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

#### mxyplizk

1. 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 [Broken]

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

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

3. 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!
1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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#### LowlyPion

Homework Helper
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.

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