Finding Escape Velocity from a Gravitational Potential Energy Surface

[imy786]

Homework Statement

By considering the gravitational potential energy of an object at the surface , find an expression for the escape speed from the surface and determine its value.

Homework Equations

GPE= mgh

The Attempt at a Solution

KE= 1/2* m * v^2

GPE= mgh

GPE+ KE = 0

mgh = - 1/2 * m * v^2
gh= - 1/2 * v^2


v^2= -2gh

v= sqare root of (-2gh)

this is the escape velocity...

 

[Dick]

You've computed velocity needed to reach a height h in a uniform gravitational field. Is that the same concept as 'escape velocity'?

 

[HallsofIvy]

You also appear to be assuming gravitational force is constant. If that were true, there would be no "escape velocity". It is impossible to "escape" a constant force!

 

[anantchowdhary]

Well if ur looking for escape velocity...it should be$$\sqrt{\frac{2GM}{R}}$$

 

[imy786]

thanks for the info...
so how shall i start off instead

 

[anantchowdhary]

you shud use the work energy theorem

 

[Dick]

You should change your expression for gravitational potential energy to one appropriate for a nonconstant field.

 

[HallsofIvy]

Remember that gravity is an "inverse square formula"!