Can someone help me figure this out?

[curiousgeorge99]

Homework Statement

How many revolutions per minute would a 15m diameter Ferris wheel need to make for a person to feel 'weightless' at the topmost point?

Homework Equations

F= mv~2/r - mg
v = 2pi r/ T

The Attempt at a Solution

I get 8.57 m/s using the equation F= mv~2/r - mg
I think I need to use v = 2pi r/ T to figure out T. If I do this, I get T=5.49. I have no idea if this is right. If it is, then I'm not sure what 5.49 represents and how to turn it into rev/minute. The answer is supposed to be 11 rev/min.

 

[ice109]

do you know what the relationship between V and \omega is?

 

[curiousgeorge99]

V = displacement / time elapsed,

W = number of radians / second

Is that right?

Acceleration is A = change in velocity / change in time
Angular accel. A = change in # of radians / change in time.

This is about all I know. I'm not sure how they are related or how you get rev/min from here.

Its probably staring me right in the face but I still can't see it

 

[sam1]

You are on the right track with mv^2/r = mg, but that solves for the linear/tangential velocity (in m/s). Remember to convert that to angular velocity (rad/s) on your way to finding rpm.

 

[ice109]

v=r\omega

do you know the relationship between \omega and rev/min?

 

[curiousgeorge99]

Is the relationship between W and rev/min: 0.1047 rad/s = 1 rev/min.

 

[ice109]

Is the relationship between W and rev/min: 0.1047 rad/s = 1 rev/min.

yes, do you know why?

 

[curiousgeorge99]

No, no idea why. I just have that at the front of my textbook.

 

[ice109]

No, no idea why. I just have that at the front of my textbook.

2 * \pirad/s = 1rev/s right? cause 2 * \pi is the whole circle

 

[curiousgeorge99]

ok, that makes sense!

thanks

I'm going to see if I can solve this problem now.

 

[curiousgeorge99]

nope, still lost!

I think I'm stuck on where to start.

I keep trying to figure out the velocity in m/s then convert to rev/min.

Is there a better way to do it?

 

[BMWPower06]

i have the same problem...

 

[BMWPower06]

can any1 help?

 

[esalihm]

try to do a free body diagram showing all forces when the person is at the top of the ferris wheel
then equate them
one of them will have what u want in it
and u are provided with what u don't know in the question

let us know if u still can't get it