Checkpoint: Conservative Forces And Potential Energy

[alha0382]

Homework Statement

Consider two identical objects released from rest high above the surface of the Earth (neglect air resistance for this question).

In Case 1 we release an object from a height above the surface of the Earth equal to 1 Earth radius, and we measure its kinetic energy just before it hits the Earth to be K1.
In Case 2 we release an object from a height above the surface of the Earth equal to 2 Earth radii, and we measure its kinetic energy just before it hits the Earth to be K2.
1) Compare the kinetic energy of the two objects just before they hit the surface of the earth.

Homework Equations

Ugrav= -G*me*mb/ (R-earth)
KE= 1/2mv^2
conservation of energy- k+u=0

The Attempt at a Solution

K=-U
1/2mv^2 = Gmemb/r-earth

K1= 1/2mv^2
K2= 1/4mv^2

Wouldn't the K2= 1/2(k1) due to the conservation of mechanical energy. The radius of the Earth is inversely proportional to the kinetic energy

 

[UltrafastPED]

The distances from the center of the Earth are 2R and 3R.