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

Answer:

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

b)3.296 x  $10^{-7$J

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