Question

Derive an expression for the kinetic energy of the body of mass ‘m’ when placed at a height ‘h’from the earth’s surface?

Answer 1

Answer:

From equations of motion, the relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is  

But from Newton’s second law of motion F = m a.

work done by the force, F is written as the following:

w = ma(v^2 - u^2/2a) = 1/2m(v^2 - u^2)

If the object is starting from its stationary position, that is, u = 0, then

w = 1/2mv^2

From work and energy theorem, work done is equal to the change in the kinetic energy of the object.

 w = (1/2) mv ^2

If u = 0, the work done will be,

Thus the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is

 K.E = (1/2) mv^ 2