# Rolling Motion Question

1. Dec 15, 2006

### ecksee

1. The problem statement, all variables and given/known data

The axle of a uniform solid cylinder of mass m1=7.1 Kg is attached to a string that runs over a massless, frictionless pulley. The other end of the string is attached to a mass m2. The coefficient of static friction between the cylinder and the table is U=0.202. What is the max mass m2 (in Kg) for which the cylinder will roll without slipping?

2. Relevant equations

Torque=I*alpha
F=ma

3. The attempt at a solution
m2
Tension-m2*g=m2*a

a=(Tension-m2*g)/m2

m1

a=2*U*g

System

2*U*g=(Tension-m2*g)/m2

See diagram:

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2. Dec 15, 2006

### cristo

Staff Emeritus
I think you're making this more difficult than it needs to be! The question, worded in another way, is asking for the maximum force that can be exerted on the cylinder so that it rolls and does not slip. [hint: limiting friction]

3. Dec 15, 2006

### Staff: Mentor

Be careful with your signs: The tension is up, but the acceleration is down.
Good. You've applied the condition for maximum static friction to find the maximum acceleration. Now use this to find the corresponding value of m2 that will produce such an acceleration.

You need one more equation: Apply Newton's 2nd law to the translation of m1. Your goal is find m2 in terms of known quantities (not in terms of tension).

4. Dec 15, 2006

### ecksee

I get this equation to be F=ma=T=m1*a

This doesn't really get me anywhere. Am I missing something?

5. Dec 15, 2006

### Staff: Mentor

Right. Now put it to work.

You found the acceleration using your second equation. Combine that result with your first equation and this one to solve for m2. (You'll need to correct the sign error in your first equation.)