Tension At Two Points With Acceleration

[myxomatosii]

Hi, I am here to ask a check to my work, I think that I have the idea down but I would like if someone could look over my concept and see if I am seeing things right as on my homework I used 3/5 of my attempts at the solution brashly without thinking, like a moron, I would like to check my next attempt here before I apply it there.

Homework Statement

A house painter uses the chair and pulley arrangement of Figure P8.42 to lift himself up the side of a house. The painter's mass is 90 kg and the chair's mass is 10 kg. With what force must he pull down on the rope in order to accelerate upward at 0.20 m/s^2?

http://img27.imageshack.us/img27/8056/p842.gif

Homework Equations

I believe the only formula needed is simple F=MA. F being the force of Tension. So I will say T=MA.

The Attempt at a Solution

First, forget the pully, man and chair.

Its just a mass of 100kg pulling itself up from a support point by another support point.

I believe to solve the problem I should take the acceleration(a) which I am trying to cause on the mass(M) and add it to the acceleration due to gravity(g), causing the total(A) to be 10.0m/s^2.

There, we have A and M. Simple.

The equation we could use to write this problem out (if we so chose at this point) would be.

2T=M(g+a) therefore T=(M(g+a))/2

Which gave me 500N.

I can't find a logic flaw, hopefully if there is one then you can.

 

[redargon]

seems ok to me