# Frictionless Roller Coaster Problem

1. Dec 30, 2007

### danrochester

1. The problem statement, all variables and given/known data
Consider the frictionless roller coaster shown. (Diagram attached)

If a 12000 kg car starts at rest from Point A, calculate:

a) the total energy of the system
b) the speed of the car at point B
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

2. Relevant equations

for a): E(total) = mgh
for b): E(total) = mgh + 1/2mv^2 (rearrange to solve for v)

3. The attempt at a solution

The problem I'm having is with parts c) and d): in the book it looks like there is supposed to be a measurement at point E, but there isn't any value given. Do I need this to calculate an answer? (I haven't done anything on "momentum" yet, so I am working with gravitational potential energy, force, work and energy).

Thanks for any assistance
-Dan

#### Attached Files:

• ###### diagramL5Q20.JPG
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2. Dec 31, 2007

### Irid

Do you know a relation between force applied and work done? I can't see your diagram, but at E you should have some stopping distance given. Use it to find the force.

3. Dec 31, 2007

### beocom6000yello

you dont expect us to just give you the answer do you? this is so easy!

4. Dec 31, 2007

### danrochester

I know the relationship. As I said in my post, there is no value given for the stopping distance, but it looks like there was supposed to be one and it was left out. That was actually my whole question; do I need this value, and is this a text error as I suspected.

I didn't ask for the answer, just whether or not I needed a value for stopping distance. You didn't even read the question.

5. Dec 31, 2007

### Irid

Well, using dimension analysis, you can determine whether you need some quantity or not. If you wish to combine energy (joules) and force (newtons) you MUST have some quantity which is expressed in meters. If it is not given, maybe you're supposed to assume some value or smth.

6. Dec 31, 2007

### Staff: Mentor

Did you post the complete problem exactly as given?

If I understand the problem, you'll need the stopping distance to answer c), but not to answer d).

Last edited: Dec 31, 2007
7. Dec 31, 2007

### danrochester

The problem as posted is verbatim from the book, so it looks like there is an error in the book as I suspected. If I had the distance it would be a simple problem, for c) F=W/d, and the work would equal the total energy of the system. And again, for part d), the work required to bring the train to a stop is equal to the energy in the system.

Sorry about the confusion everyone, I do know how to do these questions!!! But a book error is a book error...I guess that's just the way it goes.

Thanks a lot
-Dan