# How does the mass distribution and center of gravity affect the speed of a lego car down a ramp? [closed]

we are doing a research involving motion of an object with a nonuniform mass distribution, and we have to explain how mass concentration, mass distribution, and center of gravity will affect a Lego car's speed when we let it go down a ramp. We're trying to understand the physics in motion here.

Pinewood derby engineers have done lots of research into this problem. Fundamentally, cars go faster the more gravitational potential energy is converted into kinetic energy in the forward direction.

Real pinewood derbies usually start with a ramp and then level off into horizontal. In cases like this it's important to put as much mass as you can at the rear of the vehicle so the vehicle starts with slightly more gravitational potential energy. This won't change the car's speed while it's on the ramp but will give a slight boost to the car's speed when it transitions from the ramp and to the horizontal section.

On the ramp itself what matters is your wheels. The more mass there is in the wheels and the more of that mass is concentrated on the outside of your wheels, the slower the car will go. Why? Because we are producing two kinds of kinetic energy. There's the car's speed and then there's the wheels' rotational kinetic energy.

$$mgh=\frac12mv^2+\frac12I\omega^2$$

Speed is the magnitude of $$v$$. Any energy that goes into rotational kinetic energy $$\frac12I\omega^2$$ isn't going into translational kinetic energy $$\frac 12mv^2$$ and therefore isn't going into $$v$$. You can reduce $$I$$ by moving mass from the wheels to the body of the car, moving mass from the outside of the wheels to the inside of the wheels or by removing a wheel.

I assume you have a basic understanding the physics of a mass with wheels going down a ramp. The velocity of car down the ramp is the translational velocity of the system in the equation below: $$mgh=\frac 12 mv^2 + \frac 12 I\omega^2$$

Now with nonuniformity in the mass distribution, the CG of the whole system always point straight downward regardless of position of CG, thus the component of the force parallel to the ramp is also always pointing straight ahead. The only effect of the nonuniformity of mass distribution, hence CG decentralization is the increase of friction on some wheels than the other, causing asymmetrical force on the whole mass, and the Lego car might sway and steer sideways. This might not be very evident with a low mass Lego, but that's just the physics in action.

The OP happens to post a new question stating:

if i was to move a piece of mass attached to the back of a lego car to the rear of the car, what would the effect be on the gravitational potential energy when the car goes off of a ramp. we are measuring the distance.

Gravitational potential energy is a function of height and if by moving the mass backwards the height above ground of the total mass CG increases, then the potential energy increases, and can be calculated using: $$E_p=mgh$$