Engineering Mechanics

Chapter 30 : Work, Power and Energy „„„„„ 609

Power of the locomotive

We know that resistance due to inclination

= mg sin α = 200 × 9.8 × 0.008 = 15.7 kN

∴ Total resisting force = Tractive resistance + Resistance due to inclination

= 20 + 15.7 = 35.7 kN

and work done in one second = Total resisting force × Distance

= 35.7 × 8 = 285.6 kN-m/s = 285.6 kJ/s

∴ Power = 285.6 kW Ans.

Speed which the train can attain on a level track

Since the train is to move on a level track, therefore it has no resistance due to inclination. Thus
it has to overcome tractive resistance only. We know that power of the locomotive,

285.6 = Tractive resistance × Speed of the train

= 20 × Speed of the train

∴∴∴∴∴ Speed of the train

285.6

14.3 m/s 51.5 km.p.h.

20

== = Ans.

Example 30.12. An engine of mass 50 tonnes pulls a train of mass of 250 tonnes up a
gradient of 1 in 125 with a uniform speed of 36 km. p.h. Find the power transmitted by the engine, if
the tractive resistance is 60 newtons per tonnes.

Also find the power transmitted by the engine, if the acceleration of the engine is 0.2 m/s^2 up
the gradient.

Solution. Given : Mass of the body i.e. mass of the engine + mass of the train (m) = 50 + 250

= 300 t ; Gradient

1

(sin ) 0.008

125

α= = ; Speed of the train (v) = 36 km.p.h. = 10 m/s ; Tractive

resistance = 60 N/t = 60 × 300 = 18 000 N = 18 kN and acceleration of the engine (a) = 0.2 m/s^2.

Power transmitted by the engine when the train moves with a uniform speed

We know that resistance due to inclination

mg sin α= 300 × 9.8 × 0.008 = 23.5 kN

∴ Total resisting force = Resistance due to inclination + Tractive resistance

= 23.5 + 18 = 41.5 kN

and work done in one second = Total resisting force × Distance

= 41.5 × 10 = 415 kN-m/s = 415 kJ/s

∴ Power = 415 kW Ans.

Power transmitted by the engine when the train is moving up with a uniform acceleration

We know that force required to accelerate the engine and train

=ma = 300 × 0.2 = 60 kN

∴ Total resisting force = Resistance due to inclination + Tractive resistance

+ Force required for acceleration

= 23.5 + 18 + 60 = 101.5 kN