Download PINEWOOD DERBY RACE Conservation of Energy Conservation of

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
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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.
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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 ½I2
 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, mgh
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 ½I2
3