# Mechanics: Power and Force problem.

• knowlewj01
In summary, the engine exerts a power of 4000 kW and is pulling a train of mass 400 tonne along a horizontal track. The tension in the couplings between the engine and the train is 736000 N.
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

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).

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

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!

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?

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

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?

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

the Tension in the couplings is pulling in both directions?

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.

## What is the definition of power?

Power is the rate at which work is done or energy is transferred, measured in watts (W).

## What is the formula for calculating power?

The formula for power is P = W/t, where P is power in watts, W is work in joules (J), and t is time in seconds (s).

## How is force related to power?

Force is a component of power, as power is equal to the force applied multiplied by the velocity at which the force is applied.

## What is the difference between power and energy?

Power is the rate at which energy is transferred or work is done, while energy is the capacity to do work. Power is measured in watts, while energy is measured in joules.

## How can power be increased?

Power can be increased by either increasing the force applied or increasing the speed at which the force is applied. Additionally, using more efficient tools and equipment can also increase power.

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