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Shreya your question answerA 8000 kg engine pulls A train of 5 wagons each of 2000 kg , along a horizontal track if the engine exerts a force of 40000 Newton and a track offers a friction force of 5000 Newton then calculate :a} the net accelerating forceb} the acceleration of the train ; andc} the force of Wagon 1 on wagon 2Sol:-Given parametersMass of the engine (M) = 8000 kgNumber of wagons = 5Mass of the wagons (m) = 2000 kgForce exerted by the engine (F ) = 40000 NFrictional force offered by the track (Ff) = 5000 N(a) Net accelerating force (Fa) = F – FfFa = 40000 N – 5000 NFa = 35000 N(b) Let us consider the acceleration of the train be a m/s2Acceleration is the ratio of net acceleration force by mass, i.ea = Fa/mWhere m is the mass of the train, it can be calculated as followsTotal mass of the train (m) = Mass of the engine + (Mass of the wagons × Number of wagons)m = 8000 + (5 × 2000)m = 18000 kgAcceleration of the train (a) = 35000/18000a = 1.944m/s2(c) The external force is only applied to waggon 1 directly. On the last four waggons, the net force is equal to the force added to waggon 2 by waggon 1.Let us consider the acceleration of the wagons is aw35000 = 5m × awaw = 35000/5maw = 35000/(5 × 2000)aw = 3.5 m/s2Then the mass of last four wagons can be considered as mwmw = 2000 × 4mw = 8000 kgNow let us calculate the net force on the last four wagonsF’ = mw× awF’ = 8000 × 3.5F’ = 28000 N∴ The force of wagon-1 on the wagon-2 is 28000N. |
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