A 8000kg engine pulls a train of 5 wagons, each of 2000kg along a horizontal track.if the engine exerts a force of 40000N and the track offers a friction force of 5000N, then calculate.
a)the net accelerating force
b)the acceleration of the train
c)the force of wagon 1 on wagon 2.
Answers
Answer:
Explanation:
Mass of the engine = 8000 kg
Mass of each wagon = 2000 kg,
Np. of wagons = 5
Total mass of train = 8000+2000×5= 18000 kg
Force, F = 40000 N
Track resistance , R = 5000 N
Total accelerating force = F −R =40000−5000=35000 N
Let acceleration = x m/s²
Acceleration , = Accelerating force / mass
x=35000/18000= 35/18=1.94 m/s²
Frictional resistance of 4 wagons = 5000×(2000×4)/18000 =2222 .22 N
Accelerating force on 4 wagons =2000×4×1.944 =15552 N
Hence total force exertred by wagon on wagon 2= Accelerating force +Frictional resistance
=2222 .22 +15552=17774.22 N
Total force required to produce acc
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Answer: 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
∴ F
′
=(5m+M)a
35000=(5×2000+8000)a ⟹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
′
⟹35000=10000×a
′
Acceleration of the wagons a
′
=3.5 ms
−2
Mass of last 4 wagons m
′
=4×2000 kg
∴ Net force on last 4 wagons F
1
=8000×3.5 =28000 N
Thus force on wagon 2 by wagon 1 is 28000 N.
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