To solve for Intensity I 2 means that we want to know what the radiation intensity is at a given, second location or known distance D 2. To solve for Intensity use the following formula:. To solve for a safe distance use the following formula:. Radiation Safety by J. Ballard is licensed under a Creative Commons Attribution 4. Skip to content Learning Objective: Understand the application of the Inverse Square Law as it pertains to Radiation Safety Apply the Inverse Square law to create safe distances, times, or radiation amounts.
Previous: Science of Gamma Radiography. Quite amazingly, the laws of mechanics that govern the motions of objects on Earth also govern the movement of objects in the heavens. Of course, Newton's dilemma was to provide reasonable evidence for the extension of the force of gravity from earth to the heavens. The key to this extension demanded that he be able to show how the affect of gravity is diluted with distance.
It was known at the time, that the force of gravity causes earthbound objects such as falling apples to accelerate towards the earth at a rate of 9. And it was also known that the moon accelerated towards the earth at a rate of 0. If the same force that causes the acceleration of the apple to the earth also causes the acceleration of the moon towards the earth, then there must be a plausible explanation for why the acceleration of the moon is so much smaller than the acceleration of the apple.
Newton knew that the force of gravity must somehow be "diluted" by distance. But how? What mathematical reality is intrinsic to the force of gravity that causes it to be inversely dependent upon the distance between the objects? The riddle is solved by a comparison of the distance from the apple to the center of the earth with the distance from the moon to the center of the earth. The moon in its orbit about the earth is approximately 60 times further from the earth's center than the apple is.
The mathematical relationship becomes clear. The force of gravity between the earth and any object is inversely proportional to the square of the distance that separates that object from the earth's center. The force of gravity follows an inverse square law. The relationship between the force of gravity F grav between the earth and any other object and the distance that separates their centers d can be expressed by the following relationship.
Since the distance d is in the denominator of this relationship, it can be said that the force of gravity is inversely related to the distance. And since the distance is raised to the second power, it can be said that the force of gravity is inversely related to the square of the distance. This mathematical relationship is sometimes referred to as an inverse square law since one quantity depends inversely upon the square of the other quantity. The inverse square relation between the force of gravity and the distance of separation provided sufficient evidence for Newton's explanation of why gravity can be credited as the cause of both the falling apple's acceleration and the orbiting moon's acceleration.
The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object's centers.
Altering the separation distance d results in an alteration in the force of gravity acting between the objects. Since the two quantities are inversely proportional, an increase in one quantity results in a decrease in the value of the other quantity. That is, an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity. Furthermore, the factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed.
So if the separation distance is doubled increased by a factor of 2 , then the force of gravity is decreased by a factor of four 2 raised to the second power.
And if the separation distance is tripled increased by a factor of 3 , then the force of gravity is decreased by a factor of nine 3 raised to the second power.
Thinking of the force-distance relationship in this way involves using a mathematical relationship as a guide to thinking about how an alteration in one variable affects the other variable. Equations can be more than recipes for algebraic problem solving; they can be guides to thinking. Check your understanding of the inverse square law as a guide to thinking by answering the following questions below. When finished, click the button to check your answers.
Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between the two objects? If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 2 2. If the distance between the two objects is tripled, then what is the new force of attraction between the two objects? If the distance is increased by a factor of 3, then force will be decreased by a factor of 9 3 2.
If the distance between the two objects is reduced in half, then what is the new force of attraction between the two objects? If the distance is decreased by a factor of 2, then force will be increased by a factor of 4 2 2.
The new force is then 4 times the original 16 units. If the distance between the two objects is reduced by a factor of 5, then what is the new force of attraction between the two objects? If the distance is decreased by a factor of 5, then force will be increased by a factor of 25 5 2. The new force is then 25 times the original 16 units. Having recently completed his first Physics course, Noah Formula has devised a new business plan based on his teacher's Physics for Better Living theme.
Noah learned that objects weigh different amounts at different distances from Earth's center. His plan involves buying gold by the weight at one altitude and then selling it at another altitude at the same price per weight.
Should Noah buy at a high altitude and sell at a low altitude or vice versa? To profit, buy at a high altitude and sell at a low one. Gold will weigh less at a high altitude and so you will get more gold for your money by buying at the high altitude. Then sell at a low altitude where the gold will weigh more than it did where it was purchased.
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