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On a horizontal table, block A (2 kg) and block B (3 kg) rest in…

Question

On a horizontal table, block A (2 kg) and block B (3 kg) rest in line, joined by a light string (A behind B). A second light string runs from B horizontally to a frictionless pulley at the table edge and down to a hanging block C (5 kg). The coefficient of friction between the table and each of A and B is 0.20; the hanging side is friction-free. The system is released from rest. Taking g = 10 m/s^2, find the tension (in newtons) in the string connecting A and B.

✓ Verified answer: 12checked by our engine — not a guess

Step-by-step solution

Treat the whole system: driving force = weight of C = 50 N; opposing friction on A and B = mu(mA+mB)g = 0.2*5*10 = 10 N.

Total mass = 2+3+5 = 10 kg.
Acceleration a = (50 - 10)/10 = 4 m/s^2.

For block A alone, the only forward pull is the A-B string tension T_AB, opposed by its friction mu*mA*g = 0.2*2*10 = 4 N: T_AB - 4 = mA*a = 2*4 = 8, so T_AB = 12 N.

Final answer12

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