..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 Newton and a track offers a friction force of 5000 Newton then calculate :

a} the net accelerating force

b} the acceleration of the train ; and

c} the force of Wagon 1 on wagon 2

..Answer..

Given ,

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

Fa = 40000 N 5000 N

Fa = 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 x 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 x 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 x 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-2 is 28000 N.

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