Transport Engineering 2

Physics on the RoadLesson 13

LI… Know that when an object gains

height it gains gravitational potential energy Egp=mgh

Know that changes in GPE are often matched by equal and opposite changes in KE

A vehicle moving at constant velocity against resistive forces loses energy at the same rate it gains it from the source which drives it.

Power = rate of doing work = force x velocity

F

Apples and energy

If you lift an apple the the force you need to lift it is the apples weight and the distance you lift is the apples new height.

If you apply force over a distance work is being done. W = F x d

What happen to this energy?

d

Work done lifting the appleW = force x distance = weight x height = mass x gravity x height

This energy cannot disappear.It is now “stored” in the apple.This is called gravitationalpotential energy or GPE.

GPE = weight x change in height

Egp = mgh

Designing railway gradients

Trains are very heavy and take a lot of energy to drag uphill. This energy has to come from it’s motors. So less energy can be used to keep the train at a steady high speed.

Too avoid this limits are set for railway gradients about 1 in 100.

height h

weight mg

Le Shuttle is 2400 tonnes if it rises up a slope of 100m it will transfer…Egp = mgh = 2400 000 x 9.8 x 100 = 2 352 000 000 J = 2352 MJ (or 2.352 GJ)

Back to apples and energy

If you drop the apple we lifted what happens to the GPE stored in the apple?

It is all transferred to KEEk = 1/2mv2

So for an object falling often

GPEtop=KEbottom

mgh = 1/2 mv2

Using the energy stored Having used a huge

amount of energy to get a train uphill it would be pity to throw the energy away.

As the train runs downhill the train will gain KE (and lose GPE) it could be dangerous to let the train continue to gain speed.

In modern electric trains this KE is used to turn generators which feed electricity back to Grid system powering the train.

height h

GPEmax

KEmin

GPEmin

KEmax

Le Shuttle descends a slope of 100m it will transfer…E = mgh = 2352 MJ…to kinetic energy

1/2mv2 = 2352 MJv2 = 2 x 2352 000 000 2400 000v = 44 ms-1 (158 kmh-1)

More energy changes

The engine’s motors work when the train is accelerating or moving at a constant speed.

There is constant flow of energy through the train.

Explain (in terms of energy) the three things can happen to the motion of the train

Energy to motors

Energy air, heat in motor, deforming rails etc..

KE of train

Power and work done Power is the rate of doing

work and is measured in Joules per second (Js-1) or watts (W)

Power = work done timeWhen the train is moving at a constant speed.

work done = frictional forces x displacement

work done = frictional forces x distance moved per second per second

Power = force x velocity [ P=Fv ]

E F

Working out with a cycle

You will need to resolve forces and think about energy conservation in this question.

Uphill or down – the same principles apply

A particularly macho mountain biker sets out to prove something. He attacks a 20% hill:

Draw the forces acting on the cyclist, whilst in motion.The mass of the cyclist plus bicycle is 100 kg.1. Calculate the size of the retarding force due to gravity, acting along the slope.

Working out with a cycle

2. Calculate the energy he must supply to move 200 m up this slope.

The cyclist covers this 200 m of road, whilst travelling up the hill, in 120 s. Previous tests show that the retarding frictional force at this speed is 15 N.

3. Calculate the energy he must also supply, just to cover any 200 m at this speed.

4. Find his power output.