Minimum coefficient of static friction problem

[mrknowknow]

Homework Statement

I know the diameter is 30 m and the radius is 15
The period for one revolution I suppose is some multiple of 7.03

Homework Equations

The Attempt at a Solution

I couldn't think of an equation where friction was involved where rotational motion was concerned. I used 2pir/7.03 to answer b but of course it was wrong.

 

[BOYLANATOR]

There is a downward force due to gravity which is balanced by a frictional force. This frictional force is proportional to the central force caused by the rotation (the constant of proportionality is the friction coefficient. Can you find an equation for the central force?

 

[mrknowknow]

F=μ_kn ?

 

[BOYLANATOR]

F=μ_kn ?

This equation will be used. But first you must calculate the central force. It is given by
F=m v² / R. This gives the force normal to the rotating surface.

 

[mrknowknow]

So the central force is the same as the centripetal force?

 

[BOYLANATOR]

So the central force is the same as the centripetal force?

Yes. Different names for the same thing

 

[mrknowknow]

okay because I've never heard central force. So how can I use that equation when I don't know the mass or velocity?

 

[BOYLANATOR]

okay because I've never heard central force. So how can I use that equation when I don't know the mass or velocity?

You know that he returns to the same point after 7.03 seconds. How far has he travelled? So what was his speed?

Leave mass in as an unknown for now. Maybe you will have to deal with it later, maybe not...

 

[mrknowknow]

how do I calculate how many rotations he made in 7.03 seconds or do I assume it was one?

 

[BOYLANATOR]

I would assume it's 1.

 

[mrknowknow]

okay so V= (2piR)/t ??

 

[BOYLANATOR]

Yes.

 

[mrknowknow]

okay so the Normal force is equal to mass * acceleration, a= (v^2)/r so N= mv^2 * 1/r ...right?

 

[BOYLANATOR]

Yes that's correct

 

[mrknowknow]

okay friction= μN

μ((mv^2)/r)=mg

m cancels out on both sides and μ=gr/v^2

μ=gr/v^2

μ= ((9.8)(15))/((2∏*15)/(7.03))^2

μ= .818

what about part B??
I really appreciate your help also

 

[BOYLANATOR]

Is the guy accelerating downward? So is there a vertical force acing on the guy? You have worked out the equation for the centripetal force (or acceleration), how fast would he have to be going for this force to equal 4 G's?

 

[mrknowknow]

I don't understand what 4 G's is...how would I know if he is accelerating downward?

 

[BOYLANATOR]

G is the gravitational acceleration at the Earth's surface. i.e 9.8 m/s^2.

What would be the consequence of accelerating downward in a room with no floor? Does this happen to the man?

 

[mrknowknow]

oh okay I didn't deduce that from the question, don't laugh at me but I thought he was referring to the price of the special suit at 4g's meaning $4000. This question totally doesn't make any sense to me. The consequence of accelerating downward in a room with no floor would be a fall right? Where would I find the clue to tell if it had happened to the man.

 

[mrknowknow]

so actually it's 4*9.8?

 

[BOYLANATOR]

Haha. He remains stuck to the wall, so he hasn't fallen out of the ride. If people fell out, they wouldn't allow these rides. So the only force acting on him is the centripetal force.

What speed does he need to go for this to be equivalent to 4G?

 

[mrknowknow]

(v^2)/r=4(9.8) right?

 

[BOYLANATOR]

Sounds good to me.