Escape speed

1. Mar 26, 2007

imy786

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

GPE= mgh

3. 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...

2. Mar 26, 2007

Dick

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

3. Mar 26, 2007

HallsofIvy

Staff Emeritus
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!

4. Mar 26, 2007

anantchowdhary

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

5. Mar 26, 2007

imy786

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

6. Mar 26, 2007

anantchowdhary

you shud use the work energy theorem

Last edited: Mar 26, 2007
7. Mar 26, 2007

Dick

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

8. Mar 26, 2007

HallsofIvy

Staff Emeritus
Remember that gravity is an "inverse square formula"!