Power and rate of potential energy

[thoradicus]

Homework Statement

A train of mass 2.0*10^5 kg moves at a constant speed of 72km/h up a straight incline against a frictional force of 1.28*10^4N.The incline is such that the train raises vertically 1m for every 100m traveled along the incline.
(i)Calculate the rate of increase per second of the potential energy of the train.
(ii) THe necessary power developed by train.

Homework Equations

P.E=mgh
P=W/t
=Fv

The Attempt at a Solution

Heres how i tried to solve it..
(i)convert 72km/h to m/s we get 20m/s
for 1 second, the train travels 20m
To find height when train traveled 20m,
sin^-1(1/100)=0.573 degrees
sin0.573=x/20
x=0.2m
so,

P=mgh/t
=(2x10^5)(10)(.2)/1s
=400kW

(ii)P=Fv
Since there is constant velocity, F-1.28*10^4=0
F=above N
P=Fv
=(1.28*10^4)(20)
=256kW

is this correct?

 

[LawrenceC]

What about power needed to move train?

 

[thoradicus]

oh wait, so the total power needed by the train is just adding up the two anwsers above?

 

[LawrenceC]

Yes.

 

[thoradicus]

oh ok thx