(^606) „„„„„ A Textbook of Engineering Mechanics
Example 30.5. Find the power of an engine, which can do a work of 1200 joules in
8 seconds.
Solution. Work = 1200 J and time (t) = 8 s
We know that work done by the engine in one second
1200
150 J/s
8

∴ Power = 150 W Ans.
Example 30.6. A motor boat is moving with a steady speed of 10 m/s. If the water resistance
to the motion of the boat is 600 N, determine the power of the boat engine.
Solution. Given : Speed of motor boat = 10 m/s and resistance = 600 N
We know that work done by the boat engine in one second
= Resistance × Distance = 600 × 10 = 6000 N-m/s
= 6 kN-m/s = 6 kJ/s
∴ Power = 6 kW Ans.
Example 30.7. A railway engine of mass 20 tonnes is moving on a level track with a con-
stant speed of 45 km.p.h. Find the power of the engine, if the frictional resistance is 80 N/t. Take
efficiency of the engine as 80 %.
Solution. Given : Mass of railway engine (m) = 20 tonnes ; Velocity (v) = 45 km.p.h.
= 12·5 m/s ; Frictional resistance = 80 N/t = 80 × 20 = 1600 N = 1·6 kN and efficiency of the
engine (η) = 80% = 0·8.
We know that work done by the railway engine in one second
= Resistance × Distance = 1·6 × 12·5 kN-m/s
= 20 kN-m/s = 20 kJ/s
∴ Power = 20 kW
Since efficiency of the engine is 0·8, therefore, actual power of the engine,
20
25 kW
0·8
P== Ans.
Example 30.8. A train of weight 1000 kN is pulled by an engine on a level track at a
constant speed of 45 km.p.h. The resistance due to friction is 1% of the weight of the train. Find
the power of the engine.
Solution. Given : Weight of the train = 1000 kN ; Speed of the train (v) = 45 km.p.h.
= 12·5 m/s and resistance due to friction = 1% of the weight of train.
We know that frictional force (or resistance)
= 0·01 × 1000 = 10 kN
and work done in one second = Resistance × Distance = 10 × 125 = 125 kN-m/s = 125 kJ/s
∴ Power = 125 kW Ans.
Example 30.9. A locomotive draws a train of mass 400 tonnes, including its own mass, on
a level ground with a uniform acceleration, until it acquires a velocity of 54 km.p.h in 5 minutes.
If the frictional resistance is 40 newtons per tonne of mass and the air resistance varies
with the square of the velocity, find the power of the engine. Take air resistance as 500 newtons
at 18 km.p.h.