2 weights on a pully, show formula

1. Sep 30, 2009

man_in_motion

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

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 [Broken]
a) draw a free body diagram of each block
http://img16.imageshack.us/img16/3523/diagrams.th.png [Broken]
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

2. Relevant equations

Fnet=ma
Fg=mg

3. 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)

Last edited by a moderator: May 4, 2017
2. Sep 30, 2009

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.