what is the tension?, how far does A move in the first 0.290 s?

Question

three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are mA = 27.0 kg, mB = 42.0 kg, and mC = 13.0 kg. When the assembly is released from rest, (a) what is the tension in the cord connecting B and C, and (b) how far does A move in the first 0.290 s (assuming it does not reach the pulley)?

Answer 1

We can assume no friction and uniform acceleration

A FBD of the hanging box shows
27*g-T=27*a in the direction of motion
T is the tension in the core.
Since there is no friction, just combine the other two boxes as a single mass
T=(42+13)*a
plug this into the equation above and solve for a
once you have a, the distance is
s(t)=.5*a*t^2

for the tension between b and c, look at c
T2=13*a
solve for T2

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