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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 after a friction force of 5000 N then calculate:
(i) the net accelerating force.
(ii) the acceleration of the train, and
(iii) the force of wagon 1 on wagon 2
Engine mass M = 8000 KG
Mass of 1 waggon m = 2000 kg
Mass of 5 waggon m = 2000 x 5 kg = 10000 kg
Force exerted by engine F = 40000N
Friction force f = 5000 N
(i) net accelerating force f' = F -f
f' = 40000N - 5000N
f' = 35000N
(ii) Force = total mass x acceleration
f' = (M + m) x a
35000N = (8000 + 10000) kg x a
35000N = 18000 kg x a
35000N/18000kg = a
a = 1.94 ms-2
(iii) Only on waggon 1, the external force will be applied. The net force on the remaining 4 waggons is equal to the force applied by waggon 1 on 2.
Assume the acceleration on waggons = a'.
f' = m x a'
35000N = 10000 kg x a'
a' = 35000N / 10000 kg
a' = 3.5 ms-2
Mass of 4 waggons m'= 4 x 2000 kg
m'= 8000 kg
∴ Net force on last 4 waggons F' = 8000×3.5
=28000 N
force applied by waggon 1 on 2 is 28000 N
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