Question

Show that the total mechanical energy of a freely falling body remains constant throughout its fall

Answer 1

Answer:

Explanation:

It may be shown that in the absence of external frictional force the total mechanical energy of a body remains constant. ... Thus we have seen that sum of potential and kinetic energy of freely falling body at all points remains same. Under the force of gravity, the mechanical energy of a body remains constant

Answer 2

we have to show that the total mechanical energy of a freely falling body remains constant throughout its fall.

proof : Let a particle is falling from a height h.

initial velocity of the particle, u = 0

so, kinetic energy of the particle must be zero.

potential energy of particle, P = mgh

case 1 : Total mechanical energy at height h, T.E = mgh + 0 = mgh

now the particle falls and reaches h/2 distance from the ground.

velocity of the particle, v = √2g(h/2) = √gh

so kinetic energy of the particle = 1/2 mv² = 1/2 mgh

potential energy of the particle = mgh/2

case 2 : Total mechanical energy at midpoint of journey of the particle , T.E = mgh/2 + mgh/2 = mgh

now finally the particle reaches the ground.

velocity of the particle, v = √(2gh)

kinetic energy of the particle = 1/2 mv² = 1/2 m(2gh) = mgh

potential energy of the particle = 0

case 3 : Total mechanical energy of the particle on the ground, T.E = mgh + 0 = mgh

here it is clear that Total mechanical energy of a freely falling body remains constant throughout its fall.

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