Transcript The concept of “speed” - School of Physics at UNSW, Sydney

Moving about
A look at the new Stage 6 Physics
syllabus for NSW Schools
Professor John Storey
There are many
kinds of vehicles
on our roads...
Image: http://www.tourdestrees.org
…and off our roads.
Source: http://imagine.gsfc.nasa.gov
1. Vehicles do not typically
travel at constant speed.
Note: This and other excerpts from the
Stage 6 syllabus are copyright, Board of
Studies, NSW, 1999.
The concept of “speed”
• Estimates of time taken, distance travelled,
routes.
• Modes of transport:
–
–
–
–
–
Walking
Bicycles
Bus/train
Car
Boat, aeroplane, etc.
Measuring speed
• SI units: metres/sec
• Other units:
– Kilometres/hour (kph)
– Miles per hour
– Knots (nautical miles per hour)
Changes in speed and direction
• How do these changes affect the time for a
journey?
• Concept of “average speed”.
• Relationship between speed, distance and
time.
Possible exercises: I
• Narrative. Three students describe the same
journey in terms of:
– Distance versus time
– Speed versus distance (or location)
– Acceleration versus distance.
Possible exercises: II
• Study train time-table and map of Sydney to
determine average speed between stations.
Plot graph of journey from, say, Hornsby to
Central.
• Record car odometer reading every 60
seconds (passenger do this, not driver!)
Analyse results.
Possible exercises: III
Use bicycle computer
to measure
instantaneous speed,
average speed, time
and distance. Plot
graph and analyse.
A typical journey involves speed
changes.
Source: http://www.bikebrain.com
Vectors and scalars
• A vector has magnitude and direction:
v
Examples of vectors
Scalar
Vector
• Distance travelled
• Speed
• Displacement
• Velocity
Other examples are:
• Temperature
• Mass
• Etc.
Other examples are:
• Force
• Acceleration
• Etc.
Speed and velocity
• Velocity can be changing even if speed is
v1
constant:
v2
Caution
• We often use the word “velocity” when we
mean “speed”, and vice versa—especially
in normal conversation.
Velocity and displacement
v = s /t
• Distinguish and compare:
– instantaneous speed
– instantaneous velocity
– average speed average velocity
Relative motion
• Examples:
–
–
–
–
Travelling walkway at airport
Person walking on a boat or train
Boat travelling along a flowing stream
Etc.
• Why are racing cars closer together in the
slow parts of a circuit than on the main
straight?
Frames of reference
• Not explicitly in syllabus
• Worth including because:
– The concept is essential to understanding
relativity
– It enormously simplifies some problems
• Inertial versus non-inertial frames
2. An analysis of the external
forces on vehicles helps to
understand the effects of
acceleration and deceleration.
F = ma
• Recall concepts of:
– Force
– Mass
– Acceleration
Force
• Qualitative understanding
• Examples:
–
–
–
–
Pushing/pulling
Gravity
Electrostatic
Etc.
Mass
• Qualitative understanding
• Distinguish mass and weight
• Measurement:
– Measure weight and derive mass
– Other methods (leads into ideas of inertia and
Newton’s second Law: F = ma).
Acceleration
• Rate of change of velocity (magnitude or
direction)
• Physical sensation
• Measurement:
– Accelerometer
– GPS?
Addition of vectors
v
v
v + v
Forces on a car
Road pushes up
Engine pushes
forward
Drag etc. pulls back
Weight pulls
car down
Forces on a car
Engine pushes
forward
Drag etc. pulls back
(Horizontal forces only shown)
Friction
• Friction always opposes motion.
• Friction even opposes attempted motion.
• Friction depends on the nature of the
surfaces in contact, and how hard they are
pressed together.
Coefficient of friction
• Static coefficient (s) always greater than
sliding coefficient (k)
• Static case: Ffriction = zero to s.Fnormal
• Sliding: Ffriction = k.Fnormal
Tyres: coefficient of friction
1
0.9
new
worn
0.8
s
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Dry
Wet
Heavy Rain
Puddles
Data from: Automotive Handbook (Bosch).
