In Fig. 5-31, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The three masses are `m_(A)=30.0` kg, `m_(B)=40.0` kg, and `m_(c)=10.0` kg.
(a) When the assembly is released from rest, what is the tension in the cord connecting B and C?
(b) When the assembly is released from rest, how far does A move in the first 0.250 s (assuming it does not reach the pulley)?

Explanation

We use Newton.s second law of motion to find the tension.
Calculation: The net force on the system (of total mass M = 80.0 kg) is the force of gravity acting on the total overhanging mass `(m_(BC)=50.0" kg")`. The magnitude of the acceleration is therefore `a=(m_(BC)" g")//M=6.125" m"//"s"^(2)`. Next we apply Newton.s second law to block C itself (choosing down as the +y direction) and obtain
`m_(C)g-T_(BC)=m_(C)alpha`.
This leads to `T_(BC)=36.8" N"`.
(b) When the assembly is released from rest, how far does A move in the first 0.250 s (assuming it does not reach the pulley) ?
Calculation: We use equation of motion (choosing right ward as the +x direction):
`Delta x=0+(1)/(2)at^(2)=0.191" m"`.