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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?

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Rau7star

Answer:

a)-1.014x [tex]10^{-7[/tex]J

b)3.296 x  [tex]10^{-7[/tex]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

[tex]U_{i[/tex] = -GMaMb/ d

[tex]U_{i[/tex]= - 6.67 x [tex]10^{-11}[/tex] x 47 x 110/ 3.4 => -1.014x [tex]10^{-7[/tex]J

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

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

[tex]K_{i[/tex] + [tex]U_{i[/tex]= [tex]K_{f[/tex] + [tex]U_{f[/tex]

As sphere starts from rest and sphere A is fixed at its place, therefore [tex]K_{i[/tex] is zero

[tex]U_{i[/tex]= [tex]K_{f[/tex] + [tex]U_{f[/tex]

The final potential energy is

[tex]U_{f[/tex]= - GMaMb/d

Solving for '[tex]K_{f[/tex] '

[tex]K_{f[/tex] = [tex]U_{i[/tex] + GMaMb/d => -1.014x [tex]10^{-7[/tex] + 6.67 x [tex]10^{-11}[/tex] x 47 x 110/ 0.8

[tex]K_{f[/tex] = 3.296 x  [tex]10^{-7[/tex]J

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