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1/31/2011 Conservation of Energy mg h PINEWOOD DERBY RACE Gravitational potential energy lost - GOOD 1 2 1 2 mv I Ethermal 2 2 Translational kinetic energy gained i d - GOOD Rotational kinetic energy gained BAD Thermal energy gained - very BAD Some Hints and Some Physics h v Conservation of Energy mg h Parameters and their Effects 1 2 1 2 mv I Ethermal 2 2 1. 2. 3. m g h v I Ethermal – mass – acceleration of gravity (9.8m/s2) – change in height of center of gravity – speed at bottom – moment of inertia – angular velocity – change in thermal energy mg h 1. Air resistance - Drag Drag can be modeled as: 1 D cd Av 2 2 http://en.wikipedia.org/wiki/Drag_coefficient 5. 6. mg h 1. Air resistance – Drag 1 2 1 2 mv I Ethermal 2 2 The cross-sectional area A matters But so does flow of air around the obstacle (cd). cd drag coefficient (depends on shape etc.) etc ) density of fluid (i.e. air) A cross-sectional area v speed 1 2 1 2 mv I Ethermal 2 2 4. Air resistance Friction Weight 1 1 mgg h mv 2 I 2 Ethermal C t off Mass Center M 2 2 Stability Rotation of Wheels 1 1/31/2011 mg h 1. Air Resistance - Ideas 1 2 1 2 mv I Ethermal 2 2 How can you reduce drag? 2. Friction 1 2 1 2 mv I Ethermal 2 2 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. 1 D cd Av 2 2 Reduce drag coefficient cd: You don’t want to reduce v Reduce cross-sectional area A You cannot control density of air • streamline profile • smooth surface (sand or paint) mg h Rolling Friction Sand wheel surface Should your wheels be square? Notes: probably not a great advantage. Might be counterproductive if done poorly. Kinetic Friction between wheel and axle Sand axles Might not be that important. Lubricate axles Not 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 … 3. Weight Demo: paper and book 1 D cd Av 2 2 Observation: Movie: coin and feather Same A A, same cd. Book has greater mass and falls faster. faster Conclusion: … there is air resistance (or some other opposing force that is independent of mass). The relative effect of drag is smaller when the weight is greater. Idea: Maximize weight (max is 5 ounces) a mg D m 4. Center of Gravity 4. Center of Gravity The center of gravity of an object depends on how the mass is distributed in the object. The two cars have the same mass but different centers of gravity Demo: meter sticks with taped-on mass Note that the car on the left must be made of denser material to have the same mass (Idea: metal filling). Objects can have the same mass but different centers of gravity. 2 1/31/2011 4. Center of Gravity mg h 1 2 1 2 mv I Ethermal 2 2 h 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. 4. Center of Gravity A mg h 1 2 1 2 mv I Ethermal 2 2 B h v0=0 •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 v 5. Stability mg h 1 2 1 2 mv I Ethermal 2 2 6. Rotating Objects mg h 1 2 1 2 mv I Ethermal 2 2 Demo: incline and rolling objects. Demo: cars on table test Observation: 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. 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) This is VERY important but hard to model (Experiment) Idea: work on wheel geometry to reduce I. Summary 1 Summary 2 Streamline Profile Sand/paint surfaces Reduce area facing wind reduce air resistance, Ethermal Sand wheel surface Sand axles Lubricate axles reduce friction, Ethermal Maximize weight (5 ounces) reduce effect of air resistance Put center of gravity to the rear of the car increase potential energy, mgh Make sure car rolls straight Center of gravity not behind rear axle Add extra mass to underside reduce friction, Ethermal Reduce moment of inertia I reduce rotational kinetic energy ½I2 3