Grav. Potential Energy question

[ElliottB]

Advertisement - Members don't see this ad

I'm confused conceptually by one of the EK questions (Lecture 3, 30 minute quiz, question 67)

A rocket is launched from earth to explore our solar system and beyond. As the rocket moves out of the earth's atmosphere and into deep space, the gravitational constant "g" decreases and approaches zero and the gravitational potential energy of the rocket:

A) also decreases and approaches zero.
B) continually increases.
C) remains constant.
D) increases at first and then decreases and approaches zero.

The answer apparently is B, but I chose D. Wouldn't the rocket eventually escape the grasp of the earth's gravity, nearing zero gravitational PE? Or does h (from PE = mgh) increase much more rapidly than g decreases?

Thanks for any insight.

 

[wanderer]

http://forums.studentdoctor.net/showthread.php?t=643408

 

[ElliottB]

Great.... another EK typo. 😡

 

[wanderer]

The answer is B.

 

[yummyoatmeal]

The answer is B. The gravitational potential energy continuously increases.

Note that this is regardless of where you set the reference point for potential energy. The usual convention is that the the gravitational potential energy is zero at an infinite distance. In that case, the gravitational potential energy starts at some negative number and continuously increases towards zero as the distance goes towards infinity. The change in potential energy is positive and continuously increasing, however.

Try drawing a graph of the gravitational potential energy vs. distance between the rocket and Earth.

 

[LostInStudy]

You can never escape gravity. The PE technically increases as the farther you get. You'll have what you had on earth and that little bit from space. So increases as you get farther.

-LIS

 

[bxadook]

Okay so the force due to gravity is inversely porportional to the square of the separation distance, so in that case the further you move out, the faster the rate of change of the force. I.E. It will tend towards zero much faster. If the height H is governed by a linear relationship in GPE, then the growth of r^2 will outweigh the height. Which means g will become smaller much faster than h is growing. Therefore mgh will tend towards 0 but never actually reach it.

I think they explained this in the other thread, but they seem to go much further in depth than just general MCAT physics. They used calc based physics in which GPE is an integral, which the area under that graph tends toward infinity.

My 2 cents. 👍