General gravitational potential energy question

[iceman99]

Homework Statement

if the angle of the slope is increased, the change of gravitational potential energy between the two heights: (Select all that apply) (It may be more that one option)


increases
depends on the path followed.
decreases.
depends only on the difference between the two heights
sometimes decreases and sometimes increases.
remains the same

Homework Equations

DeltaPE=mgh

The Attempt at a Solution

Well, this is for an online homework assignment for my summer physics class. I have tried multiple combinations, we are allowed 5 submissions, I have wasted 4... I at first thought it was merely "depends only on the difference between the two heights" based on the aforementioned equations. Yet this was marked wrong. So then I thought I misread it and put increases/ dependsonly on the diference between the two heights... I cannot remember the other two things I put, maybe remains the same. Not sure. Please help me, I am beginning to think it is just "Increases".

 

[Disconnected]

The potential energy is dependent only on the field strength at that point. Just look at the equations. Path, gradient etc. do not come into it, so altering these things will have no effect.

It seems like you understood this when you first said that it depends only on their height. I think that the answer they are looking for is "there is no change", and that the answer "it depends on their height" is saying that depending on the difference in heights, it could increase, stay the same, or decrease.

 

[yster]

I agree.
The trick is in the english not the actual physics. This is the type of question my friend used to call "curve balls" when we were still studying. The answer is that it remains the same and it only depends on the two heights.

 

[iceman99]

Thanks for the help everyone. I really appreciate it.

 

[rwisz]

I would say that the change in gravitational potential energy between two heights is directly proportional to the angle of the slope. This means that as the angle of the slope increases, the change in gravitational potential energy also increases. This can be seen in the equation DeltaPE=mgh, where the height (h) is directly related to the angle of the slope. Therefore, the statement "increases" is the correct answer. The other options may also be true in certain cases, such as when the path followed is not a straight line or when other factors, like friction, are involved. However, in general, the change in gravitational potential energy will increase with an increase in the angle of the slope.