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16. Two bodies of masses m, and m2 are connectedbt string which passes over a frictionless,massless pulley. If the pulley is moving upward withuniform acceleration, then tension in the string willbe2m, + m24m,m2m,m23m.m22m,m2m +m+ m2 |
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Answer» Let m2 > m1. Consider the masses m₁ and m₂, with forces Tension T in the string upwards and their weights downwards, acting on them. Both of these masses are moving with same acceleration a up (m1) or down (m2 as m2>m1), asthe string is tight and has a uniform tension all along its length. This explanation is valid in the frame of reference of moving pulley with an acceleration g/2 upwards. In the frame of reference of pulley, with an acceleration g/2 upwards, the two masses are having acceleration a and -a. To balance forces in this non-inertial frame, we need to add a fictitious force of m₁g/2 downwards on m₁ and -m₂ g/2 downwards on m₂. Then we write free body diagrams and apply Newtons' laws. T - (m₁ g +m₁ g/2) = m₁ a => T - 3 m1*g/2 = m1 a (m₂ g +m₂ g/2) - T = m₂a => 3 m₂*g/2 - T = m₂ a Add the two equationsto get a = (3g/2) *(m₂- m₁) / (m₁ + m₂) then, T = 3m₁ g/2 + m₁ a = 3 m₁m₂ g / (m₁ + m₂) |
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