An engine is hauling a train of mass `m` on a level track at a constant speed `v`. The resistance due to friction is `f`. What power is the engine producing? What extra power must the engine develop to maintain the speed up a gradient 1 in l. What is the new total power developed by the engine develop to maintain the speed up a gradient 1 in l. What is the new total power developed by the engine ?

Explanation

`F=f`
`P=Fv=fv`

`F^(')=mgsintheta+f=(mg)/(l)+f` [since `sintheta=(1)/(l)`]
`P^(')=F^(')v=((mg)/(l)+f)v`
Extra power `=P^(')-P=(mgv)/(l)`