# Hemisphere on a ramp

1. Jan 26, 2010

### PennyGirl

[/tex]1. The problem statement, all variables and given/known data
http://emweb.unl.edu/negahban/em223/sexam3/sexam3.htm" [Broken]

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

2. Relevant equations
$$\Sigma$$ F_x = 0
$$\Sigma$$ F_y = 0
$$\Sigma$$ M=0
f = $$\mu$$ * N

3. 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...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Jan 26, 2010

### 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.

3. Jan 26, 2010

### PennyGirl

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...

4. Jan 26, 2010

### Gear300

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.

5. Jan 26, 2010

### PennyGirl

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...

6. Jan 26, 2010

### Gear300

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).

Last edited: Jan 26, 2010
7. Jan 26, 2010

### PennyGirl

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