Question

A train of mass 200 tonnes moves on a level track having a track resistance of 85 newtons per tonne. Find the maximum speed of the engine, when the power developed is 320 kW.

Answer 1

First, draw the figure as per the question.

Now,during the motion of train at level track, the maximum speed will achieved when its acceleration will be zero.

• $\rm V_{max} = uniform\: speed$

$\implies\rm \dfrac{dV}{dt} = a = 0$

$\implies\rm F_{ext} = F_{driving}-F_{opposing}=0$

$\implies\rm F_{driving}=F_{opposing}$

$\implies\rm F_{engine}=F_{resistance}$

$\implies\rm F_{engine} = 85 N-per-tonne$

so, for whole mass of 200 tonne, force by engine:

$\implies\rm F_{engine} = 85\times 200\: Newtons$

$\implies\bf F_{engine} = 17000\: Newtons$

We know that,

$\longrightarrow \rm \vec{P} = \vec{F}. \vec{V}$

$\longrightarrow \rm 320\times 1000 = 17000\times \vec{V}$

$\longrightarrow \rm \vec{V} = \dfrac{320\times 1000}{17000}= \dfrac{320}{17}= 18.82 ms^{-1}$

★so, maximum speed of the engine is 18.82 m/s.