(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A block of mass m1 = 2 kg rests on a table with which it has a coefficient of friction µ = 0.53. A string attached to the block passes over a pulley to a block of mass m3 = 4 kg. The pulley is a uniform disk of mass m2 = 0.4 kg and radius 15 cm. As the mass m3 falls, the string does not slip on the pulley.

With what acceleration does the mass m3 fall?

Hint: For each block, apply Newton's 2nd law. For the pulley, apply the rotational analog of Newton's 2nd law. And remember that since the string does not slip on the pulley, there is a relationship between the acceleration of the blocks and the angular acceleration of the pulley. You will end up with three equations and three unknowns (the answers to a,b,c). EDIT: is pulley -> (1/2)m*r*a = T3-T1?

2. Relevant equations

Kinematics

3. The attempt at a solution

I believe I created the correct formulas for each mass.

Block 1: T_{1}- Frictional Force = m*a

Block 3: m_{3}*g - T_{3}= m*a

Pulley 2: Torque = I*alpha -> Torque = (1/2)m_{2}*r*a

I'm however not sure if these are correct, but more importantly, how I would combine them in order to find the acceleration of the falling mass.

I realize that I need 3 equations and unknowns (T1, T2, and a). I believe my Pulley isn't correct because it also has T. Is my assumption correct? And, How would I change the pulley equation so that it works?

EDIT: I believe now that my pulley should be, (1/2)m*r*a=T3 - T1. Is this correct?

EDIT: Still having trouble. Using my above assumptions I came up with this: (m3*g-m1*g*u)/(m3+m1+.5*m2*r)=a

This unfortunately still doesn't work. Any help would be much appreciated, I'm really trying my hardest to figure this out. :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear and Rotational Kinematics System.

**Physics Forums | Science Articles, Homework Help, Discussion**