Question

The relationship F=GM1M2/(d^2) is an example of an ______ ________ relationship. Thanks for the help!

Answer 1

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Answer 2

I'm not exactly sure the very specific answer to this. But I can help you see the different relationships that can be made from this equation.

First off, we see that \[\large F_G \propto m_1 ~~~\text{and}~~~ F \propto m_2\]This is direct relationship between the force and the two masses. If one mass were to increase, then the force would increase. If either of the masses were to decrease, then the force would decrease.

Additionally, we can also see that\[\large F_G \propto \frac{1}{d^2}\]This means that the force is inversely proportional to the distance between the two masses squared. If we were to increase the distance, we would see that the force would actually decrease rather than increase. Subsequently, if the distance decreases, that means that the force will increase!

In more scientific terms, if you were to put to objects closer together, the gravitational force that both objects have on each other grows bigger! It doesn't cause either one to start orbiting the other because the force is quite small, but there is in fact a force between the two.

Answer 3

The force has a direct relationship with the masses and an indirect relationship with the distance between them.

Answer 4

wow, thanks for the detailed explanation! It makes a lot more sense now!

Answer 5

seriously, that was really well written

Answer 6

Thank you! I'm glad I could help X)

Also, when we make note of these relationships, we should note when things are changing and when they're not. For instance, since the force is directly proportional to m_1, I should have noted that that the force will increase if the mass increases if the other variables remain constant (aka do not change!) Why's that? Because there's a slight complication that occurs when multiple variables are changing simultaneously, and we cannot say for sure (unless we're given numbers) whether or not the force *truly* increases. For example, one mass increases but the other decreases, we cannot say with certainty whether the force will increase or decrease.

If we're given numbers or quantitative observations such as "mass 1 is tripled and the distance between them is doubled" then we can come up with an idea of how our force will end up! But if we're just given a general, simple statement that one increases while the other decreases, etc., then we can't say for sure.

Answer 7

I guess an easier way to look at it is this:
If we increase m1, then the force will increase! If we decrease m2, then the force will decrease. Both causes the value of the force to change, but we do not know how this value compares with the original value. We do not know if it will be less than, equal to, or greater than its original value.

More than likely, you won't be given a problem like this, though.

Answer 8

Ahh, I see