Rotational Motion / Torque problem (what did i do wrong?)

[PsychonautQQ]

Homework Statement

A thin, light wire is wrapped around the rim of a wheel,. The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius R = .280m. An object of mass m=4.2kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration. If the suspended object moves downward a distance of 3m in 2s what is the mass of the wheel?

Homework Equations

Idisk = 1/2mr^2
τ=Iα
αr=a
1/2at^2=x

The Attempt at a Solution

First I figured out the acceleration of the block with 1/2at^2=x. With x = 3 and t = 2 you get a=6/4.
Then i set up τ=Iα=1/2*mw*r^2*(a/r)=mb*g*r
(mb = mass bock and mw = mass wheel, i also substituted a/r for α.

This equation reduces to 1/2*mw*a = mb*g
with a = 6/4 we get
6/8*mw = mb*g
mb is given at 4.2 so mw equals 55kg which is wrong. What am I doing wrong? The answer key has them giving the answer using energy equations which is all fine and good, but I'm confused why this isn't working.

 

[barryj]

I think you are on the right track. Do you know the correct answer?
You have a correct at 1.5. Alpha = a/r. T = I X alpha. Find the torque. Knowing the acceleration of the 4.2 kg mass you can find the tension in the string. The tension will give you the torque. Plug in and you should be successful.

From your incorrect answer of 55kg, it seems that you did not calculate the tension in the wire correctly. Draw a FBD of the block show the mg and the T and using the acceleration find the T correctly.

 

[haruspex]

Then i set up τ=Iα=1/2*mw*r^2*(a/r)=mb*g*r

That last part is wrong. Let the tension in the wire be T, and treat the forces on and acceleration of the wheel separately from those on the block .

 

[harts]

The tension in the string, which is the source of torque for this scenario, is not equal to m_b*g. Remember that the acceleration that you calculated wasn't g.