# Roller coaster K/P energy problem wheeeee!

The question:

(I am given a diagram; I'll attempt to describe it here.)

Consider a frictionless, 12000-kg roller coaster that starts at rest at the top of a hill, point A, 95 m high. It goes all the way down the hill and coasts horizontally (for an unspecified distance) before reaching point B (0m high) .

Calculate:

a) The force that must be applied to bring it to a stop at point B

b) The work done to bring it to a stop at point B

My answers:

a) Now, I usually don't post a question without SOME attempt at an answer, but I'm really stumped here. If I can determine the magnitude of the force of the roller coaster at B, it's simply that magnitude in the opposite direction. However, I can't because F = ma, and I can't find the acceleration because it's an expression of change in velocity over time, and I can't figure out the time because no distance is given! *head explodes*

Please, somebody start me off on the right foot here!

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## Answers and Replies

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Think of this in terms of work and energy, instead of forces.

Dorothy

I don't have much of a problem with b); I use the equation

Ep{A} = Ek{B}

and proceed,

mgh{A} = 0.5mv{B}^2
v(B) = (2gh{A})^0.5
v{B} = 43.2 m/s

With the final velocity obtained,

Ek{B} = 0.5mv{B}
Ek{B} = 1.1 * 10^7 J

I can't seem to do anything with this answer to help me with a), though, because the work, in Joules, is an expression of applied force over a distance, and I don't know the distance, so I can't figure out the force. Do you see what's hanging me up?

Thanks for replying btw, any help is greatly appreciated.

Wait... If it's a frictionless roller coaster then it's horizontal distance is irrelevant, which means the distance travelled would be the vertical distance from point A to point B (95 m) ?

So, W = Fd or F = W/d

Am I on the right track here? Man, I feel like a dope if I am...

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It sounds like something is missing, I agree. Without knowing what is stopping the coaster, then it's hard to say what the force is. Is it supposed to stop suddenly at B? That would involve talking about the impulse.

Or if there is friction on the horizontal track, and it slows gradually.

Maybe someone else will have a bright idea. I'm sure you've checked the diagram and problem a thousand times to see if you neglected anything...

Dorothy

Gyroscope
You need additional information:

The time the force acts or the displacement of the roller coaster when the force is acting.

Okay, here's the question exactly as shown in the book:

Consider the frictionless roller coaster shown in Figure 5.11.

(see attached image)

If a 12000-kg car starts at rest from point A, calculate

a) the total energy of the system

[finished this, no problems]

b)the speed of the car at point B

[finished; again, no problems]

c)the force that must be applied to bring it to a stop at point E

d) the work done to bring it to a stop at point E

...Now, these books have been wrong before, but no distance or time have been stated - that is the question, word for word.

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cristo
Staff Emeritus
Science Advisor
https://www.physicsforums.com/showthread.php?t=114722 [Broken] is a link to (what looks like) the same question. Although the pic is missing from this post, I think it is the same one as yours (for eg, there is talk of a double ended arrow upto E, and the numbers are the same).

As you can read from the link; the general consensus was that there is not enough information to answer the question. Your diagram does look like it should have a distance assigned to the arrow pointing to E, and since noone can find an answer, I'd say that there wasn't enough information given.

If Hootenanny's about, he might be able to remember the diagram from the post! (Although, I realise that might be asking for an excellent memory!)

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Ahhh! Thanks for this. It's tough enough doing these without a tutor/teacher, when the book itself is wrong it gets REALLY frustrating!

Don't sweat it Legking. Those ILC courses are a nightmare. If you have the same book as me, take a look at what I had to do for question 18...

https://www.physicsforums.com/showthread.php?t=152795

I basically rewrote the pre-calculus course for them, before I gave up submitting the mountain of errors that is their material.

I am just trying to get through this physics course with the least amount of misinformation as possible.

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For anyone doing this course, I had to assume a distance for line "E"
I chose 50 meters.

I received full marks for the question.