted that the work energy theorem is valid for both constant as well as variable force.