Energy stores and transfer on a rollercoaster

[Jigneshbharati]

Homework Statement

My son is in year 7. Please see attached image for more details and context. We don't understand why the answer to the question no 4 is "F" and not "D"?
The rollercoaster travelling at the fastest speed.....
He put D but the correct answer is F.
Please help.
Thank you in advance.

Relevant Equations

Not applicable

My son is in year 7. Please see attached image for more details and context. We don't understand why the answer to the question no 4 is "F" and not "D"?
The rollercoaster travelling at the fastest speed.....
He put D but the correct answer is F.
Please help.
Thank you in advance.

 

[Orodruin]

Turning things around: Why do you think the answer is D?

What determines the speed of the roller coaster?

 

[Jigneshbharati]

Thank you. Because at D the height is maximum so the GPE would be maximum so the corresponding transfer to KE will be maximum.

 

[Orodruin]

Thank you. Is it because of the height from the ground?

What physical concepts are relevant here? What is the total energy and how is it split into kinetic and potential energy? Which of these is related to the speed of the roller coaster?

... and what was your answer to 3?

 

[Jigneshbharati]

D

 

[Jigneshbharati]

I want to help him but I am not sure.

 

[Jigneshbharati]

I know KE is 1/2mv2.

 

[Orodruin]

I want to help him but I am not sure.

Rather than you guessing, I believe your son would be better served by answering the questions I have posed here himself. And please answer the questions, they are designed to lead you to the correct answer rather than just serving it on a silver platter (which does not help in the long run).

 

[Jigneshbharati]

Thanks.
Total energy is KE + PE. At C, GPE is maximum but KE is 0. Then from C, GPE will be converted into KE. At D, KE would be maximum. I am trying.

 

[Jigneshbharati]

KE is related to speed.

 

[Orodruin]

Thanks.
Total energy is KE + PE.

Correct. So since total energy is conserved, KE + PE must be conserved. What does this mean for the relation of where the KE is maximal seen in relation to the potential energy? What must be true for the potential energy where the kinetic energy is maximal?

At C, GPE is maximum but KE is 0. Then from C, GPE will be converted into KE. At D, KE would be maximum.

Why would KE be maximal at D?

KE is related to speed.

It is indeed. The more KE, the higher the speed. Speed is maximal where kinetic energy is.

 

[Jigneshbharati]

Thank you so much. I am so sorry I still don't know why F is the correct answer.
My logic: C is the highest point so it will have the maximum GPE compare to the point E. As C has the maximum GPE so it will have the maximum KE at D. Sorry for asking again.
Once again, thank you for your help.

 

[erobz]

Thank you so much. I am so sorry I still don't know why F is the correct answer.
My logic: C is the highest point so it will have the maximum GPE compare to the point E. As C has the maximum GPE so it will have the maximum KE at D. Sorry for asking again.
Once again, thank you for your help.

Is the coaster moving at point E?

 

[Orodruin]

C is irrelevant to the question. The main issue is the question I asked:

What must be true for the potential energy where the kinetic energy is maximal?

 

[Jigneshbharati]

Is the coaster moving at point E?

No

 

[Jigneshbharati]

C is irrelevant to the question. The main issue is the question I asked:

It should be minium. I am so sorry but why KE is maximum at F and not at D.

 

[Orodruin]

It should be minium.

So where is potential energy minimal? Remember that we are always considering energy conservation here so the reference level must be the same all the time.

I am so sorry but why KE is maximum at F and not at D.

The roller coaster is assumed to not be powered and energy is therefore conserved (given that we also ignore energy losses, which is yhe typical assumption in problems like this).

 

[Orodruin]

No

Why not?

 

[Jigneshbharati]

Thanks. At point E, it's not moving because it will have reached the top so only GPE but no KE.

 

[Orodruin]

Thanks. At point E, it's not moving because it will have reached the top so only GPE but no KE.

That’s incorrect. Being at the top does not mean that there can be no KE. E is also not the top point of the roller coaster - that would be C. E is just a local maximum, not a global one.

 

[Jigneshbharati]

Thank you so much. I really appreciate your help. Good night!

 

[erobz]

Thank you so much. I really appreciate your help. Good night!

Did you have an epiphany or are you just going to sleep on it?

 

[Jigneshbharati]

Thank you for your reply. I am glad that it makes sense. I love helping him and I also get chance to learn with him. I am so grateful that this type of Forums exists. Take care. Bye...