Simplification
• For a road vehicle (bike, car, etc.) the road
rarely has a slope greater than 1 in 6. The
error resulting from the approximation:
Fnormal = mg
is less than 1 %.
Possible exercises IV
• Calculate stopping distance of a car from
various initial speeds, assuming a
coefficient of friction between the tyres and
the road of s = 1.0.
• Compare s and k. Discuss anti-lock
braking systems (ABS).
Rolling resistance
• This is not part of the syllabus. However, it
is a simple concept and adds greatly to an
understanding of vehicle behaviour.
• Rolling resistance is exactly analogous to
sliding friction.
• Define CRR as the coefficient of rolling
resistance.
Rolling resistance
• Frolling = CRR.Fnormal
= CRR.m.g
(for reasonably level road)
• Frolling depends on the type of tyre, the tyre
pressure, the vehicle mass and the road
surface. It is independent of the number of
wheels.
Rolling resistance / tyre friction
• Rolling resistance determines how hard it
is to push the vehicle.
• Tyre friction determines the maximum
possible acceleration of the vehicle (ie,
acceleration, braking and cornering).
Aerodynamic drag
• Also called “air resistance” or “wind
resistance”.
• Aerodynamic drag depends on the size and
shape of the vehicle, its speed (relative to
the air), and the density of air.
• For a given vehicle, aerodynamic drag is
proportional to the square of the velocity.
Drag coefficient
• We define CD as the “drag coefficient”, such
that:
Fdrag = 1/2 ..CD.A.v2
where  is the density of air (1.2 kg/m3)
and A is the frontal area of the vehicle.
• The formula holds for the range of speeds
encountered by bicycles and cars.
Source: http://www.lerc.nasa.gov
http://www.grc.nasa.gov/WWW/K-12/
• A truly fabulous site, with lots of slides like
the previous one.
• Both aerodynamics and jet-engines are
discussed.
• What a pity Australia doesn’t have its own
NASA!
Minimising drag (aircraft)
• “Streamlined” shape (low CD)
• Fly as high as possible (low )
Minimising drag (bicycle)
• Ideas?
Other forms of drag
• Bearing friction (typically Fbearing is
independent of speed).
• Engine drag (“Steep descent: trucks engage
low gear”).
• Exhaust brakes: noisy but effective!
For a car or bike coasting in neutral:
Fdrag = Frolling + Faerodynamic drag + Fbearing
+ mgsin
Equilibrium
If velocity is not changing, then a = 0.
If a = 0, then
F = 0.
ie, the body is in “equilibrium”.
We can then equate forces along any axis.
Possible exercises: V
• Investigate bicycle calliper brakes. What
different mechanisms are used to increase
the contact force between the shoes and the
rim? How does this contact force affect the
friction? How does the friction change
when the shoes and rim are wet? How do
shoes from different manufacturers
compare?
3. Moving vehicles have kinetic
energy and energy transformations
are an important aspect in
understanding motion.
Kinetic Energy
• A moving object has “kinetic energy”.
• The faster it goes, the more kinetic energy it
has.
• The heavier it is, the more kinetic energy it
has.
EK = 1/2 .m.v2
Note: Kinetic energy is not a vector quantity!
Energy transformations
• Energy can be transformed from one form
to another, for example:
–
–
–
–
Fuel (chemical) energy to kinetic energy
Gravitational potential energy to kinetic energy
Kinetic energy to heat
Etc.
Conservation of energy
• When energy is transformed from one form
to another, the total amount of energy
remains the same.
• This is a very useful principle if you can
identify where all the energy has come from
and where it is going.
Coast-down tests
• Use to estimate aerodynamic drag, rolling
resistance, etc.
• Need a long, flat, straight road, zero wind
(early morning is often best), and an
understanding of conservation of energy!
