I constantly hear from dads who remember from high school physics classes that mass doesn’t affect the rate at which something falls. If dropped in a vacuum, a bowling ball and a feather fall at exactly the same speed, so the same should be true of a Pinewood Derby car as well, right? If this logic holds up, a three ounce car should be just as fast as a five ounce car.
The problem with this logic is twofold. We’re not just testing the rate at which something falls; on most tracks, half the track is sloped and half is flat. And we aren’t running in a vacuum; there’s lots of friction involved.
The only propulsion your car gets is the conversion of potential energy to kinetic energy as it rolls down the sloped portion of the track. Once it reaches the flat part of the track the only thing that keeps it going is the energy it already has. The more energy it has when it reaches this point, the faster it will go.
Let’s perform an imaginary experiment. Imagine that bowling ball and that feather both dropped from 3 feet in a vacuum. Both will reach the ground at the same time, but they’ll have very different amounts of energy when they hit. Now, put an egg under both before you drop them. The egg underneath the feather will survive the impact. But when the bowling ball hits the egg — well, let’s just be glad this was an imaginary experiment.
The bowling ball had more energy after its fall because it weighed more. A Pinewood car that weighs more will have more energy after it “falls” down the slope of the track. And more energy is good, beacause that’s what keeps the car speeding along.
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5 comments so far ↓
Tod // Jan 12, 2008 at 7:03 pm
This article is so funny because the physics it purports to be true are simply not so. If you want to understand where weight fits into the grand scheme of pinewood derby, you need to understand the concept of inertial mass versus what we generally refer to as mass. This is very challenging territory. Einstein used this very concept to unravel the secrets of General Relativity. And the person that wrote this page is, quite simply, no Einstein.
The bottom line, don’t buy the bunk on this page. Weight location in the car is several orders of magnitude more important than the actual weight. Friction is even more important than weight. Done properly, the weight is just about as important as aerodynamics.
Adam Kalsey // Jan 14, 2008 at 9:39 pm
Tod, I smell a troll. I considered simply deleting your comment as not to confuse people, but since other people might hold the same belief as you state in your second paragraph, I thought I’d address it.
First off, readers, don’t get confused about Tod’s mention of inertial mass and other mass types. Gravitational mass is simply how an object interacts with a gravitational field (what we often refer to as weight). Inertial mass is how an object resists changes in motion (inertia). Unless you’re studying quantum mechanics or very advanced physics, you can assume the two are the same thing. Einstein pointed out that it should be impossible to measure an difference between an object’s gravitational and inertial masses.
Your car needs to have as much inertia as possible when it reaches the flat part of the track. That’s all that keeps it going. Friction will rob your car of energy, so the more of it you have to start with, the faster you will be.
Here’s how you can determine the amount of energy your car will have. The formula for calculating potential energy is PE=mgh, where m is the mass of the object, g is gravity, and h is the height of the center of mass. On Earth gravity is constant. So the only ways to increase PE is to increase mass and height. You’ll only be able to raise your mass’s height an inch or two from its default of four feet, an increase of a few scant percent. But you can double your mass from it’s default of around 2.5 ounces.
So Tod, you build a car weighing an ounce and using ball bearings or whatever. And I’ll build a 5 ounce car using stock kit parts. And I’ll beat you down the track by several feet every time.
Redneck Joe // Mar 22, 2008 at 8:47 pm
Adam,
You’re putting down Tod and vice versa. You’re both missing the point. Loosely throwing around physical quantities like mass and energy. Come on.
The heavy car wins for this reason…
The net force acting upon the car and sending it down the track is the sum of three main components:
1) Gravity: mg * sin(angle of the track from horizontal)
2) Friction: mg * (coefficient of friction between wheels and axles) * cos(anle of the track from horizontal)
3) Air drag
Yes, there are other frictional forces. They are beyond the scope of the discussion I have read between the two of you.
The heavy car wins because with increasing mass, #3 becomes a less significant fraction of the sum of the forces. The air drag is the same for the 3 oz car and the 5 oz car at the same speed. Force of gravity and force of friction increase roughly proportionally with increasing mass. But the delta between the two (the NET force on the car due to gravity - friction) becomes greater as a ratio to the retarding force applied by the air.
Let me know if you want it explained in more detail with deeper math.
The heavier car doesn’t win because it has “more energy” after the sloped part of the track to carry into the horizontal part. For goodness’ sake, man. You cause me physical pain.
The 5 oz car would have no advantage in a vacuum.
It wins because the air drag is a smaller fraction of the difference between the gravity vector and the friction vector.
I have spoken.
Adam Kalsey // Mar 23, 2008 at 6:58 am
Redneck Joe — In most races, the cars are roughly even when they reach the bottom of the slope. The winning car is always the one that slows down least after this point.
The way to accomplish that is maximize the energy the car has when it reaches this point, and minimize the energy losses after this point.
I’ve observed many races in which an significantly underweight car and a car that eventually ended up in the top 5 were within a car length of each other at the bottom of the slope, but the underweight car didn’t even have enough energy to carry it over the finish line.
Kevin Butler // Apr 2, 2008 at 8:25 pm
The cars start out with no kinetic energy (KE), and potential energy
PE = mass * height*gravity.
As they roll down the track, that potential energy is converted to kinetic energy - assume no friction, 100% conversion:
mhg = PE = KE = 1/2 m * v-squared
If you increase the initial potential energy, you get more kinetic energy.
You can increase that initial potential energy by:
1- increasing the mass - more mass, more potential energy, more kinetic energy, but velocity remains constant, because the increased mass is on both sides of the equation. This increased kinetic energy helps you avoid slowing down as much from the forces of friction.
2- increasing the height (how do you do that? the track is a constant height?). The height that matters is the difference in height between the center of gravity of the car at the top of the track, and the center of gravity at the bottom of the track. Since the car starts out on a slope downwards to the front, putting the center of gravity further back increases the initial height (and thus potential energy, kinetic energy, and more velocity).
So, increase mass to help the car retain its speed as it travels, position the mass toward the back to give additional velocity from the increased height based on the sloped starting track.
kb
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