1. Some Hints and Some Physics
Pinewood Derby Race
Some Hints and Some Physics

2. 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

3. 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

4. Parameters and their Effects
Air resistance
Friction
Weight
Center of Mass
Stability
Rotation of Wheels

5. 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

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

7. 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

8. 2. Friction Rolling Friction Sand wheel surface
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 wheel surface
Notes: probably not a great advantage. Might be counterproductive if done poorly.
Sand axles Might not be that important.
Lubricate axles Not with a liquid! We have what you need. Race Day.
Kinetic Friction
between wheel and axle

9. 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).

10. 3. Weight Demo: paper and book Observation: Conclusion:
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)

11. 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.

12. 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).

13. 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

14. 4. Center of Gravity Dh A B
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.

15. 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)

16. 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.

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

18. Summary 2 Maximize weight (5 ounces) reduce effect of air resistance
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

19. Have Fun 