# Homework Help: Tension with a with a massless rope

1. Oct 23, 2008

### kbka

Hi...

I have a little assignment where I'm not quite sure, what would be the correct answer...

A massless pulley, is mounted to the ceiling with a massless rope. Over the pulley runs another massles rope, with a box with mass m in one end and a box with mass 2*m in the other.

Q1) In this first question, the friction holds the whole system in equilibrium.
What is the tension T0 between pulley and ceiling, T1 between pulley and box with mass m, T2 between pulley and box with mass 2*m

A1: T1=m*g, T2=2*m*g and T0=(m*2m)*g=3*m*g

Q2) Now, friction is negligible, and the system starts to move... What is the tension T0, T1 and T2
A2: I have calculated T1=T2=4/3*mg and T0=3*m*g (still)

Is the last answer for T0 correct? My assumption is that this part of the system (pulley+rope) is still in equilibrium, and therefore Fres=m*g-T=0

2. Oct 23, 2008

### LowlyPion

Re: Tension

If T1 + T2 = T0, then isn't T0 = 8/3mg ?

3. Oct 23, 2008

### kbka

Re: Tension

Thank you for the reply, but i highly doubt that's the case... I have drawn the situation to make it more clear...

4. Oct 23, 2008

### LowlyPion

Re: Tension

Is it your suggestion then that T1 + T2 ≠ T0 ?

Looks to me like T1 = m*(g + 1/3g) = T2 = 2m*(g - 1/3g)

2*T1 = 2*T2 = 8/3*m*g = T0