An engine, working at a constant rate, is pulling a train of mass 500 tonne along a plane of inclination `sin ^(-1) (1/(100))`. If the frictional force per metric tonne is 49 N and the train is moving with a velocity of `10 m *s^(-1)`, what is the power of the engine in kilowatt ? [ 1 tonne (metric ton) =1000 kg]

Explanation

Downward effective force on the train along the inclined plane `=mg sin theta`+frictional force (f)
`=500xx1000xx9.8xx1/(100)+500xx49=7500xx9.8 N`
Velocity of the train `=10 m*s^(-1)`
Since the car is moving upward with a constant velocity the force applied by the car.s engine , F must exactly balance the net downward force.
`therefore F=3136 N`
Hence, power of the engine
`=7500xx9.8xx10=735000 J s^(-1)`
=735000 W =735 kW.