The diagram above shows two identical masses, M1 and M2 of mass m each, attached by a string hung over a light frictionless pulley. M1 hangs in mid air while M2 rests on a smooth inclined slope that forms an angle of 30° to the horizontal. Calculate:
(a) The acceleration of the system.
(b) The tension in the string (in terms of m)
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Answer:
Let the tension in the string be T, and the acceleration of the system be a
Weight of each mass = mg = 10 m N
Consider free body diagram of M2:
T - 10 m sin 30° = ma ------------------- (1)
Consider free body diagram of M1:
10 m - T = ma ------------------- (2)
(a)
(1) + (2): 10 m - 10 m sin 30° = 2 ma
2a = 5
a = 2.5 ms-2
(b)
(1) - (2): 2T = 10 m sin 30° + 10m
T = (7.5 m) N
