Question

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.

Answer 1

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 T2-m2.g newtons.
Thus applying F=ma
(T2-m2g)=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
=T1-m1g-T2.
Thus, again
T1-m1g-T2 = m1(a)
Solve for T1.