Problems with GPE (1 Viewer)

[Sylar23]

These two syllabus dot points are giving me a hard time in note preparation for my half-yearlies.

Anybody have any suggestions?

[FONT=&quot][/FONT]explain that a change in gravitational potential energy is related to work done

[FONT=&quot][/FONT]define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field
Ty in advance for any help/suggestions.

 

[me121]

This is a hard concept to understand, and it took me a while to understand it. But i'll do my best.

I've attached the relevant pages from my syllabus notes. (Original file available at http://andrew.harvey4.googlepages.com/)

 

[watatank]

explain that a change in gravitational potential energy is related to work done

change in GPE= mgh
work done = fd

if you lift something up that's work done and a change in GPE.

d = h, and f = mg. so they are equivalent.

 

[me121]

What do you think of this for the second syllabus dot point in space?

Gravitational potential energy (GPE) is a measure of the work done in moving an object from infinity to a point within the gravitational field. A change in GPE represents a movement either closer or further away from the gravitational field, therefore work must be done in order to move the object either closer or further away.

"A change in GPE represents a movement either closer or further away from the gravitational field"
A change in GPE represents movement either closer or further away from the centre of a gravitational field. If you we in an aeroplane that circled the Earth at a constant altitude you are moving inside the gravitation field, but your GPE does not change.

A way to understand GPE is with the conservation of energy laws. Energy cannot be created or destroyed. Now, if for example you jump out of an aeroplane, your velocity increases as you get closer to the earth, and because your speed is increasing your kinetic energy is increasing (KE=1/2mv^2), thus you are gaining energy. But this energy must come from somewhere as energy cannot be created or destroyed. This kinetic energy that you gain when you fall down to the earth comes from your GPE.

This is hard to explain, but try to read my notes again or even better you can read the source where I learnt about it from. Which is pages 329-331, from Halliday, D., Resnick, R., & Walker, J. (1997). Fundamentals of Physics Extended (5th Edition ed.). John Wiley & Sons, Inc.

“You are now going to consider the energy of a mass within a gravitational field. You have already seen that a mass within a gravitational field will experience a force (its weight). If that force meets no resistance, like a floor, then the mass will fall and as it falls it speeds up and gains kinetic energy. But energy cannot be created, so where does that kinetic energy come from?

The answer is that the mass has energy to begin with. This is simply because of its position within a gravitational field. This energy is called ‘gravitational potential energy’; it has the symbol Ep and the units joules (J). As the mass falls it has less and less gravitational potential energy (because its being converted into more and more kinetic energy). Therefore it is moving away from positions of higher potential energy and towards positions of lower potential energy.

The next thing to consider is the location of the zero potential energy level. In other words, at what position would a mass have to be in order to have no gravitational potential energy at all? Give this question just a little thought and you will realise that for gravitational potential energy to be zero, the mass cannot lie anywhere within a gravitational field. You saw in the last section that in order to be completely free of a gravitational field a mass must lie an infinite distance away. Infinity, then, is our zero level: Ep = 0 at ∞.

By now you may have realised something rather curious. If you were to place a mass, say, ten kilometres above the surface of the Earth and let it go it would fall toward the Earth. It is falling away from the zero level (which is at infinity), and yet it is falling to points of lower and lower gravitational potential energy. This means that its gravitational potential energy is negative, and its most negative value will be at the surface of the Earth! This idea can be a little hard to grasp at first. The diagram below is a graph of the gravitational potential energy of a mass along a line from the surface of the Earth out to infinity.”
-OTEN, HSC Physics Space. pp.16-17.