Posted by Josh on .
How can I calculate the tension in the two cords that are labeled A and B in a two mass system? Cord A is on top with a 1 kg mass attached and Cord B connects this mass to a 2 kg mass. The two mass system accelerates directly upward at 2m/s^2.

physics 
MathMate,
The diagram looks like this:
UP > T1 <1Kg> T2 <2Kg DOWN
The whole system is accelerating upwards at 2 m/s².
Start with the 2kg mass (m2).
The acceleration is due to T2 in excess of the weight due to the 2kg block, or T2m2.g newtons.
Thus applying F=ma
(T2m2g)=m2(a)
where a is the acceleration of 2 m/s²
Solve for T2
Now similarly consider the m1=1 kg mass.
Net force causing acceleration
=T1m1gT2.
Thus, again
T1m1gT2 = m1(a)
Solve for T1.