A train of mass 2000 quintals is moving up an incline of 1 in 200 at the rate of 72 kilometres per hour. Calculate the power of the engine required to pull the train, neglecting friction.
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m = mass of the train = 25000 quintal = 25000 x 100 kg = 2.5 x 10⁶ kg
Sinθ = 1/100
fg= parallel component of force of gravity acting on the train = mg Sinθ = (2.5 x 10⁶) (9.8) (1/100) = 245000 N
f' = frictional force acting per quintal of train = 2 N
f = total frictional force acting on the train = m f' = 25000 x 2 = 50000 N
F = force at which the train pulls
a = accelerattion of the train = 0 m/s
force equation for the motion of train is given as
F - fg - f = ma
F - 245000 - 50000 = m (0)
F = 295000 N
v = speed of the train = 10.8 km/h = 10.8 (5/18) m/s = 3 m/s
Power of the engine is given as
P = F v
P = (295000) (3)
P = 8.85 x 10⁵ Watt
Explanation:
Hope it helps
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