Solving Newton's Law: Calculating Acceleration and Force in a Pulley System

[newcool]

Hi, I have been given this problem to do as extra credit:

An inventive child named Pat wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley, Pat pulls on the loose end of the rope with such a force that the spring scale reads 250 N. Pat’s true weight is 320 N, and the chair weights 160 N.

Show that the acceleration of the system of Pat and the chair is upward and find its magnitude.

Find the force Pat exerts on the chair.

Diagram:
http://www.geocities.com/newc00l/physics.html

I made 3 free body diagrams, but am stuck.

Thanks in advance for any help.

 

[Moose352]

Can you show us your free body diagram?

 

[newcool]

I don't have access to a scanner so Ill try to draw them as best as I can:


T
^
|
Pat - A ^
|
\/
480 N


T
^
Spring scale - A \/
\/
250 N

T
^
Pat on Chair -A \/
\/
X

Are these right? What would the proper equations be?

Thanks