# Rollercoaster normal force question

## Homework Statement

In an amusement park ride called The Roundup, passengers stand inside a 19.0m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure

1. Suppose the ring rotates once every 5.50s . If a rider's mass is 52.0kg , with how much force does the ring push on her at the top of the ride?

2. What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?

## The Attempt at a Solution

I'm pretty sure that I have to use the equation n=m(v^2)/r - mg to get the force, but I keep getting the wrong answer HelP~

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## Answers and Replies

BvU
Science Advisor
Homework Helper
Well hello Leejos, welcome to PF

The way things work here is you can get top notch assistance -- provided you make an effort yourself too, and show it.

##F_c = {m\;v^2\over r}## is a good start and you can list it under 2. relevant equations. You have m, you have r but you need another equation to get a grip on v. What could that be ? And then you can calculate an ##F_c##, but how does that relate to the force the ring exercises on the person ?

Suraj M
Gold Member
Try relating time period to centrifugal force, without using v
Using ##\omega##,, any idea?

OK first I did 5.50rps*2*pi*9.5 to get velocity. Than I used it in the equation n=52kg(328m/s)^2/9.5 - (52*9.8)
Is something wrong?

BvU
Science Advisor
Homework Helper
No YES! 5.5 s/turn is not the same as 5.5 turns per second !

BvU
Science Advisor
Homework Helper
Except I hadn't seen that equation before in this thread. But it's the right one.

BvU
Science Advisor
Homework Helper
But that's because I didn't read carefully enough
I am now so brainwashed that I look for relevant equations under relevant equations.
And for attempt at solution I look under attempt at solution

hmm then are you saying that my velocity is wrong then? Any suggesstions how to solve it then?

BvU
Science Advisor
Homework Helper
See post #5.

Suraj M
Gold Member
Leejos, if your have so much trouble finding v.
try ##find \omega## from the given time $$\omega = \frac{2 \pi}{T}$$
then use
$$F_c = MR\omega²$$

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