# Homework Help: Three Pulleys 3 masses, find tension

1. Dec 9, 2012

### Purple Grind

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

Three objects mI. m2 and m3 are suspended
from three massless and frictionless pulleys as
shown in the diagram. ml is 6 kg, m2 is 2 kg
and m3 is 3 kg. Find the tension of the string
when the system is set in motion (i.e. all
masses are moving). Answer in N

Options are:
(a) 11.3 (b) 12.1 (c) 13.5 (d) 14.2

..O....O...... Top 2 pulleys attached to ceiling, m1 hangs from 1st pulley, m2 is attached
.| |..| |..... to the middle pulley, m3 hangs from third pulley.
.|..O...|
.|..[]..|
[] m2 []
m1....m3

2. Relevant equations
Fg=mg
F=ma

3. The attempt at a solution

I made 3 equations, tried to relate them but I am getting 15.68N instead of any of the options (this was an old exam question). It's too far from 14.2 to be right. Here were the four equations I made:

a1=(m1g-T)/m1
a2=(2T-m2g)/m2
a3=(m3g-T)/m3

2a2=a1+a3

I keep getting none of the possible answers but I think I'm doing it right. Where did I go wrong?

2. Dec 9, 2012

3. Dec 9, 2012

### Purple Grind

a1=(m1g-T)/m1=g-T/m1=g-T/3
a2=(2T-m2g)/m2=2T/m2-g=T-g
a3=(m3g-T)/m3=g-T/m3=g-T/6

From 4th eqn:

2T-2g=g-T/3+g-T/6

2T+T/2=4g

5T/2=4(9.8)

T=15.68

4. Dec 9, 2012

### haruspex

Oh, sorry, I misread the end of your first post. I thought you were getting 14.2. So, I agree with you, it's something around 16.

5. Dec 9, 2012

k thanks