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Home Concept Builders Circular and Satellite Motion Universal Gravitation Help Help 16

Universal Gravitation - Questions 16 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 one-fourth the original value AND the mass of object 2 is tripled AND the distance separating Objects 1 and 2 is halved, 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 both 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 three 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 decreased by a factor of four 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, making the mass of Object 1 to be one-fourth of the original value will have the effect of making the gravitational force one-fourth the original value. And so one of your tasks is to take the given force value and change it by this one-fourth factor.

The second change that you will make will take into account the change that was made to the mass of Object 2. The mass was tripled and this will alter the gravitational force. Since the gravitational force is directly proportional to the mass of both of the objects, you will also have to account for the change in the second mass. A tripling of the mass of Object 2 causes a tripling of gravitational force. And so the second task is to take the given force value and change it by this tripling factor.

The third change that you will make will take into account the change that was made to the separation distance. The separation distance was halved 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 a decrease in distance leads to an 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).

These three 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