A 6.1-kg bowling ball and a 7.2-kg bowling ball rest on a rack. If the force of gravity pulling

step 1 Two bowling balls. One has a mass of 6 .1 kilogram, and another has a mass of 7 .2 kilograms, or

A 6.1-kg bowling ball and a 7.2-kg bowling ball rest on a...

A $6.1-\mathrm{kg}$ bowling ball and a $7.2-\mathrm{kg}$ bowling ball rest on a rack. If the force of gravity pulling each bowling ball toward the other is $3.1 \times 10^{-9} \mathrm{~N}$, what is the separation between the balls?

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Key Concepts

Newton's Law of Universal Gravitation

This law describes the gravitational force between two masses, stating that the force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. It provides the foundational equation F = G * (m1 * m2) / d² for understanding how masses interact gravitationally.

Gravitational Constant

The gravitational constant, denoted by G and approximately equal to 6.674 × 10^-11 N·m²/kg², is the proportionality factor in Newton's law of universal gravitation. It ensures that the units and magnitudes of gravitational forces can be consistently calculated for any two masses.

Algebraic Manipulation to Solve for Distance

To find the separation between two masses when given the gravitational force, one must rearrange Newton's law of gravitation to solve for the distance d. This process involves isolating d² on one side of the equation by multiplying both sides by d² and dividing by the force, followed by taking the square root of the resultant expression.

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