In deep space, spheres A of mass MA is located at the origin of an x axis and sp

Question

In deep space, spheres A of mass MA is located at the origin of an x axis and sphere B of mass MB is located on the axis at a point x. Sphere B is released from rest while sphere A is held at the origin. What is the gravitational potential energy of the two-sphere system just as B is released? (Use any variable or symbol stated above along with the following as necessary: G for the gravitational constant.) What is the kinetic energy of B when it has moved a distance d toward A? (Use any variable or symbol stated above along with the following as necessary: G for the gravitational constant.)

Explanation / Answer

a)

The gravitational potential energy at distance x

U = GM­AMB/x

b)

if sphere A moved distance A then the new potential energy

U’ = GM­AMB/(x-d)

The kinetic energy K = U – U’

K = GM­AMB/x   - GM­AMB/(x-d)

K = GM­AMB {-d/x(x-d)}

k = GM­AMB d/x(d-x)

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