Finding the Angle of Tipping for a Semi-Cylinder on a Ramp

[PennyGirl]

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Homework Statement

http://emweb.unl.edu/negahban/em223/sexam3/sexam3.htm"

number 3...the one about the semicylinder on a ramp

Homework Equations

$$\Sigma$$ F_x = 0
$$\Sigma$$ F_y = 0
$$\Sigma$$ M=0
f = $$\mu$$ * N

The Attempt at a Solution

I got the first part to be 16.7 degrees. However, I can't find \phi I just need to be pointed in the right direction...

 

[Gear300]

If you were to draw a line from G to the point of contact between the cylinder and ramp, phi occurs when that line coincides with the direction of mg.

 

[PennyGirl]

If you were to draw a line from G to the point of contact between the cylinder and ramp, phi occurs when that line coincides with the direction of mg.

So then I know that the distance between G and the ramp is r*(1-4/(3*pi)), but I don't know how that helps me solve the problem...

 

[Gear300]

So then I know that the distance between G and the ramp is r*(1-4/(3*pi)), but I don't know how that helps me solve the problem...

I wouldn't say that would be the distance...that would be the case when the line from G to contact falls on a radial line, which wouldn't be the same case as when the line from G to contact falls on the vector mg.

 

[PennyGirl]

I wouldn't say that would be the distance...that would be the case when the line from G to contact falls on a radial line, which wouldn't be the same case as when the line from G to contact falls on the vector mg.

right...that makes sense. I'm still having a hard time picturing how this fact will help me solve the problem...
isn't the distance between G and the contact surface going to be in the same direction as mg, otherwise the semi-cylinder would try and move back to the place where they are in the same direction (because g will cause a torque?) sorry if that doesn't make sense...

 

[Gear300]

...isn't the distance between G and the contact surface going to be in the same direction as mg, otherwise the semi-cylinder would try and move back to the place where they are in the same direction (because g will cause a torque?) sorry if that doesn't make sense...

Yup...that is what is going on...and the line covering that distance for this particular case does not necessarily coincide with a radial line (by radial line, I'm referring to the line from the center of what would have been the complete cylinder to the point of contact).

 

[PennyGirl]

Yup...that is what is going on...and the line covering that distance for this particular case does not look like it would coincide with a radial line (by radial line, I'm referring to the line from the center of what would have been the complete cylinder to the point of contact).

So right before it is going to tip, torque = zero...maybe?