# How to find speed with just height given?

1. Mar 8, 2013

### Sneakatone

you are to design a roller coaster in which cars start from rest at a height h=26.0 m , roll down into a valley and then up a mountain. neglect friction.

a) what is the speed of the cars at the bottom of the valley?

B)if the passangers are to feel 8g at the bottom of the valley, what must be the radius R of the arc of the circle that fits the bottom of the valley?

c)the top of the next mountain is an arc of the circle of the same radius R. if the passengers are to feel 0g at the top what must be its height h?

there is a given picture, I do not know where to start.

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2. Mar 8, 2013

### haruspex

You're told there's no friction. What equation does that allow you to write down wrt energy?
When you've worked out the speed at the bottom, do you have an equation relating speed, radius of curvature and acceleration?

3. Mar 8, 2013

### Sneakatone

v^2=2gh
sqrt(2*9.81*26)=22.5 m/s

for part b I tried to use M=rv^2/g but the radius ended to be too small.

Last edited: Mar 8, 2013
4. Mar 8, 2013

### haruspex

That's a strange looking equation. What's M? It seems to have dimensions of area.

5. Mar 9, 2013

### lep11

Correct.

What 8g means?

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