Why Does Calculating Train Engine Power Result in Different Values?

[Bix]

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Hi. I'm new and am trying to solve a simple question 'Find the max power of a train engine traveling level at 50 metres per second if total resistance to motion is 30 KiloNewtons.

I get power = force times velocity so 30000 x 50 = 1500000 = 1.5 Mega Watts. My answer book says 1.47 Mega Watts. I can see how 1.5MW minus 30KW = 1500000 - 30000 = 1.47MW. Also I can see that power times gravity of 9.8 = 1.5 MW times 9.8 N gives the same answer.

I can't see how you should subtract the force from the sum of the force and the distance, or how vertical gravity can reduce the speed of a horizontally moving train. Thanks :)

 

[Halc]

Your math seems fine. Subtracting 30KW doesn't make sense since 30KW hasn't been computed anywhere, making it a random number. Subtracting the force doesn't make sense since force and power are different units and cannot be added. And yes, gravity plays no role since the problem says 'level'. Also 1.5MW * 9.8 m/sec² results in 14.7 mega-something, not 1.47 mega-something.

I cannot explain the book answer.

 

[haruspex]

I think these book/web errors often arise when someone modifies the question and fails to check the answer given elsewhere.
That 9.8 produces the right leading digits is suggestive. The original might have been something like "a train of mass 30,000 kg and rolling resistance (or "rolling friction" or whatever) of 0.1..."

 

[Bix]

Thanks guys, massively appreciated :)
Interesting insight haruspex..