Notions of Work and Kinetic Energy
- The work-energy theorem states that the change in kinetic energy of a particle is equal to the work done on it by the net force.
- Kf – Ki = W
- We know the equation in 3D : v2 – u2 = 2a.d (where u-initial velocity, v-final velocity, a-acceleration, d-displacement)
now multiplying the equation by m/2 we have, ½ mv2 – ½ mu2 = ma.d = F.d (Since ma = F)
The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement. W = F.d .
No work is done if:
- The displacement is zero
The force is zero.
Work done by a variable force
- The variable force is more commonly encountered than the constant force.
- If the displacement Dx is small, we can take the force F (x) as approximately constant and the work done is then
DW =F (x) Dx
For total work, we add all work done along small displacements.
Example: A force F = 3x2 start acting on a particle which is initially at rest. Find the work done by the force during the displacement of the particle from x =0m to x = 2m.
- The kinetic energy of an object is a measure of the work an object can do by the virtue of its motion.
- If an object of mass m has velocity v, its kinetic energy K is
- Kinetic energy is a scalar quantity.