  Question

A $$8000$$kg engine pulls a train of $$5$$ wagons, each of $$2000$$kg, along a horizontal track. If the engine exerts a force of $$40000$$N and the track offers a friction force of $$5000$$N, then calculate:$$(a)$$ The net accelerating force:$$(b)$$ The acceleration of the train; and$$(c)$$ The force of wagon $$1$$ on wagon $$2$$.

Solution

Given :    Mass of engine    $$M = 8000$$ kg                Mass of each wagon    $$m =2000$$ kg                Frictional force acting in backward direction    $$f = 5000$$ N(a)  :   The net force acting on the train  $$F' = F - f = 40000- 5000 = 35000$$ N(b)  :     Let the acceleration of the train be  $$a$$         $$\therefore$$    $$F' = (5m+M) a$$            $$35000 = (5\times 2000+ 8000) a$$          $$\implies a =1.944$$  $$ms^{-2}$$(c)   :    External force is applied directly to wagon 1 only. The net force on the last four wagons is equal to the force applied by wagon 2 by wagon 1.             Let the acceleration of the wagons be  $$a'$$              $$35000 = (5m) a'$$            $$\implies 35000 = 10000 \times a'$$           Acceleration of the wagons      $$a' = 3.5$$ $$ms^{-2}$$           Mass of last 4 wagons     $$m' = 4 \times 2000$$ kg      $$\therefore$$  Net force on last 4 wagons     $$F_1 = 8000 \times 3.5$$ $$= 28000$$ NThus force on wagon 2 by wagon 1 is 28000 N.ScienceNCERTStandard IX

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