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Home Concept Builders Circular and Satellite Motion Universal Gravitation Help Help 11

Universal Gravitation - Questions 11 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 mass of Object 1 is doubled AND the distance separating Objects 1 and 2 is tripled, then the new gravitational force will be _____ units.

You are provided a gravitational force value for two objects. You are then told that changes are made to the mass of one of the objects and the separation distance between the objects. You are asked to determine the new gravitational force that results from these two changes. To do so, get yourself organized and be prepared to make two changes to the original force.

The first change that you will make will take into account the change that was made to the mass of Object 1. The mass was doubled and this will alter the gravitational force. Newton's law of Universal Gravitation states that the gravitational force is directly proportional to the mass of both of the objects. This means that an alteration in one of the masses would alter the force value by the same factor. Thus, a doubling of mass causes a doubling of gravitational force. And so your task is to take the given force value and change it by this doubling factor.

The second change that you will make will take into account the change that was made to the separation distance. The separation distance was tripled and this will affect the force. 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 an increase in distance leads to a decrease 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 increasing the separation distance by a factor of three decreases the gravitational force by a factor nine (32).

These two changes, when made to the original force value, will provide the accurate answer for the new force value.

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

Newton's Law of Universal Gravitation

The Apple, the Moon, and the Inverse Square Law

Concept Builder Teacher Notes Directions