# Mass, velocity and inertia [closed]

If 5 ozs of weight is my engine, and this weight starts in the back of a four wheeled vehicle traveling down a decline gaining speed due to the engine mass to allow its inertia to carry it across a flat level surface; would the laws of physics allow this to travel faster once at this flat surface if the weight stayed put, if the weight was ejected, or if the weight shifted to the front?

I am trying to understand the physics behind the forces at play... If this rewording is not acceptable, please let me know as I am not trying to break the rules, rather, am trying to understand these forces at play to try to then engineer something. I am not trying to cheat, and can certainly offer more explanation if requested and allowed.

## closed as off-topic by ACuriousMind♦, CuriousOne, user36790, Norbert Schuch, Kyle KanosFeb 6 '16 at 12:16

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• The kinetic energy in your car's mass is the only thing that propels you against the friction of wheels and aerodynamics. It's basically your "engine". Why in the world would you want to ditch the engine???? – CuriousOne Feb 5 '16 at 21:37
• Do the rules allow things to deliberately fall off? – DJohnM Feb 6 '16 at 2:42

The things I learnt in years of pinewood derby racing:

• use the maximum weight
• keep it at the back
• make sure the car tracks straight
• focus on stability

The weight is your "engine". Since you start at a slope, mass at the back has further to drop than mass at the front (really!). You can think about it like this: if the weight of the car is evenly distributed on front and back wheels, then the curvature of the track (which gives rise to a slightly off-vertical force in the frame of reference of the car) results in balanced forces; but if you have the weight at the back, the curvature of the track will propel the car. That's the mechanism by which you take advantage of the extra potential energy.

Once you leave the curved section, you have to roll straight without friction. Now there are four sources of friction: the wheel "bearing", the ground (rolling friction), the air, and the ridge between the wheels. It is my observation that this is the one that gets people - if the car starts to rattle from side to side, you will get increased lateral force from the wheels against the guide track, and that will lose you the race.

So focus on stability of the car (this actually means increasing the moment of inertia about the vertical axis - so you need a little bit of mass at the front), minimal friction between the inside of the wheel and the guide (the wheels can have burrs on the inside), and of course make sure that the wheels are well lubricated. In particular look at the point where the head of the nail contacts the wheel, and where the wheel touches the car. Those are the two points where there can be unexpectedly high torque.

Ditching the weight will do nothing for you. The friction in the axle, and the air drag, are small. It's the other friction that kills you. The car will be less stable (and have less kinetic energy with which to overcome friction) if you drop the weight.

Disclaimer: This answer was written before I found out that a pinewood derby is for miniature wooden cars that run in a track. Therefore, only part of it will apply to a pinewood derby.

As I understand your situation, you will be traveling down an incline and then on to a horizontal surface. You are saying you want to maximize the effect of gravitational acceleration on the incline, and then to eliminate weight on the horizontal surface in order to minimize friction. But remember that the car will have beneficial momentum along the horizontal. If you jettison weight, you will reduce that momentum, which you don't want to do.

Here are some other suggestions:

As there's no engine in your car, aerodynamic efficiency is a large part of the vehicle's performance. Design the car with a tapering rear in order to reduce air suction directly behind the car, and a tapering front in order to reduce wind resistance.

A proposed re-design of Santa's sleigh in this link will give you an idea of the lines to strive for: http://www.popsci.com/why-santas-sleigh-poorly-designed-aerodynamic-efficiency. Integrate the wheels into the aerodynamic shape of the vehicle by placing them inside properly designed fender wells.

Make your wheels as light as possible in order to reduce rotational inertia. It takes more energy to rotate weight attached to the wheels than it does to propel weight attached to the body of the vehicle. The center of the wheel travels at the same speed as the vehicle, but the top of the wheel travels faster than the vehicle, so it takes more energy to move the wheel a given horizontal distance than it does to move the body of the vehicle that same distance.

The moment of inertia of weight on the rim of the wheel is greater than the moment of inertia of weight in the center of the wheel. Therefore, try to make the wheel lighter toward the rim. You can do this by tapering the wheel disk toward the rim. An added benefit is less contact with the center ridge in the track. But the inside surface must be precisely machined so it contacts the edge of the ridge evenly and continuously to avoid energy-absorbing shimmy.

The larger the wheel, the less rolling friction on the road surface. But a larger wheel means more rotating weight. Also, a larger wheel presents more surface contact with the center ridge of the track. (Applicable for soapbox derby: Steering a large wheel may absorb more of the vehicle's kinetic energy than steering a small wheel. You might want to make the rear wheels larger, and the front steering wheels smaller.)

The only motive power you have is gravitational acceleration. Make it as easy as possible for gravity to pull your vehicle down the incline, and don't do anything to impair the vehicle's momentum as it rolls on the horizontal.