How Far Does the Mass Fall Before the Dime Slides Off the Disk?

[kornwestheim]

Okay here is the problem.
A metal disk ( mass 250g , radius12 cm) is free to rotate about frictionless vertical axle through its center. The axle itself has negligible mass and a radius of 2 cm. A string wrapped around the axle passes over an ideal pulley to a hanging 85 g mass. A dime ( mass 2 g) sits on the edge of a metal disk. The statis coefficient of friction between the dime and the metal disk is u= 0.250.
The 85g mass is released from rest and beginns to fall. How far does it fall before the dime slides of the disk?

I have a hard time to setup the equation.
Any hint or help is appriciated

 

[kornwestheim]

This is what I tried so far

Ui+Ki=Uf+Kf
mgh= (1/4 M(R squared) +m(r squared) +1/2m(V squared) +

I am not sure if this is complete since I can’t figure out if the dime has also final potential energy and also how to add the friction in this
I know for dime that n=mg and that Ffr= u*mg but how should I know the h height when the system starts to move.
If I try to calculate the angular velocity I am still having one unknown ( h) but even if I would know I am not sure how to relate the angular velocity with Ffr.
If I try via torque I don't have the angular accel ?

 

[kornwestheim]

Is there anyone to help me on this one ??

 

[Doc Al]

Start by figuring out the maximum rotational speed that the disk can have before the dime starts to slide off. Hint: Consider that static friction is providing the centripetal force.

Once you have that, then use conservation of mechanical energy to determine how far the falling mass drops.

 

[kornwestheim]

Thanks Doc Al,

Can you check work I did to see if I did it right

 

[Doc Al]

Can you check work I did to see if I did it right

Some comments. First, you seem to confuse tangential acceleration with radial acceleration. Second, you use the same symbol (m) to represent both the 85g and 2g masses. Third, you stopped too soon: Your final answer should not be in terms of v or $\omega$. (What's the relationship between them?)

 

[kornwestheim]

Some comments. First, you seem to confuse tangential acceleration with radial acceleration.
Second, you use the same symbol (m) to represent both the 85g and 2g masses. Third, you stopped too soon: Your final answer should not be in terms of v or $\omega$. (What's the relationship between them?)

I am not quite sure what do you mean with confusion of radial and tangetinal acceleration. I know I acctually did not need the radial accel., but I needed the tangential to find the angular velocity ( ar= r *omega ^2) This is was actually only part I was not quite sure about. Is this relationship cvorrect?
And, Yes I was a little bit careless with subscripts of masses.
The relationship between them them is v= r*omega.

 

[Doc Al]

I am not quite sure what do you mean with confusion of radial and tangetinal acceleration. I know I acctually did not need the radial accel., but I needed the tangential to find the angular velocity ( ar= r *omega ^2) This is was actually only part I was not quite sure about. Is this relationship cvorrect?

This is just my point. You need radial acceleration, not tangential. But, yes, radial acceleration is given by $a_r = \omega^2 r$.

The relationship between them them is v= r*omega.

Yes--just be sure to use the correct radius.

 

[kornwestheim]

This is just my point. You need radial acceleration, not tangential. But, yes, radial acceleration is given by $a_r = \omega^2 r$.


Yes--just be sure to use the correct radius.

Thanks Doc Al