Two 0.59 -kg basketballs, each with a radius of 12 cm, are just touching. How much energy is req

step 1 Two basketballs, each with a mass of 0 .59 kilograms and a radius of 12 centimeters, are arrange

Two 0.59 -kg basketballs, each with a radius of 12 cm, are...

Two 0.59 -kg basketballs, each with a radius of $12 \mathrm{cm},$ are just touching. How much energy is required to change the separation between the centers of the basketballs to (a) 1.0 $\mathrm{m}$ and (b) 10.0 $\mathrm{m}$ ? (Ignore any other gravitational interactions.)

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Key Concepts

Work Done Against a Conservative Force

In the context of gravitational forces, when separating two masses, the work done is equal to the change in gravitational potential energy. Because gravitational force is conservative, the energy required to move the masses from one distance to another is independent of the path taken and can be directly computed as the difference between the initial and final gravitational potential energies.

Newton’s Law of Universal Gravitation

This principle describes how two masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. It provides the framework for calculating the gravitational interaction between objects by introducing the gravitational constant and establishing the fundamental inverse-square law dependency.

Gravitational Potential Energy

Gravitational potential energy quantifies the energy stored in a pair of masses due to their gravitational interaction. It is given by the formula U = -G(m1*m2)/r, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between their centers. This energy represents how much work is required to separate the masses to a point where their mutual gravitational attraction becomes negligible.

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