Find the power of an engine in kilowatts which pulls a train of mass $600$ tonnes up an incline of $1$ in $100$ at the rate of $60 \; km/hr$. The weight of the engine is $200$ tonnes and the resistance due to friction is $50$ Newton's per tonne.

Given,

Mass of train = 600 tonnes

Mass of engine = 200 tonnes

Total mass (m) = (600 + 200) tonnes = 800 * 10$^3\;kg$

Inclination = 1 in 100

Speed of train (u) = $60\;km/h = 16.67\;m/s$

Frictional Force $(F_r) = 50\;Newton/tonnes = 50 * 800 = 40000\;N$

Power of engine $(P) = \;?$

The total force needed is,

$F = F_r\;+\;mg\;sin\theta = 40000 + 800 * 10^3 * \frac{1}{100} * 10 = 120000$

Now, 

Power $(P) = F.v = F.u = 120000 * 16.67 = 2000\;kW$

Return to Main Menu