Tricky Tipping Problem; 11 sided figure

[tachu101]

Homework Statement

A regular polygon of 11 sides is on an adjustable incline. The polygon has sides on 1.32 meters each. At what angle of the incline will the polygon tip over. Extra: what is the area of a cross section of the polygon.

The Attempt at a Solution

This problem has to do with center of mass. I have to calculate at what angle the center of mass will be over the 90 degree mark.

I found that each interior angle of the 11 sided figure is 147.27 degrees. I then don't know how to explain it but I took half of that angle and ended up with 73.63 degrees. Because the center of mass has to be at a right angle to tip over I then did 90-73.63= 16.4 degrees and I think that this is my answer.

The area of the cross section I think is 16.3 m^2 because I looked up an equation on wikipedia that said the area is equal to 9.356*(side length)^2

Can anyone confirm this.

 

[Dick]

Right on both. You might try thinking about how to derive the wikipedia formula. It's not that hard. Split the polygon into 11 isosceles triangles with a vertex at the center. The central angle is 360/11. Do trig.

 

[ogb p]

I would approach this problem by first verifying the given information. I would double check the number of sides, as well as the length of each side, to ensure accuracy in my calculations. I would also clarify what is meant by "adjustable incline" - is it a ramp or a platform that can be tilted? This will affect the calculations for the tipping angle.

Next, I would use the formula for calculating the center of mass of a regular polygon to determine the location of the center of mass for the 11-sided figure. This will give me a better understanding of how the weight is distributed within the figure and how it will affect its stability on the incline.

Once I have determined the center of mass, I can then use principles of torque and equilibrium to calculate the tipping angle. This will involve considering the weight of the figure, the angle of the incline, and the location of the center of mass.

As for the area of the cross section, the formula given in the attempt at a solution seems to be correct, but it is always important to double check and verify any equations used for calculations.

In conclusion, solving this tricky tipping problem requires a thorough understanding of geometry, physics, and mathematical principles. It is important to double check all given information and to carefully consider the forces at play in order to arrive at an accurate solution.