Question

A 1.9 kg mass and a 4.4 kg mass are connected by a massless string over a pulley that is in the shape of a solid wheel having a radius 0.4 m and mass 4.7 kg. Determine the linear acceleration of the blocks. Answer in "m/s^2"

Answer 1

val 12V Page ma) my Imag Writing equation for me and m2 using the Newton I lova_F=ma T - Mg g = mia i Mag-T2 = mza — ii) adding both the. Relation, Ti - m. g + mag-T2 = m, at ma - T-T2 + g (ma-my) = (m. tma) a For Ratational Motion to occur, T. & Tz - For Pulley, and, T27 Torque is quien as, z = (T2-T;) x R ------ > z={I2-T12R

also Pere Torque is given as, where, I is moment = I. a of mentia, and a ia angular (T2-T₂) R = It for disc, I = 1 MR² [moment of Inertic (Te-T) R = IMR² x (T2-T) = (T2-T) = 1 M R² a ₂ M (RX) we know and linear a = &R angular Acceleration acceleration are related as T (T2-T,) = 1 m a putting this result in een (T. -T2) + g (m2-m.) = (m. tme) a - - mat g (ma-my) = (m + m2) a (m + m)a tema = 9 (ma-me) 2

а mitma + M g (ma-m,) = ma-mo) g (m, + m₂ + M) where, m, ; Ma are mass of objects g 4 acceleration due to grauiga M mass of Pulley guen : m, =log Kg m2 = 4.4 kg and, g = 9.8 m/s² M = 4.7 kg (4.4 -1.9 x 9.8 11.g+ 4.4 +4.7) a = 24.5 = 2.83 m/s2 8.65 a = 2.83 m/s² This is the required answer

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