PINEWOOD DERBY RACE

Some Hints and Some Physics

Conservation of Energy2 21 1

2 2 thermalmg h mv I E

Gravitational potential energy lost - GOOD

Translational kinetic energy gained - GOOD

Rotational kinetic energy gained - BAD

Thermal energy gained - very BAD

hv

Conservation of Energy

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m – massg – acceleration of gravity (9.8m/s2) h – change in height of center of gravity v – speed at bottomI – moment of inertia – angular velocityEthermal – change in thermal energy

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Parameters and their Effects1. Air resistance2. Friction3. Weight4. Center of Mass5. Stability6. Rotation of Wheels

1. Air resistance - DragDrag can be modeled as:

cd drag coefficient (depends on shape etc.) r density of fluid (i.e. air) A cross-sectional area v speed http://en.wikipedia.org/wiki/Drag_coefficient

212 dD c Avr

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1. Air resistance – Drag

The cross-sectional area A matters But so does flow of air around the obstacle (cd).

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1. Air Resistance - Ideas

212 dD c Avr

How can you reduce drag?

Reduce drag coefficient cd:• streamline profile• smooth surface (sand or paint)

You cannot control density of air

Reduce cross-sectional area A

You don’t want to reduce v

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2. Friction

Kinetic Friction between wheel and axle

Sand wheel surfaceNotes: probably not a great advantage. Might

be counterproductive if done poorly.

Rub your hands and they get warm. If your car has significant friction then some of its initial potential energy is NOT used for SPEED but instead for HEATING purposes.

Rolling Friction

Should your wheels be square? Sand axles

Might not be that important.

Lubricate axlesNot with a liquid! We have what you need. Race Day.

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3. Weight Objects fall at the same rate (in

vacuum), i.e. weight does not matter, unless …

Movie: coin and feather

… there is air resistance (or some other opposing force that is independent of mass).

3. WeightDemo: paper and book

Observation: Same A, same cd. Book has greater mass and falls

faster.Conclusion: The relative effect of drag is smaller when the weight is

greater.

Idea: Maximize weight (max is 5 ounces)

212 dD c Avr

mg Dam

4. Center of GravityThe center of gravity of an object depends

on how the mass is distributed in the object.

Demo: meter sticks with taped-on mass

Objects can have the same mass but different centers of gravity.

4. Center of GravityThe two cars have the same mass but

different centers of gravityNote that the car on the left must be made of

denser material to have the same mass (Idea: metal filling).

4. Center of Gravityh is the change in height of the center of gravity.We cannot move the car higher up the incline BUTwe can move the center of gravity higher up.

v0=0

hv

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4. Center of Gravity

•The center of mass of car A travels a greater vertical distance h.•Therefore, car A loses more gravitational potential energy.•Therefore, it gains more kinetic energy and is faster at the bottom.

h

A B

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5. Stability

Demo: cars on table test

Make sure your car rolls straight.Don’t put your center of gravity behind the

rear axle.Add extra mass preferably to underside of

car.

This is VERY important but hard to model (Experiment)

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6. Rotating ObjectsDemo: incline and rolling objects.

Observation:Same gravitational potential energy, same kinetic energy, but hoop is

slower. Why?Explanation:Hoop has greater moment of inertia I. more rotational kinetic energy, or ½I2 less translational kinetic energy, or ½mv2 (i.e. less speed)

Idea: work on wheel geometry to reduce I.

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Summary 1

Streamline ProfileSand/paint surfacesReduce area facing wind

Sand wheel surfaceSand axlesLubricate axles

reduce air resistance, Ethermal

reduce friction, Ethermal

Summary 2Maximize weight (5 ounces)

Put center of gravity to the rear of the car

Make sure car rolls straightCenter of gravity not behind rear axleAdd extra mass to underside

Reduce moment of inertia I

reduce effect of air resistance

increase potential energy, mgh

reduce friction, Ethermal

reduce rotational kinetic energy ½I2

HAVE FUN