Total Mechanical Energy & Escape Velocity: Explained

[computerages]

Hi,

I just had a question that why the total mechanical energy has to be zero in order for an object to achieve escape velocity?

Thanks!

 

[harshant]

Basically when we want a body to escape the gravitational field of earth, what we want is that it goes far away from the vicinity of earth. Far away from the earth, the gravitational potential energy is zero and because gravity is a conservative force the total mechanical energy is same throughout i.e. zero. Also note that this is a limiting case, even if the the total mechanical energy is positive the body will escape but it cannot escape the field if the total energy is negative.

 

[Shooting Star]

Perhaps, it may be better to say that if we throw a body directly up, we don't want the body ever to fall back on earth. That minimum speed for that is the escape speed. The rest is as harshant said.