# A popular amusement park ride

1. Jul 31, 2007

1. The problem statement, all variables and given/known data

a rotating cylinder of radius 3 m is set in rotation at an angular speed of 5 radians/second. the floor then drops away, leaving the riders suspended against the wall in a vertical position. what minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rier from slipping?

2. Relevant equations

3. The attempt at a solution

i've attempted to draw a free body diagram, cause i'm pretty sure that's the first thing i have to do. but i have to say, this FBD, is VERY VERY tricky.

2. Jul 31, 2007

### dontdisturbmycircles

What forces are acting on the people?(list them please What does the fact that the people do not accelerate upwards or downwards tell you about the vertical forces acting on the people?

3. Jul 31, 2007

### nrqed

What forces did you come up with and in what direction do you think they are pointing? It's actually not that hard once you knwo what forces are involved and you get their directions right. Hint: there are three forces.

4. Jul 31, 2007

okay...so i chose the position when the person is standing to the far most right hand side so that the centripetal acceleration is towards the left. i also have a normal force from the floor, her mass and gravity acting downwards, and then friction acting in the downwards direction ( i think)

5. Jul 31, 2007

### nrqed

Watch out.

You are ok with the centripetal acceleration. Just be careful to remember that it's not a force (so, to be strictly speaking, it is not suppoed to be in a free body diagram).

The floor is no longer there so there is no normal force exerted by the floor!

Gravity is acting downward, yes.

But the person has no vertical acceleration, right? So what does it tell you about the net vertical force?

6. Jul 31, 2007

okay...so i do have friction acting on the person right (towards the right?) but nrged said that there were three forces...i still have no idea what force i'm missing.

7. Jul 31, 2007

and also...does that mean that the net vertical force is equivalent to the mass and gravity?

8. Jul 31, 2007

### nrqed

well, the vertical acceleration is zero so the net vertical force is zero, right?
This means that there must be an other force upward which cancels gravity (well, there could be in general several other forces but it turns out here that there is only one other vertical force, acting straight up).

Now, picture the situation and think: what could be the force acting straight up??

9. Jul 31, 2007

my only guess is that friction is preventing the person from flying out of the cylinder or falling out from under it.

10. Jul 31, 2007

### nrqed

Let's tackle these two questions one at a time. It's clear that friction plays a role here but the question is: in what direction is the friction force acting?

11. Jul 31, 2007

okay...if friction isn't acting upwards, that means that friction is acting towards the right right?

12. Jul 31, 2007

### nrqed

Well, if friction is not acting upward, what force could be acting upward to cancel the force of gravity?

13. Jul 31, 2007

okay. no normal force, gravity we already have. not friction in that direction. what other forces are there? acceleration is not a part of the diagram. is there tension? no...that can't be it.

14. Jul 31, 2007

### nrqed

I never said there was no normal force

There is a normal force. And there is friction. The trick is to figure out in what directions they are acting. Can you tell?

15. Jul 31, 2007

really....alright...so if the normal force isn't acting up...does that mean that it's acting down? ...trying to push the person down? but i don't understand how that would make sense.

16. Jul 31, 2007

OR..since the normal force is a contact force, does that mean that the normal force is between the person and the cylinder?

17. Jul 31, 2007

### nrqed

You must recall a basic property of a normal force. First, why is it called a normal force in the first place? why the adjective "normal"?

18. Jul 31, 2007

normal means a force caused by contact perpendicular to the contact surface. so that does mean that the normal force is between the person and the cylinder right?

19. Jul 31, 2007

### nrqed

Yes, a normal force is always perpendicular to the surface. And it points away from the surface. In your drawing, the wall i sto the right of the person so the wall pushes left.

What about friction now? In what direction is the friction force between an object and a surface?

20. Jul 31, 2007