Moving aboutA 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.

• Estimates of time taken, distance travelled, routes.

• Modes of transport:– Walking– Bicycles– Bus/train– Car– Boat, aeroplane, etc.

The concept of “speed”

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• Distance travelled• Speed

Other examples are:• Temperature• Mass• Etc.

Vector• Displacement• Velocity

Other examples are:• Force• Acceleration• Etc.

Speed and velocity

• Velocity can be changing even if speed is constant: v1

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

Weight pulls car down

Road pushes up

Engine pushes forward

Drag etc. pulls back

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

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dry Wet Heavy Rain Puddles

new worn

Tyres: coefficient of friction

s

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 )

• Ideas?

Minimising drag (bicycle)

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 speed-limit 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.

To floor (~1 metre)

Ingenious release mechanism

Crumple zone: Foam rubber, corrugated cardboard, etc.

Mr Egg-head

Sturdy wooden or metal box

Mr Egg-head’s car

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

Movie from: http://www.nrma.com.au

A Holden Barina (with airbag)

NRMA crash testing

Movie from: http://www.nrma.com.au

A Subaru Impreza (no airbag)

NRMA crash testing

Movies from: http://www.nrma.com.au

A Holden Commodore

no airbags with airbags

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

Source: http://www.bikebrain.com

Attaches to a “PalmPilot”

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 solar-powered 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 carsee, 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

1 10 100 1000 10000 100000

Snake (slithering)

Caterpillar (caterpillaring)

Rabbit (leaping)

Human (walking)

Horse

Car

Bicycle

Railway

Energy consumption

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.