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Moving about A look at the new Stage 6 Physics syllabus for NSW Schools Professor John Storey

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There are many kinds of vehicles on our roads... Image: http://www.tourdestrees.org

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…and off our roads. Source: http://imagine.gsfc.nasa.gov

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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.

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Estimates of time taken, distance travelled, routes. Modes of transport: –Walking –Bicycles –Bus/train –Car –Boat, aeroplane, etc. The concept of speed

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Measuring speed SI units: metres/sec Other units: –Kilometres/hour (kph) –Miles per hour –Knots (nautical miles per hour)

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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.

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Possible exercises: I Narrative. Three students describe the same journey in terms of: –Distance versus time –Speed versus distance (or location) –Acceleration versus distance.

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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.

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Possible exercises: III Use bicycle computer to measure instantaneous speed, average speed, time and distance. Plot graph and analyse.

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A typical journey involves speed changes. Source: http://www.bikebrain.com

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Vectors and scalars A vector has magnitude and direction: v

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Examples of vectors Scalar Distance travelled Speed Other examples are: Temperature Mass Etc. Vector Displacement Velocity Other examples are: Force Acceleration Etc.

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Speed and velocity Velocity can be changing even if speed is constant: v1v1 v2v2

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Caution We often use the word velocity when we mean speed, and vice versaespecially in normal conversation.

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Velocity and displacement v = s / t Distinguish and compare: –instantaneous speed –instantaneous velocity –average speed average velocity

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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?

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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

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2. An analysis of the external forces on vehicles helps to understand the effects of acceleration and deceleration.

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F = ma Recall concepts of: –Force –Mass –Acceleration

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Force Qualitative understanding Examples: –Pushing/pulling –Gravity –Electrostatic –Etc.

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Mass Qualitative understanding Distinguish mass and weight Measurement: –Measure weight and derive mass –Other methods (leads into ideas of inertia and Newtons second Law: F = ma).

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Acceleration Rate of change of velocity (magnitude or direction) Physical sensation Measurement: –Accelerometer –GPS?

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Addition of vectors v + v v v

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Forces on a car Weight pulls car down Road pushes up Engine pushes forward Drag etc. pulls back

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Forces on a car Engine pushes forward Drag etc. pulls back (Horizontal forces only shown)

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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.

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Coefficient of friction Static coefficient ( s ) always greater than sliding coefficient ( k ) Static case: F friction = zero to s.F normal Sliding: F friction = k.F normal

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Tyres: coefficient of friction s Data from: Automotive Handbook (Bosch).

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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: F normal = mg is less than 1 %.

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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).

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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 C RR as the coefficient of rolling resistance.

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Rolling resistance F rolling = C RR.F normal = C RR.m.g (for reasonably level road) F rolling depends on the type of tyre, the tyre pressure, the vehicle mass and the road surface. It is independent of the number of wheels.

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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).

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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.

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Drag coefficient We define C D as the drag coefficient, such that: F drag = 1 / 2..C D.A.v 2 where is the density of air (1.2 kg/m 3 ) and A is the frontal area of the vehicle. The formula holds for the range of speeds encountered by bicycles and cars.

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Source: http://www.lerc.nasa.gov

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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 doesnt have its own NASA!

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Minimising drag (aircraft) Streamlined shape (low C D ) Fly as high as possible (low ) Ideas? Minimising drag (bicycle)

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Other forms of drag Bearing friction (typically F bearing 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: F drag = F rolling + F aerodynamic drag + F bearing + mgsin

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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.

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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?

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3. Moving vehicles have kinetic energy and energy transformations are an important aspect in understanding motion.

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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. E K = 1 / 2.m.v 2 Note: Kinetic energy is not a vector quantity!

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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.

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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.

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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!

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4. Change of momentum relates to the forces acting on the vehicle or the driver.

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Newtons 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…)

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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.

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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.

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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.

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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.

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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.

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5. Safety devices are utilised to reduce the effects of changing momentum.

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Newtons first law is not always apparent. Friction and air resistance are omnipresent. You dont always realise youre 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.

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Crash testing Ready Set Go! Source: http://www.inrialpes.fr

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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 speed- limit zones in suburbia. Compare the kinetic energy, stopping distance etc. of cars travelling at 50 and 60 km/hr respectively.

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Possible Exercises: VIII Mr Egg-heads car. This idea can be developed as a project, a competition, or as an in-class demonstration.

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To floor (~1 metre) Ingenious release mechanism Crumple zone: Foam rubber, corrugated cardboard, etc. Mr Egg-head Sturdy wooden or metal box Mr Egg-heads car

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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).

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Further modifications II Less messy alternatives to an egg: –Accelerometer –Inked tennis ball

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Airbags Source: http://www.hyge.com/products

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NRMA crash testing Movie from: http://www.nrma.com.au A Holden Barina (with airbag)

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NRMA crash testing Movie from: http://www.nrma.com.au A Subaru Impreza (no airbag)

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NRMA crash testing Movies from: http://www.nrma.com.au A Holden Commodore no airbagswith airbags

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Seat belts Movie from: http://www.nissan-europe.com

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6. The models applied to motion and forces involving vehicles can be applied to a wide variety of situations.

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And not just on the earth... Source: http://www-aig.jpl.nasa.gov

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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

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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.

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Digital data loggers Images from http://www.vernier.com

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Bike computers are available from many manufacturers Picture from http://www.avocet.com

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Bikebrain Source: http://www.bikebrain.com Attaches to a PalmPilot

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Aston Martin Vantage 600 Weight: 5170 lb Twin-supercharged DOHC V8, 5300 cc Power: 600 bhp Source: Road & Track magazine

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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.

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Further questions Would fitting bigger brakes help the Aston Martin stop more quickly? Would fitting a more powerful engine make it accelerate more quickly?

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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.

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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

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The Aurora solar- powered car is probably the most efficient means of transport ever built. Images: http://www.aurorasolarcar.com

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Highly recommended! See http://www.pv.unsw.edu.au

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Possible exercises: XI Design and build: –a human-powered vehicle. –a solar car –a solar boat –a mileage marathon car

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Human-powered vehicle: http://www.ihpva.org Source: http://entropy.me.calpoly.edu/~hpvasme/images/hpv/old/nitemare.jpg

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Solar car: http://www.wsc.org.au

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Edible car see, for example: http://www.sou.edu/physics/ACTIVITY/edible.HTM Source: http://www.mailtribune.com/archive/99/may99/archgifs/52199n3a.jpg

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Mileage marathon cars Source: http://www.laketuggeranongs.act.edu.au

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or get really ambitious... Image from: http://ourworld.compuserve.com/homepages/j_d_mcintyre/VELAIR2.GIF

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Energy consumption Watts/kg @ 1 m/s Adapted from: Bicycling Science (Whitt and Wilson).

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Source: Bicycling Science (Whitt and Wilson).

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Moving about…by people who can really move. Source: Bicycling Science (Whitt and Wilson).

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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.

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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 dont fall over. –Is the bicycle the only invention that can be completely understood?

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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, andwould you believea 20-knot hydrofoil. –Every time I pick it up I want to rush out and build something. –Physics, physiology, and fabulous ideas.

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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.

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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.

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