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Two blocks, one of mass M and one of mass 3M, are connected by a massless string over a pulley that is a uniform disk of mass 2M and moment
Question
Two blocks, one of mass M and one of mass 3M, are connected by a massless string over a pulley that is a uniform disk of mass 2M and moment of inertia MR^2. The two masses are released from rest, and the masses accelerate as the pulley rotates. Assume there is negligible friction between the pulley and the axle. What is the linear acceleration, a, of the masses?
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Physics
3 years
2021-09-04T11:33:11+00:00
2021-09-04T11:33:11+00:00 1 Answers
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Answers ( )
Answer:
4.9 m/s²
Explanation:
Let T be the tension in the string
If a is the linear acceleration in the direction of the 3M mass, the equation of motion on the 3M mass is
3Mg – T = 3Ma (1)
Since the mass M moves upwards, its equation of motion is
T – Mg = Ma (2)
From (2)
T = Ma + Mg
substituting T into (1), we have
3Mg – (Ma + Mg) = 3Ma
3Mg – Ma – Mg = 3Ma
collecting like terms, we have
3Mg – Mg = 3Ma + Ma
2Mg = 4Ma
dividing both sides by 4M, we have
2Mg/4M = 4Ma/4M
g/2 = a
a = g/2
Since g = 9.8 m/s²,
a = 9.8 m/s²/2
a = 4.9 m/s²