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 (c)the force of wagon 1 on wagon 2.

Answer:

Given parameters

Mass of the engine (M) = 8000 kg

Number of wagons = 5

Mass of the wagons (m) = 2000 kg

Force exerted by the engine (F ) = 40000 N

Frictional force offered by the track (Ff) = 5000 N

(a) Net accelerating force (Fa) = F – Ff

F= 40000 N – 5000 N

F= 35000 N

(b) Let us consider the acceleration of the train be a m/s2

Acceleration is the ratio of net acceleration force by mass, i.e

a = Fa/m

Where m is the mass of the train, it can be calculated as follows

Total mass of the train (m) = Mass of the engine + (Mass of the wagons  × Number of wagons)

m = 8000 + (5 × 2000)

m = 18000 kg

Acceleration of the train (a) = 35000/18000

a = 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 aw

35000 = 5m × aw

aw = 35000/5m

aw = 35000/(5 × 2000)

aw = 3.5 m/s2

Then the mass of last four wagons can be considered as mw

mw = 2000 × 4

mw = 8000 kg

Now let us calculate the net force on the last four wagons

F’ = mw× aw

F’ = 8000 × 3.5

F’ = 28000 N

∴ The force of wagon-1 on the wagon-

 

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