Question

A train of mass 200kN has a frictional resistance of 5N per kN. The speed of the

train, at the top of an inclined of 1 in 80 is 45 km/h. Find the speed of the train after

running down the incline for 1km.

Answer 1

Given:

$W=200\:\rm kN$

$F_f=1000\:\rm N$

$\sin\theta=1/80$

$l=1000\:\rm m$

The net force

$$F=W\sin\theta-F_f\\ =200\:000*1/80-1000=1500\:\rm N$$

The acceleration of a train

$$a=\frac{F}{m}=\frac{Fg}{W}=\frac{1500*9.8}{200\: 000}=0.0735\:\rm m/s^2$$

The final velocity

$$v=\sqrt{2la}=\sqrt{2*1000*0.0735}=12.1\:\rm m/s$$