# Problem: Work and Energy; Need urgent answer

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1. Feb 14, 2015

### Graeme

1. The problem statement, all variables and given/known data

You get a new job working for a railroad company and your first task is to work out the refuelling strategy and fuel budget for the new trains. Your company has recently purchased charger locomotives which have a mass of 120,000kg and a top speed of 210km/h and run on diesel fuel which in an ideal situation can deliver 35,000,000J of energy per liter. The first train you decide to study will travel from Vancouver at sea level across Canada rising steadily in the process passing through Dawson City which is 370m above sea level. This train will pull another 20 freight cars each with a mass of 10,000kg. In order to find out how many liters of diesel you need to have onboard the locomotive so that you can get to the altitude of Dawson city and for the train to pass through the station with a speed of 50km/h (without stopping) you perform a number of calculations. You start with the simplest possible, assumptions, neglecting any kinds of kinetic friction (obviously this is just an under estimate as you know there will be plenty of friction in reality). You also assume your locomotive has perfect efficiency in terms of turning the fuel energy into work. Thinking back to your introductory physics course you remember which quantity you calculated was the external work done and which was the net work done

Total mass of train: 320,000 kg

max speed: 210 km/h

final speed: 50 km/h

Energy per liter of fuel: 35,000,000 J

change in height: 370m

2. Relevant equations

Work = Final Energy - Initial energy

Kinetic Energy = 1/2 m v^2

gravitational potential energy = m g h

3. The attempt at a solution

I really don't know where to start with the problem. I tried conservation of energy, but I don't know what to do with the energy from the fuel or how to calculate the required amount of fuel.

All help is appreciated, as I need to solve this by 11:59 PM tonight.

Regards,

Graeme

2. Feb 14, 2015

### Suraj M

11:59PM ?? Which time zone?
Any way, the question.. how did you get the mass of the train to be 320,000? I mean, are you ignoring the weight of the fuel. If so then you might as well, after ignoring all that friction.
Equate the energy from the fuel to the change in potential energy + the energy required to move the distance,
for the energy spent in the horizontal trip, find the work done, again for that split up the journey, find the distance covered to get to it's high speed, then to change in kinetic energy.
, you say you've done it, why dont you post that too, it would help us to tell you where you're going wrong.

3. Feb 14, 2015

### SteamKing

Staff Emeritus
1. If the train is moving at 50 kph when it goes thru Dawson City, how much energy does that take?

2. If you raise the train 370 m, how much energy does that take?

What's the combined amount of energy to do 1 and 2 above?

If each liter of diesel fuel contains 35 million joules, how many liters must the engine carry to get thru Dawson City from sea level?