Pinewood derby with a slight difference

[headtackle]

I am currently in the process of building a pinewood derby car for a pinewood related project with a slight difference. The winner is not the fastest car but instead the car that overcomes friction and travels the longest distance.

I need to predict how far my car will go using the usual motion and energy calculations but after hours of searching, these all seem to be focussed on speed rather than distance.

Have been looking at potential energy and can calculate that easy enough along with the acceleration forces associated with the ramp. My problem seems to be calculating the effect of the various frictions that will bring my car to a halt and also comparing like with like and not Newtons v Joules.

Am trying to rearrange to work out a predictive formula for distance based on weight, height, slope angle etc and also need formulae to identify and quantify the effect of rotational friction, kinetic friction and air drag.

Seem to be going round in circles. If anyone has looked at Pinewood cars from this perspective and has any thoughts they would be much appreciated.

Thanks in advance

 

[jvicens]

I can understand your frustration in trying to predict how far your pinewood derby car will go using motion and energy calculations. While most resources may focus on speed, there are ways to incorporate these calculations to predict distance as well.

First, let's start with the basics of motion and energy. The distance an object travels is related to its initial velocity, acceleration, and time. This can be calculated using the equation d = v0t + (1/2)at^2, where d is the distance, v0 is the initial velocity, a is the acceleration, and t is time. This equation can be used to predict the distance your car will travel down the ramp based on the slope angle and the time it takes to reach the bottom.

Next, let's consider the effects of friction on your car's motion. Friction is a force that opposes motion and can significantly affect the distance your car travels. There are three types of friction that you mentioned: rotational friction, kinetic friction, and air drag.

Rotational friction is the resistance caused by the rotation of your wheels. This can be minimized by using smooth, well-lubricated wheels and axles. Kinetic friction, on the other hand, is the resistance between two surfaces in contact while in motion. This can be reduced by using a lightweight car and ensuring that the wheels are aligned properly. Lastly, air drag is the resistance caused by the air pushing against your car as it moves. This can be reduced by making your car more aerodynamic, such as by using a streamlined design and minimizing any protruding parts.

To incorporate these types of friction into your calculations, you can use the equation F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force (the force perpendicular to the surface). The coefficient of friction will vary depending on the type of friction and the materials in contact. By including this force in your calculations, you can get a more accurate prediction of how far your car will travel.

In addition, you can also consider the potential energy of your car at the top of the ramp and how it is converted into kinetic energy as it moves down the ramp. This can be calculated using the equation PE = mgh, where PE is potential energy, m is the mass of the car, g is the acceleration due to gravity, and h is the height of the ramp. By comparing the potential