Centripetal force equation help

[cheez]

You are standing 39 feet from the center of a massive turnable which is rotating at 0.022 revolutions per second. If you try to walk to the centre of the turn table it will turn faster and faster till you slip and slide off. How many feet from the center will you be when you slip if your shoes have a coefficient of friction of 0.36?

I have set up an equation like this:
v= r x omega
mu x m x g = m v^2 /r


but I didn't get the answer, which is 15.7.
Is the setting right? If not, can anyone show me the right steps?
thx!

 

[vaishakh]

Your equations are correct. Show your calculations. Probably your omega valuemight not be perfect.

 

[cheez]

Your equations are correct. Show your calculations. Probably your omega valuemight not be perfect.

v= r x omega

= (39 ft) x (0.022 rev/s) x ( 2 pi / 1 rev)

=5.391 ft/ s

mu x m x g = m x v^2 / r

mu x g = v^2/ r

(0.36) (32 ft/s^2) = (5.391 ft/s) ^2 /r

r= 2.5 ft

but the answer if 15.7

 

[Doc Al]

Your equations are correct for finding the distance from the center where the centripetal force just equals the maximum static friction for a given angular speed. But note that the problem says:

If you try to walk to the centre of the turn table it will turn faster and faster till you slip and slide off.

You need to figure out how the angular speed increases as you walk towards the center. This requires additional information (the masses involved, for example); did you leave anything out of the problem statement?

 

[cheez]

Your equations are correct for finding the distance from the center where the centripetal force just equals the maximum static friction for a given angular speed. But note that the problem says:
You need to figure out how the angular speed increases as you walk towards the center. This requires additional information (the masses involved, for example); did you leave anything out of the problem statement?

no, I have typed the whole question.

 

[Doc Al]

no, I have typed the whole question.

Then I don't see how you have enough info to solve the problem. If you assume that the turntable is massive enough that the person's walking does not affect its angular speed (which seems to contradict what was stated in the problem), then only by walking away from the center will you get to a point where the required centripetal force is greater than friction can provide.

Note that in your last post you calculated the speed at 39 ft and used it to solve for a different distance. That doesn't make sense. If anything, the angular speed would remain fixed, not the tangential speed (which depends on the distance from the center).

 

[Tide]

Perhaps the OP meant "massless turntable?"

 

[Doc Al]

Good thinking, Tide! That will get the answer they want.