The 4 kg mass will accelerate down with accelerationsay.If we assume the 2 kg mass also accelerates down, withacceleration
say,the 1 kg mass will accelerate up with acceleration
Ifwe are wrong about the direction of any of the accelerations, thatacceleration will come out negative. With these assumption, we canlabel the diagram as below.
Applying
For the 2 kg mass: (1)
For the 1 kg mass: (2)
For the 4 kg mass: (3)
(1)-(3) gives (4)
2*(1) + (2) gives (5)
5*(4)+(5) gives
Substitute this into (4) to give
From (1)