Misc Questions: Virtual work, RMS, Friction on incline, and Virtual Displacement

[mishima]

I have a few questions I thought I'd post together instead of making separate threads, hope that's ok. They are more or less unrelated...

1. Are there 2 conceptual ideas that use the term "virtual work"? I am familiar with the one from intro level physics, but I read there is also one from calculus of variations and could not tell if it was really the same thing or not (due to hardcore ignorance of calculus of variations). Also "virtual work" is totally unrelated to "pseudo work" (internal energy), right?

2. Why is the root mean square used in kinetic theory as opposed to other averaging methods? I understand it accounts for negative velocities but can't other statistical methods do that as well? Was it that this just happened to be chosen by Maxwell?

3. What is the direction of the force of friction for a cylinder rolling up an incline? I know its up the incline for when its rolling down...need help with a better way to think about this. I know that the net acceleration must be down for the object to decelerate as it travels up the incline, but not sure if friction is adding to the force due to gravity or subtracting. I feel stupid for not getting this.

4. Can someone give an example of a problem which requires the solver to use an impossible virtual displacement?

Thank you.

 

[rcgldr]

3. What is the direction of the force of friction for a cylinder rolling up an incline? I know its up the incline for when its rolling down.

The friction force is related to acceleration, not velocity, so it doesn't matter if the initial state has the cylinder rolling up or down the incline, the friction force is up the incline (due to the angular inertia of the cylinder "resisting" the downwards acceleration of gravity).

 

[vikrambij]

3.
to find out direction of friction force,,,, just assume the surfaces smooth,,,,then find out direction of relative motion between the two surfaces,,,,the friction will always try to stop this relative motion,,,,
in ur case when the cylinder is rolling up,,,frictional force (acting upward) will provide necessary torque to retard(angular velocity)