# Why are motorless cars light?

#### ShawnD

If you've ever seen races where cars are just rolling down a hill with no engine, you would notice that they always emphasize how light their car is. Why? Isn't heavier better? Just follow me through my thinking here and see where the error is.

assumption 1: all objects, without drag (look at that later), fall at the same speed.
A 100kg car and a 1000kg car will roll down the hill at exactly the same rate if there is absolutely no drag or friction.

assumption 2: energy in this race is entirely dependant on mass.
Both the 100kg and 1000kg car are starting at the same relative height on the hill, so the only factor is mass.

assumption 3: drag is based on shape and velocity
The 100kg and 1000kg cars have the same shape and go the same speed (assumption 1 with a bit of error, just follow along)

assumption 4: friction from the wheels is negligable compared to air drag
The wheels on these cars are just paper thin, but the cars in these races can go pretty fast which makes considerable drag.

assumption 5: effective energy in the system is based on potential energy (good) and drag (bad); just subtract the two

E = m*g*h - drag

Just say g is 10 to make this easier, m is 100 and 1000 for the cars, and let's say h is 100 meters. Also let's just say drag is 20. Here would be the 100kg car:
E = (100)(10)(100) - 20
E = 99980 Joules

Here would be the 1000kg car:
E = (1000)(10)(100) - 20
E = 999980 Joules

Now put that into the kinetic energy equation (E = 0.5mv^2).
100kg car = 44.71688719 m/s
1000kg car = 44.72091233 m/s

You can see that the tank of a car goes slightly faster because the drag has less effect on it. If this is the case, why do they care so much about weight?

Vague unscientific evidence for my theory:
If you remember from one episode of mythbusters, where Jamie and Adam are racing their designs for toy cars, Adam's design won because it was essentially just a block of metal with some wheels whereas Jamie's slower design was made of wood. Heavy things are just faster when the energy is provided by gravity.

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#### Pengwuino

Gold Member
I'm almost certain friction is the reason they won't. It is not at all negligable until you get down to systems such as locomotives that run with very small surface areas contacting the ground i believe.

#### blimkie

Ever see the mythbusters where the comapred to toy car on a track to a dodge viper. The toy licked the viper for the frist 100 yards because it had less weigh and was easier to start moving but once the viper got going it prevailed.

#### Integral

Staff Emeritus
Gold Member
Pinewood Derby cars have a 5g MAX mass. The goal is to get your car as close to the max as possible. The common experiance is that heavy cars come out ahead.

So according to the Cub Scouts your anaylsis is correct.

"Why are motorless cars light?"

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