# How heavy does a roller coaster rider feel?

Walley1

## Homework Statement

A roller coaster rider has a mass of 80 kg and is riding in the coaster shown in the figure. If the vehicle has a speed of 10.0 m/s at the top of the first hill (assume same height as the top of the circle above Point A):
a) how "heavy" does the rider feel at point A?
b) how heavy does the rider feel at point B?
http://wildedgedesigns.com/RollerCoaster.PNG [Broken]

EK=(mv^2)/2
EP=mgh
F=ma
Ac=V^2/r

## The Attempt at a Solution

Potential Energy at the top of the first hill: 80 * 9.8 * 20 = 15,680J
Kinetic energy at the top of the first hill: 0.5 * 80 * 10^2 = 4,000J
Total energy: 19,680J
At the bottom of the first hill, all that energy is kinetic, so:
0.5 * 80 * v^2 = 19,680J
v = 22.18m/s
Ac = 22.18^2/10 = 49.20m/s^2
F = ma = 80 * 49.20 = 3,936N - That's the answer to Part A
But then there's an issue. The potential energy at point B is mgh = (80)(9.8)(30) = 23,520J. That's more energy than the system has. I don't know how the rider is going to make it to point B without falling back down, so I certainly don't know how heavy he feels. Is my approach to solving this totally incorrect?

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Staff Emeritus
Gold Member
Umm, so implicitly in your calculations, you decided that potential energy should be measured from point A (i.e. h = 0 at point A). That's totally fine. However, assuming that the centres of the two circles are at the same height, then point B is only 25 m above point A. So, maybe you want to re-evaluate your computation of the potential energy at point B.

EDIT: *Regardless* of the choice of reference point (h = 0), it's always true that point B is 25 m above point A, which means your computation of the change in potential energy from A to B is wrong. I just wanted to clarify that the result doesn't depend on your arbitrary choice of a zero point.

Walley1
Thanks! I'm pretty thick sometimes.

Walley1
One more question: I should still factor in his weight due to gravity, correct? That is to say, since he weights 784 N, I should add that to how heavy he feels. No?

Staff Emeritus