4. Change of momentum relates
to the forces acting on the vehicle
or the driver.
Newton’s third law
• “To every action there is always opposed an
equal reaction; or, the mutual actions of two
bodies upon each other are always equal,
and directed to contrary parts.”
(presumably Newton knew
what he meant…)
Momentum
• A moving body carries “momentum”, p.
• Unlike kinetic energy, momentum is a
vector quantity:
p = m.v
Where m is the mass and v the velocity.
Change of momentum
• The momentum of an object changes when
its velocity changes.
• A velocity change requires the action of an
external force.
 only an external force can change the
momentum of an object.
Impulse
Define “impulse” as the force on an object
multiplied by the time for which the force is
applied.
Impulse = F.t
Now F = ma = m. v /  t
 m. v = F. t
 p = F. t
Ie, impulse = change in momentum.
From which it is apparent that...
• Momentum is always conserved in a
collision.
• Energy is also conserved, but not
necessarily as kinetic energy.
• An elastic collision is one in which kinetic
energy is conserved.
Possible exercises: VI
• In a two-car collision, the lighter car will
suffer a larger change in velocity than the
heavier. Discuss the technical, ethical and
social issues raised by the four-wheel-drive
“arms race”.
5. Safety devices are utilised to
reduce the effects of changing
momentum.
Newton’s first law is not always
apparent.
• Friction and air resistance are omnipresent.
• You don’t always realise you’re moving!
– Is it your train moving forward, or the one next
to you going backwards?
• You can get a false sense of security in a
car.
Crash testing
Ready
Set
Go!
Source: http://www.inrialpes.fr
Possible exercises: VII
• Discuss the technical, ethical and social
issues raised by the fitting of bull-bars to
suburban vehicles.
• Discuss the introduction of 50 km/hr speedlimit zones in suburbia. Compare the
kinetic energy, stopping distance etc. of cars
travelling at 50 and 60 km/hr respectively.
Possible Exercises: VIII
Mr Egg-head’s car.
• This idea can be developed as a project, a
competition, or as an in-class
demonstration.
Mr Egg-head’s car
Ingenious release mechanism
Sturdy wooden or metal box
Mr Egg-head
Crumple zone:
Foam rubber, corrugated cardboard, etc.
To floor (~1 metre)
Further modifications
• Design and test a safe car with an effective
crumple zone. Then fit a “bull bar”.
• Loosely attach weight to inside of car above
egg to demonstrate effect of unrestrained
objects.
• Rest egg on small balloon (“air bag”).
Further modifications II
• Less messy alternatives to an egg:
– Accelerometer
– Inked tennis ball
Airbags
Source: http://www.hyge.com/products
NRMA crash testing
A Holden Barina (with airbag)
Movie from: http://www.nrma.com.au
NRMA crash testing
A Subaru Impreza (no airbag)
Movie from: http://www.nrma.com.au
NRMA crash testing
no airbags
with airbags
A Holden Commodore
Movies from: http://www.nrma.com.au
Seat belts
Movie from: http://www.nissan-europe.com
6. The models applied to motion
and forces involving vehicles can
be applied to a wide variety of
situations.
And not just on the earth...
Source: http://www-aig.jpl.nasa.gov
But first, what have we left out?
• Work = force times distance
• Power = rate of doing work = work/time
= force times speed.
• The work-energy theorem
• Gravitational potential energy = mgh
• Elastic & inelastic collisions
And we could usefully include...
• Rolling resistance (quantitative)
• Aerodynamic drag (quantitative)
• Power = torque times rpm
– or, quantitatively, P = 

P (kW) = 1.05 x 10-4  (Nm) x RPM
• And maybe something about efficiencies of
gearboxes, drive chains etc.
