2 weights on a pully, show formula

[man_in_motion]

Homework Statement

The apparatus (see link to image) is used to measure the free fall acceleration g by measuring the acceleration of the two blocks connected by a string over a pulley. Asume a massless, frictionless pulley and a massless string.
http://img3.imageshack.us/img3/3459/phys.th.png
a) draw a free body diagram of each block
http://img16.imageshack.us/img16/3523/diagrams.th.png
b)use the free body diagrams and Newton's laws to show that the magnitude of acceleration of either block and tension in string are a=(m₁-₂)/(m₁+₂)
c)do these expressions give reasonable results if m₁=m₂ in the limit that m₁ >> m₂ and in the limit that m₁ << m₂ ? Explain

Homework Equations

F_net=ma
F_g=mg

The Attempt at a Solution

F=ma
T_1=-T_2
T_2=(m_2)g
T_1=(m_1)g
=>m_1(g)=-m_2(g)

 

[rock.freak667]

Assume block one moves downwards, so the resultant force on m₁ is

m₁a=mg-T

So what is the resultant force on m₂?

Now you have two equations in T and a, you can now eliminate T.