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

 

[nlightner]

Hello, it seems like you have the right idea for solving this problem. You correctly identified that the force of tension (T) is equal to the mass (M) multiplied by the total acceleration (A), which is the sum of the acceleration caused by the force you are pulling with (a) and the acceleration due to gravity (g). Your equation, T = (M(g+a))/2, is correct and the resulting answer of 500N is also correct.

One suggestion I have is to make sure you are consistent with your units. In your equation, you used m/s^2 for acceleration, but in the problem statement, the acceleration is given in m/s^2. It would be clearer to use the same units in your equation and state the final answer as 500N instead of 500kg*m/s^2. Additionally, it's always a good idea to include units in your calculations to avoid any confusion.

Overall, it seems like you have a good understanding of the concept and have solved the problem correctly. Just be careful with units and make sure to double check your work before submitting it. Keep up the good work!