# Law of conservation of Energy question.

1. Jan 31, 2005

### ultimatejester

I have a exam tommorrow so i will greatly appreciate anyone who helps me on this one. The question has to be solved using law of conservation of energy.

Q: A roller coaster starts from rest at point A and weighs 1000kg with the ppl in it and goes through the designed track. The height of the track changes 5 times. There is a pic but i dont know how to post it.

Point A:9.5m
Point B:6.5m
Point C:9.2m
Point D:0.50m
Point E:5.5m

a)What is its maximum speed?
b)With what speed does the roller coaster arrive at point E?
c)What constant braking would have to be applied at point E to stop the roller coaster within 5m.?

Analysis:
I finished part B. That was easy mgh=mgh+0.5mv^2 and the speed came out to be 8.8m/s

I have no idea how to do a and c. Before i begin. i just wanna know, the more the energy the more the accelaration right. So at the heighst point of the track the roller coaster would have the max velocity. If this is right, then i know how to do part a as well. Use point A and point C to find the max veloctiy and point C.

Part c relates to the force of friction. I could use F=ma but i dont have the time so i am stuck here.

Hope you guys understand what i am saying.

Thanks

2. Jan 31, 2005

### Zorodius

Think of two glasses, with just enough water for one. The first glass is speed, and the other glass is height. You can pour water from the speed glass into the height glass, or vice versa, but you always have the same amount of water.

There will be the greatest possible amount of water in the speed glass when there is the least possible amount of water in the height glass. That is, the coaster will have the most kinetic energy when it has the least gravitational potential energy. So, to answer part A, you need to find out which part of the track is lowest. Whatever speed the coaster has there is the maximum speed it will achieve on the track.

You said, "the more energy the more acceleration right." This is not correct, kinetic energy describes only an object's velocity (and mass), it does not tell you how much it is accelerating.

The highest point of the track would have the least velocity.

Question C is worded ambiguously, they might be asking for the acceleration required to stop the car in five meters, or they might be asking for the amount of friction required to produce that acceleration. In either case, your first step should be to use your constant acceleration equations to find out how much acceleration would be required.