# Roller Coaster analogy

1. Jun 12, 2006

### coldcell

I'm not sure if this question belongs to this forum or advanced phsyics.. but since I'm still in high school, I think this is the right forum.

I'm doing physics questions based on roller coaster and am just a little bit confused on how to answer some questions.

You know :

Mass of each empty car and with passangers
Total length of track
Slope of lift
Horizontal distance from bottom of lift to top
Change in elevation at first drop
Track length at the first drop
Length of each car

Questions 1: Calculate the total energy required to raise the train to the top of the first hill

I'm thinking Eg - Ek will give you the answer, but I'm not sure.

A friend suggested that the energy required is simply 0 since the train is moving at constant velocity to the top of the hill.

Question 2: Apply the law of conservation of energy to determine the speed of the first car at the bottom of the first hill, assuming some energy is lost in overcoming friction (use a reasonable estimate)

Any help is appreciated!!

2. Jun 12, 2006

### arunbg

To raise the coaster cars to a height h (using a chain drive perhaps) you need to do work against gravity. This energy is stored as potential energy at the top. Now when you come back down this energy is converted into kinetic energy. Thus there is constant shuttling of two different forms of energy. Now due to friction some energy is lost constantly (this is why the first dip of normal coasters is the tallest) and eventually the cars come to a stop.
Can you do your question now ?

3. Jun 12, 2006

### coldcell

Hm.... let me see if I get this right:

Total energy to bring the train to the top = mgh

That's it right?

As for the second question, I'm still confused. I realize that the friction is causing energy loss.. but how do calculate the friction when you dont know the friction constant?

4. Jun 12, 2006

### Hootenanny

Staff Emeritus
Yeah that's right.
The question says, "use a resonable estimate", I would assume this means you can choose a co efficent. I believe the coefficenet of kinetic friction for steel on steel is around 0.6.

Last edited: Jun 12, 2006
5. Jun 12, 2006

### arunbg

Even if you have an approximate coefficient of kinetic friction, you would still need to know the slope of the track and not just the height .

6. Jun 12, 2006

### Hootenanny

Staff Emeritus
I think that information is given in the question;

7. Jun 12, 2006

### arunbg

Aww, shucks didn't notice that , sorry.

8. Jun 12, 2006

### Hootenanny

Staff Emeritus
No problem, we all make silly mistake, including typos (RE projectile motion thread)...