**Pinewood Derby Race ** Some Hints and Some Physics

**Conservation of Energy** Translational kinetic energy gained - GOOD Gravitational potential energy lost - GOOD Rotational kinetic energy gained - BAD Thermal energy gained - very BAD Dh v

**Conservation of Energy** • m – mass • g – acceleration of gravity (9.8m/s2) • Dh – change in height of center of gravity • v – speed at bottom • I – moment of inertia • – angular velocity • DEthermal – change in thermal energy

**Parameters and their Effects** • Air resistance • Friction • Weight • Center of Mass • Stability • Rotation of Wheels

**1. Air resistance - Drag** Drag 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

**1. Air resistance – Drag** The cross-sectional area A matters But so does flow of air around the obstacle (cd).

**1. Air Resistance - Ideas** How can you reduce drag? You don’t want to reduce v • Reduce drag coefficient cd: • streamline profile • smooth surface (sand or paint) You cannot control density of air Reduce cross-sectional area A

**2. Friction** Kinetic Friction between wheel and axle Sand wheel surface Notes: 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 axlesMight not be that important. Lubricate axlesNot with a liquid! We have what you need. Race Day.

**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. Weight** Demo: 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)

**4. Center of Gravity** The 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 Gravity** The two cars have the same mass but different centers of gravity Note that the car on the left must be made of denser material to have the same mass (Idea: metal filling).

**4. Center of Gravity** Dh is the change in height of the center of gravity. We cannot move the car higher up the incline BUT we can move the center of gravity higher up. v0=0 Dh v

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

**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)

**6. Rotating Objects** Demo: 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 ½Iw2 • less translational kinetic energy, or ½mv2 (i.e. less speed) Idea: work on wheel geometry to reduce I.

**Summary 1** reduce air resistance, DEthermal reduce friction, DEthermal Streamline Profile Sand/paint surfaces Reduce area facing wind Sand wheel surface Sand axles Lubricate axles

**Summary 2** Maximize weight (5 ounces) Put center of gravity to the rear of the car Make sure car rolls straight Center of gravity not behind rear axle Add extra mass to underside Reduce moment of inertia I reduce effect of air resistance increase potential energy, mgDh reduce friction, DEthermal reduce rotational kinetic energy ½Iw2

**Have Fun**