Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Pinewood Derby Car Weight....



Interesting responses to Ralph's original question, but I don't think any of them except John M's response was to the point.

1. Moving the extra mass to the back of the car won't help because every point of the car drops through the same vertical distance between the beginning and end of the track. the only thing that matters in potential to kinetic energy conversion is the height *difference.*

2. Taking one front wheel out of the game may help a little but it also runs the risk of having the car swerve toward the side with the functioning wheel and may take it off the track, causing disqualification.

3. Normal surface to surface friction isn't going to make much difference since it is small anyway, unless the wheels don't turn freely on their axles, so good lubrication of the axles is important, but not relevant to the mass issue.

4. The wheels are, I believe, issued, so that everyone has the same wheels, so their effect should be about the same for all cars.

5. So we are down to the mass. Why does it go faster if the mass is larger? Write the force equation for the car, including air resistance:

F = ma = mg*sin(theta) - (mu)*mg*cos(theta) - (f1*v + f2*v^2 + higher order terms which are probably negligible)

where theta is the tilt angle of the track, f1 and f2 are coefficients of air resistance, and mu is the coefficient of surface-to-surface friction.

If you solve this equation for the acceleration you get

a = g*sin(theta) - (mu)*g*cos (theta) - (f1*v + f2*v^2)/m

Note that m goes away in the first two terms but ends up in the denominator of the last term. Since not much can be done with the first two terms, short of good lubrication of the wheels and axles to reduce mu. That leaves the last term as the one that has hope of making a difference. Making f1 and f2 small means improving the aerodynamics (and it is possible that the speed of the cars does not get into the range where f2 will be a factor), and making m larger means that for any given f1 and/or f2, the effect of this term is reduced, and this is why increasing the mass helps, and as John M. implied in his response, why reducing the mass will ultimately mean the car doesn't go very fast at all.

Hugh
--

************************************************************
Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

Hard work often pays off after time. But Laziness always pays off now.

February tagline on 2007 Demotivator's Calendar