# Torque with a pulley of radius R and mass M

• holmeskaei
In summary, the conversation discusses the setup of two blocks connected by a massless string over a frictionless pulley, with one block sliding on a horizontal, frictionless surface. The conversation then goes on to solve for the acceleration of the blocks and the tension in the string using various equations for torque and force. The final part of the conversation involves taking into account the mass and radius of the pulley and adjusting the equations accordingly.

## Homework Statement

Blocks of mass m_1 and m_2 are connected by a massless string that passes over the pulley in the figure (Intro 1 figure) . The pulley turns on frictionless bearings, and mass m_1 slides on a horizontal, frictionless surface. Mass m_2 is released while the blocks are at rest.

http://session.masteringphysics.com/problemAsset/1073792/5/12.P71.jpg

I figured out A and B.
A. Assume the pulley is massless. Find the acceleration of m_1.
a=(m2g)/(m2+m1)
B. Find the tension in the string.
T=m1(m2g/m2+m1)
C. Suppose the pulley has mass m_p and radius R. Find the acceleration of m_1. Verify that your answers agree with part A if you set m_p=0.

D. Find the tension in the upper portion of the string. Verify that your answers agree with part B if you set m_p=0.

E.Find the tension in the lower portions of the string. Verify that your answers agree with part B if you set m_p=0.

## Homework Equations

torque=Fxd
torque net=sum of all forces
T1=m1a+m1g
T2=m2a+m2g
torque net=T1r-T2r=(-a/r)I

## The Attempt at a Solution

I know that the tensions change because of the mass and radius of the pulley, but I don't know what it does. I made a FBD, but I don't know what to do with my equations... I don't get it.

holmeskaei said:
T1=m1a+m1g
The weight acts vertically; just consider horizontal forces on m1. (Vertical forces cancel.)
T2=m2a+m2g
Assuming "a" is a positive number, it looks like you have the signs wrong.
torque net=T1r-T2r=(-a/r)I
OK. But what's I for the pulley? (Maybe you can treat it like a uniform disk.)

Correct these equations and solve simultaneously.