Mechanics: Power and Force problem.

[knowlewj01]

Homework Statement

An engine of mass 100 tonne pulls a train of mass 400 tonne along a horizontal track. There is a horizontal frictional force of size 1 kN acting on the engine and a horizontal frictional force of size 20 kN acting on the train. Find the tension in the couplings between the engine and the train at the instant when the speed of the train is 80 kmh-1 and the engine is exerting a power of 4000 kW.
(1 tonne = 1000 kg.)

Homework Equations

P = Fv
[maybe conservation of energy?]

The Attempt at a Solution

What I have done is, first turn all the units into SI, work out the force provided by the engine and then resolve horizontally to find the Tension. This did not really work for me because the force provided by the engine turned out to be about 180 kN. I'm not sure what I'm doing wrong, have I perhaps made the wrong assumption that the system is at a constant speed? Also given that the masses were involved in the brief i guess they have to be used somewhere. Anyone have any hints/tips? Thanks

 

[Delphi51]

You need the masses to find the friction forces.
Looks like it is accelerating, so quite complicated. That P = Fv is a good one and you will need to write F = ma for the engine and again for the train (which apparently doesn't include the engine).

 

[knowlewj01]

Ok, thanks i'll give that a go and see what i get.

 

[knowlewj01]

Ok, so I have an answer.

The power output of the Engine and the Speed (about 22.2 m/s in SI) yield 180kN Driving force of the Engine.

using F=ma on both the Engine and Train seperatly.

Engine: 180 - 1 = 100a
Train: T - 20 = 400a

a is common to both equations:

$$\frac{T - 20}{400}$$ = $$\frac{179}{100}$$

T = $$\frac{400 x 179}{100}$$ + 20

T = 736 kN

Would anyone be able to check this? I think the Tension is a bit on the high side!

 

[knowlewj01]

Must be something wrong with the value that I got for the driving force of the engine, the acceleration works out to be about 1.79 km/s^2 which is rediculous, can anyone spot my error?

 

[Delphi51]

Engine: 180000 - 1000 - T = 100000a
Train: T - 20000 = 400000a

 

[knowlewj01]

yea, these are the two equations i have, I just took out the factor of 1000 and worked in terms of kN, kM and tonnes still get 736 000 N no matter how I work it, seems very high?

 

[knowlewj01]

so for the engine 180000 - 1000 - T is the resultant force?

the Tension in the couplings is pulling in both directions?

 

[Delphi51]

Yes, tension acts on both engine and train so it appears in both equations.
You have to solve for T and a using the system of two equations.
I don't get 736 000 for T. About 5 times less. If you show your work solving the equations, someone will help you figure out what went wrong.