Frictional coin sliding on turntable

[Umphreak89]

A 5.0 g coin is placed 22 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of µs = 0.80 and µk = 0.50. What is the maximum rpm that the turntable could speed up to without the coin sliding off?
m = .005 kg
r = .22 m
µs = 0.8

Equations found..
v = angular velocity * r
Force(net) = m(v)^2 / r

Inertia > µs N when coin slips (?)

I believe this gets set equal to mg (Normal Force) but I haven't been able to generate the correct answer multiplying µs as a coefficient of either side.

I'm not sure what isn't being accounted for, what do I do?

 

[Doc Al]

You're heading in the right direction. Answer these questions:
(1) What force provides the centripetal force on the coin?
(2) What's the maximum value of that force?

Use that maximum value of force in your centripetal force equation to calculate the maximum speed. Then express that answer in rpm.

Do Not Double Post!

 

[ogb p]

I would approach this problem by first identifying the key variables and equations involved. From the given information, we know that the coin has a mass of 0.005 kg and is placed 0.22 m from the center of the turntable. We also have the static coefficient of friction (µs = 0.8) and kinetic coefficient of friction (µk = 0.5).

Using the equations you have already identified, we can calculate the maximum angular velocity (ω) of the turntable before the coin starts to slide off. This can be found by equating the centrifugal force (mω^2r) to the maximum static friction force (µsN) where N is the normal force.

mω^2r = µsN

We can also express the normal force in terms of the weight of the coin (mg) since the coin is placed on a horizontal surface.

N = mg

Substituting this into the equation above, we get:

mω^2r = µsmg

Solving for ω, we get:

ω = √(µsg/r)

Plugging in the given values, we get:

ω = √(0.8*9.8/0.22) = 5.57 rad/s

To convert this to rpm, we multiply by 60/2π, giving us a maximum rpm of approximately 503 rpm.

In conclusion, the maximum rpm that the turntable could speed up to without the coin sliding off is 503 rpm. This calculation assumes that the turntable is accelerating uniformly and that the coin is placed at the edge of the turntable. Any changes in these conditions could affect the maximum rpm.