In the figure here three ballot boxes are connected by cords, one of which wraps

Question

In the figure here 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 = 25 kg, mB = 44 kg, and mC = 12 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 0.200 s (assuming it does not reach the pulley)?

In the figure here 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 = 25 kg, mB = 44 kg, and mC = 12 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 0.200 s (assuming it does not reach the pulley)?

Explanation / Answer

For motion of box A,

T1 =25a...................(1)

For motion of box B,

44g + T2 -T1 =44a....(2)

For motion of box C,

12g - T2 = 12a..........(3)

Adding equations(1),(2) and (3)

56g =81a

a =56*9.8 / 81

a = 6.775 m/s^2

From equation (3)

T2 = 12 (g -a )

T2 = 12(9.8 - 6.775)

T2 = 36.3 N

(a)The tension in the cord that connects boxes B and C is 36.3 N

For b).

box A move in the first 0.200 s a distance =s = (1/2)at^2

s = 0.5*6.775*(0.200)^2=0.1355 m

(b)Box A moves 0.1355 m in the first 0.200 s

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