Digital data loggers
Images from http://www.vernier.com
Bike computers are available
from many manufacturers
Picture from
http://www.avocet.com
Bikebrain
Attaches to a “PalmPilot”
Source:
http://www.bikebrain.com
Aston Martin
Vantage 600
Weight: 5170 lb
Twin-supercharged
DOHC V8, 5300 cc
Power: 600 bhp
Source: Road & Track magazine
Possible exercises: IX
• Analyse speed - time graph from motoring
road test report.
• What is maximum deceleration? Compare
to tyre coefficient of friction.
• Reconcile time to reach 160 km/hr with
vehicle mass and claimed engine power
output.
Further questions
• Would fitting bigger brakes help the Aston
Martin stop more quickly?
• Would fitting a more powerful engine make
it accelerate more quickly?
Possible exercises: X
• A litre of petrol, burnt in air, releases
approximately 32 MJ of chemical energy.
Given realistic values of rolling resistance
and aerodynamic drag, what energy is
required to move a car 100 km at 60 km/hr?
• Compare this to the actual fuel consumption
and discuss.
The General Motors EV-1
Petrol, LPG, diesel, electric and hybrid vehicles represent the
immediate future. What about hydrogen?
Source: http://detnews.com/1998/autos
The Aurora solarpowered car is
probably the most
efficient means of
transport ever built.
Images: http://www.aurorasolarcar.com
Highly recommended!
See http://www.pv.unsw.edu.au
Possible exercises: XI
• Design and build:
–
–
–
–
a human-powered vehicle.
a solar car
a solar boat
a “mileage marathon” car
Human-powered vehicle: http://www.ihpva.org
Source: http://entropy.me.calpoly.edu/~hpvasme/images/hpv/old/nitemare.jpg
Solar car: http://www.wsc.org.au
Edible car
see, for example:
http://www.sou.edu/physics/ACTIVITY/edible.HTM
Source: http://www.mailtribune.com/archive/99/may99/archgifs/52199n3a.jpg
Mileage marathon cars
Source: http://www.laketuggeranongs.act.edu.au
or get really ambitious...
Image from: http://ourworld.compuserve.com/homepages/j_d_mcintyre/VELAIR2.GIF
Energy consumption
Railway
Bicycle
Car
Horse
Human (walking)
Rabbit (leaping)
Caterpillar (caterpillaring)
Snake (slithering)
1
10
100
1000
10000
100000
Watts/kg @ 1 m/s
Adapted from: Bicycling Science (Whitt and Wilson).
Source: Bicycling Science (Whitt and Wilson).
Source: Bicycling Science (Whitt and Wilson).
Moving about…by
people who can really
move.
Source: Bicycling Science (Whitt and Wilson).
My favourite books, I
• Automotive Handbook, Robert Bosch
GmbH, Stuttgart
– Over 700 pages of very informative articles and
factual data.
– A wonderful resource when you want to quote
the numbers that real car designers use.
My favourite books, II
• Bicycling Science, F.R. Whitt & D.G.
Wilson, MIT Press, Cambridge MA. (1993)
– Bicycles for physicists.
– Everything from history to aerodynamics to
materials to why they don’t fall over.
– Is the bicycle the only invention that can be
completely understood?
My favourite books, III
• Human-powered vehicles, A.V. Abbott &
D.G. Wilson (editors), Human Kinetics,
Champaign, Il (1995).
– Not just bikes but aircraft, HPVs, and—would
you believe—a 20-knot hydrofoil.
– Every time I pick it up I want to rush out and
build something.
– Physics, physiology, and fabulous ideas.
My favourite books, IV
• Speed of Light. The 1996 World Solar
Challenge, D.M. Roche, A.E.T Schinckel,
J.W.V. Storey, C.P. Humphris & M.R.
Guelden, UNSW, Sydney (1997).
– Acknowledged as the definitive book on solar
car technology (even though I wrote some of it).
– A detailed analysis of all the things important to
solar car design.
Other resources
• Automotive magazines. Two of the more
technical are:
– Road & Track (USA)
– Car (UK)
• Internet - see URLs throughout this talk.
• Standard First-year University Physics texts.