Two 0.55-kg basketballs, each with a radius of 19 cm , are just touching. You may want to review (Pages 399 - 401) . Part A How much energy is required to change the separation between the centers of the basketballs to 1.4 m ? (Ignore any other gravitational interactions.)

      ΔU = - 9,179 10-11 J

Explanation:

For this exercise the two basketballs are linked by gravitational interaction, so we can use gravitational energy

               U = - G m₁m₂ / R

In this case the mass is equal and the initial distance is r₁ = 19 cm = 0.19 m

               U₁ = - G m² / r₁

let's calculate

              U₁ = - 6.67 10⁻¹¹ 0.55² / 0.19

              U₁ = - 10,619 10⁻¹¹ J

when its centers are separated it is at r₂ = 1.4 m

              U₂ = - 6.67 10⁻¹¹ 0.55² / 1.4

              U₂ = - 1.44 10-11 J

the energy between these two points is

          ΔU = U₂ - U₁

          ΔU = (-1.44 +10.619) 10-11

          ΔU = - 9,179 10-11 J

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