Building a hovercraft, having an issue with finding center of mass

[mxyplizk]

Homework Statement

I'm building a hovercraft, and I'm familiar with how to calculate center of mass--however, there's something that will be sitting on the surface of the hovercraft that's throwing me off. I just can't seem to get it to work. I'm just trying to find what the mass would be at each of the three points of contact (the two hinges and the spring), but apparently torque is involved, and because the board would tend to tip over it's actually pulling the hinges upward, and all other sorts of issues. Is it possible to find the force of the board at each point and divide by gravity to get m? I made a sketch, giving all known values (in inches and degrees) I calculated beforehand:

http://img18.imageshack.us/img18/5536/physicsproblemsketch.jpg

The top left image is a side view, the top right is a less detailed side view with just lines and the measurement values, and the bottom left is a top-down view just to give a general idea of positioning. The mass of the hovercraft body is evenly distributed. There will, however, be other items on it, although I didn't think this would affect the problem here. The masses needed for here are:

board=0.0156 kg
spring=0.008 kg
hinges=0.024 kg each, 0.048 kg together

Homework Equations

I was just trying to find the answer with logic and free body diagrams.

The Attempt at a Solution

I've tried combining the equations for force and torque, but I keep getting different values. That's pretty much the only method I can think of.

Thanks for any and all help!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Welcome to PF.

In the schematic you've provided I'm thinking that if it is Center of Mass you are interested in then it is determined in the usual way. The center of mass of the hinged board, presuming that it is uniform in distribution will be at the geometrical center, as will the surface of the hoover base. The spring and the hinges each have their mass and should as well contribute their mass at their respective positions.

Determining then the center of mass in 3 dimensions involves just the 3 equations for the dimensions and placements of these masses.

Now are there forces and torques at the pivot from the spring. Well yes of course, but they are not going affect the center of mass location unless the masses themselves move relative to each other. For instance the object upside down will apparently yield a different location if the angle θ were to change.

 

[nlightner]

I would suggest using the equations for calculating torque and center of mass to accurately determine the weight distribution of the hovercraft. It is important to consider all the components that will be sitting on the surface of the hovercraft, including the board, spring, hinges, and any other items. These components may affect the overall center of mass and need to be taken into account in your calculations.

First, I would recommend calculating the torque of each component separately, using the equation T = F x d, where T is torque, F is force, and d is the distance from the pivot point. For the board, you will need to consider the weight of the board itself as well as any additional items that will be placed on it. Similarly, for the spring and hinges, you will need to take into account their individual weights and distances from the pivot point.

Next, use the equation for calculating center of mass, which is m1d1 + m2d2 + ... / (m1 + m2 + ...), where m1, m2, etc. are the masses of each component and d1, d2, etc. are the distances from the pivot point. This will give you the overall center of mass for the hovercraft.

If you are still having trouble, I would suggest seeking assistance from a physics teacher or tutor who can guide you through the calculations and help you troubleshoot any issues you may be having. It is important to accurately determine the center of mass in order to ensure the stability and functionality of your hovercraft. Good luck with your project!