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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     $$F_1 = 8000 \times 3.5$$ $$= 28000$$ N
Thus force on wagon 2 by wagon 1 is 28000 N.

Science
NCERT
Standard IX

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