1. Transport
Engineering 2
Physics on the Road
Lesson 13

2. 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

3. 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 apple
W = 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 gravitational
potential energy or GPE.
GPE = weight x change in height
Egp = mgh

4. 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)

5. 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 KE
Ek = 1/2mv2
 So for an object
falling often
GPEtop=KEbottom
mgh = 1/2 mv2

6. 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 MJ
v2 = 2 x 2352 000 000
2400 000
v = 44 ms-1 (158 kmh-1)

7. 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

8. 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
time
When 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

9. 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.

10. 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.