A 8000 kg engine pulls a train of 5 wagons each of 2000 kg along a horizontal track. If the engine exert force of 40,000N and track exert friction force of 5000 N, then calculate (i) Net accelerating force (ii) Acceleration of a train and (iii) force of wagon 1 on wagon 2 ?
Answers
Explanation:
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
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 + 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-2 is 28000N.