Question

Calculate the power of an engine which can pull a train of mass 25000 quintal up to incline of 1 in 100 at the rate of 10.8 km/h resistance due to friction is 2 N/quintal

Answer 1

m = mass of the train = 25000 quintal = 25000 x 100 kg = 2.5 x 10⁶ kg

Sinθ = 1/100

$F_{g}$= 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 - $F_{g}$ - 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