# Frictionless Roller Coaster Problem

## Homework Statement

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

## Homework Equations

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

## 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

#### Attachments

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.

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

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.
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.

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

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.

Doc Al
Mentor
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?
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:
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).
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