Question

Using the law of conservation of energy obtain the expression for the escape velocity

Answer 1

Explanation:

This is the escape speed - the minimum speed required to escape a planet's gravitational pull.

To find the escape velocity, apply energy conservation: Ui + Ki = Uf + Kf

For a planet of mass M and radius R, the potential energy of an object of mass m at the planet's surface is: U= - G m M/R.

Answer 2

Explanation:

How fast would you have to throw an object so it never came back down? This is the escape speed - the minimum speed required to escape a planet's gravitational pull.

To find the escape velocity, apply energy conservation: Ui + Ki = Uf + Kf

For escape, set both terms on the right to zero. We want the object to barely reach infinity, where the potential energy is zero.

For a planet of mass M and radius R, the potential energy of an object of mass m at the planet's surface is: U= - G m M/R.

Therefore:

- G m M

R

+ Kescape = 0

½ mv2escape = G m M/ R.

vescape = (

2 G M

R

) ½

For the Earth this is 11.2 km/s ≈ 25,000 mph!