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Home Concept Builders Circular and Satellite Motion Universal Gravitation Help Help 8

Universal Gravitation - Questions 8 Help

A Physics formula is more than just an algebraic recipe for solving word problems. It is a guide to thinking about how a change in one variable would alter another variable. In the case of the universal gravitation equation, the gravitational force exerted between two objects is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.

There are three similar versions of this question. Here is one of those versions:
 

Version 1:

Objects 1 and 2 attract each other with a gravitational force of 18.0 units. If the distance separating Objects 1 and 2 is changed to one-half the original value (i.e., halved), then the new gravitational force will be _____ units.

You are provided a gravitational force value for two objects. You are then told that the distance that separates the object's centers is decreased by a factor of two (halved). You are asked to determine the new gravitational force that results from the "halving" of this separation distance.

The Universal Gravitation law states that the gravitational force is inversely proportional to the square of the separation distance. The "inversely" part of this statement suggests that a decrease in distance leads to a increase in gravitational force. And the "square" part of this statement suggests that the force will change by a factor that is related to the square of the factor by which the distance changes. When these two parts of the sentence are put together, it means that the factor by which the force changes is the reciprocal of the square of the factor by which he distance changes. So decreasing the separation distance by a factor of two increases the gravitational force by a factor four (22).

Try these links to The Physics Classroom Tutorial for more help with using Newton's Universal Law of Gravitation as a guide to thinking:

The Apple, the Moon, and the Inverse Square Law

Newton's Law of Universal Gravitation

Concept Builder Teacher Notes Directions