A body of mass 10 kg is kept at a height of 5 m. It is allowed to fall and reach the ground.
(i) What is the total mechanical energy possessed by the body at the height of 2 m assuming it is a frictionless medium?
(ii) What is the kinetic energy possessed by the body just before hitting the ground? Take g = 10 m s-2.
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(i) The speed of the body when at a height of 2m above the ground i.e., after falling through 3 m is :
V2 = U2 + 2gh = (0) + (2 x 10 x 3)
= 60
∴ V = √(60) m s-1
Mechanical energy at 2m height = P.E. + K.E. = mgh + $\frac{1}{2}$ mv2
= (10 x 10 x 2) + ($\frac{1}{2}$ x 10 x 60)
= 200 + 300
= 500 J
Hence, total mechanical energy possessed by the body at the height of 2 m = 500 J
(ii) The kinetic energy on reaching the ground will be same as the potential energy at it's highest point from which it started falling.
Mechanical energy = Initial potential energy
= m x g x h = 10 x 10 x 5 = 500 J
Hence, kinetic energy possessed by the body just before hitting the ground = 500 J