Are Kinetic Energy and Gravitational Potential Energy Inversely Proportionate?

[JimmyRay]

Kinetic energy and gravitational potential energy are inversely proportionate to each other?

 

[dav2008]

No.

If A is inversly proportional to B that means that $$A \propto \frac{1}{B}$$

In the case of kinetic energy $$K$$ and gravitational potential energy $$U_g$$ it can be said that the total energy in a system is $$E_t = U_g + K$$

Obviously there are numerous other forms of energy but the above case can be applied when you're dealing with gravity only.

 

[robphy]

No.
For an object in freefall, K+U=(a constant, E)... that is, K=E-U.
This, however, does not mean K=c/U, where c is a proportionality constant.

 

[JimmyRay]

Ohh... hmm is that the only way they are related?

K + U = Et

Because I just saw that, as Kinetic energy increases gravitational potential decreases and vice versa, THAT statement is correct right? Thats why I thought inversely proportional...

thanks guys

 

[Math Is Hard]

I always think of it like accounting. Let's say I have a dollar in quarters. I give you a quarter, so now I have 75 cents, and you have 25 cents. I give you another quarter, so now we both have 50 cents. If I give you my last two quarters, you have a dollar, and I've got nothing. So you're amount increases as mine decreases, and the reverse would be true if you started handing quarters back to me, but this isn't the same as an inversely proportional relationship. It's just debit and credit from one side to the other.
Take my example with a grain of salt though - this is just my way of thinking about it. My wacky physics teacher used to say, "sometimes Mr. Potential Energy got it all and sometimes Mr. Kinetic Energy got it all!"

 

[JimmyRay]

Thats a good way to look at it.