29_universal - Lesson 29: Newton's Law of Universal...

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Lesson 29: Newton's Law of Universal Gravitation Let's say we start with the classic “apple on the head” version of Newton's work. Newton started with the idea that since the Earth is pulling on the apple, the apple must also be pulling on the Earth (Newton’s 3rd Law). Ask a person on the street where gravity comes from in this situation, and they'd probably say “the Earth.” They would never consider the apple as a “source” of gravity. But if the apple is pulling on the Earth, that must mean that an object doesn’t have to be huge to have a gravitational pull on other objects. There is nothing special about the Earth compared to the apple. .. both are sources of gravity. That would mean that one apple should be able to have a gravitational pull on another apple… that means any mass pulls on any other mass . The reason we don’t see the effect of, for example, you being pulled towards your computer monitor, is that the masses are so small that the force is also very small. Still, the force is there, and Newton wanted to come up with a way of calculating it. Using a lot of calculus and some pretty tough physics he came up with two key concepts: 1. The force due to gravity between two objects is proportional to the two masses. If one or both of the masses is big enough (like the Earth) then the force becomes noticeable. As a relationship this can be written as. F g m 1 m 2 m 1 and m 2 are both masses (kg) 2. The force due to gravity is inversely proportional to the square of the distance between the two masses. This distance is always measured from the centres of the two objects, so we usually consider it to be a radius in the formulas. As the distance increases, the force drops off exponentially. F g 1 r 2 r = distance between the centres (m) Example 1 : The force due to gravity between two objects is measured to be 160 N. Determine the magnitude of the force if . .. a) one of the masses is doubled.
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This note was uploaded on 12/02/2011 for the course PHYSICS 235 taught by Professor Staff during the Fall '08 term at Rutgers.

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29_universal - Lesson 29: Newton's Law of Universal...

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