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In Fig. 5-46, 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.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 0.250 s (assuming it does not reach the pulley)?
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(a) 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
$$m_Cg - T_{BC} = m_Ca$$.
This leads to $$T_{BC} = 36.8\, N$$.
(b) We use Eq. 2-15 (choosing rightward as the +x direction): $$\Delta x = 0+\frac {1}{2}at^2= 0.191 \, m$$
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