Question

n deep space, sphere A of mass 47 kg is located at the origin of an x axis and sphere B of mass 110 kg is located on the axis at x = 3.4 m. Sphere B is released from rest while sphere A is held at the origin. (a) What is the gravitational potential energy of the two-sphere system just as B is released? (b) What is the kinetic energy of B when it has moved 2.6 m toward A?

Answer 1

a)-1.014x
`10^{-7`J

b)3.296 x
`10^{-7`J

Step-by-step explanation:

For Sphere A:

mass 'Ma'= 47kg

xa= 0

For sphere B:

mass 'Mb'= 110kg

xb=3.4m

a)the gravitational potential energy is given by

`U_{i` = -GMaMb/ d

`U_{i`= - 6.67 x
`10^(-11)` x 47 x 110/ 3.4 => -1.014x
`10^{-7`J

b) at d= 0.8m (3.4-2.6) and
`U_{i`=-1.014x
`10^{-7`J

The sum of potential and kinetic energies must be conserved as the energy is conserved.

`K_{i` +
`U_{i`=
`K_{f` +
`U_{f`

As sphere starts from rest and sphere A is fixed at its place, therefore
`K_{i` is zero

`U_{i`=
`K_{f` +
`U_{f`

The final potential energy is

`U_{f`= - GMaMb/d

Solving for '
`K_{f` '

`K_{f` =
`U_{i` + GMaMb/d => -1.014x
`10^{-7` + 6.67 x
`10^(-11)` x 47 x 110/ 0.8

`K_{f` = 3.296 x
`10^{-7`J