in work done a specified amount of energy is consumed then during free fall how the total energy remain constant?

Question

When there is free fall there is work done then how the energy "mgh" remain constant all over the way. 

Answer 1

Hi Arghya!

 

When we speak of conservation of energy at the fundamental level, in mechanics, we are typically talking about mechanical energy, which is defined as the sum of kinetic plus all potential energy (this is the kind of energy most important in the movement and positioning of objects, which is the main subject of mechanics).

 

The total amount of mechanical energy remaining constant does not require either kinetic or potential energy individually to stay constant, only their sum.  At the start of free fall for a dropped object, just at the moment of its release (before gravity has begun accelerating it from rest to some velocity), it has zero kinetic energy, but has potential energy mgh (due to being some height h with respect to the "zero level").  Therefore, its total mechanical energy at that point is mgh.

 

If free fall rules are in effect (meaning air resistance is ignored), then that total mechanical energy is conserved -- in other words, stays constant -- through the entire fall.  This means, at any point, the total mechanical energy still equals the VALUE mgh.  When it reaches the "zero level," for example, the total mechanical energy equals mgh, even though, at this point, the potential energy is zero and the mechanical energy is thus all kinetic.  Thus, we can make the equation at that point:  (1/2)mv² (at h = 0) = mgh (at the start of free fall).

 

I hope this helps some!  If you have more questions about it, please do not hesitate to ask.

Answer 2

The TOTAL mechanical energy, which is the sum of kinetic energy and potential energy, remains constant.  

 

Kinetic energy = (1/2)mv²

 

Potential energy = mgh

 

The total mechanical energy is

 

E = (1/2)mv² + mgh

 

If kinetic energy increases, then potential energy decreases.  If kinetic energy decreases, then potential energy  increases.  But the sum of the two is constant.  During free fall, a body gains kinetic energy, but loses potential energy as its height decreases.