Simulating a system of levers with opposing force?

kperry1408

I'm trying to simulate the following situation:

Two bars are attached to each other at one end by a device which controls the angle between them. The opposite end of each bar (the end not attached to the device) is subject to a resistive, motion-opposing (friction-like) force, each with an equal maximum threshold.

How can I determine the motion (rotational and translational) that this object undergoes when the angle between the bars is changed from alpha to beta? I am planning to describe the position of the object using the position of the junction between bars and the direction that each bar currently points.

I.e. if the object is initially centered at (0,0) with bar A (length Ra) pointing to ∏ and bar B (length Rb) pointing to 0, and the angle from A to B is changed from ∏ to ∏/2, what will the new position and angles be?

Thanks in advance, I know it's a long question :)

mfb

What do you mean with "maximum threshold"?
It depends on the mass distribution of your system, the friction and the speed of the angular change.
Usual case: If you do it slow enough, just one arm moves. If you change your angle fast enough, both move.

kperry1408

Similar to friction, i.e. in the case of friction the maximum value is the coefficient of friction multiplied by the normal force. The friction opposes all motion however it can only exert that certain maximum force so when a force larger than that is put on the object the object will still move, just not as rapidly. In this case I would assume that the coefficient were the same for static and kinetic cases just to simplify things.

And let's say we are already given the moment of inertia of each lever, Ia and Ib. And the only frictional force is the one stated above. Shouldn't both arms turn proportionally to each other? I don't see why just one would move when they are being turned relative to each other, and the resistive force is the same for each..

mfb

If the force on one arm is smaller than the friction, it does not move at all - friction on a surface is usually independent on the velocity (at least as approximation). You have to apply a force which is larger than friction to get it moving.

kperry1408

If friction on a surface were independent of velocity than an object would continue sliding forever if you gave it an initial push that were stronger than friction..? Or it would first cause it to stop, then turn it around and accelerate it in the other direction which is also clearly not the case

mfb

No, as soon as your push ends, the force would slow the object down, and the object would come to rest (and stay at rest) after a finite time and distance.
F=m*a

kperry1408

Right but why does the friction force stop pushing when the object comes to rest? It has to depend on velocity to some extent. It may be that it has a constant value which points in the direction opposite of the velocity vector (which would be a zero vector when velocity is zero) but is still has to be dependent on velocity

mfb

As you already said, it is a maximal force. If you apply a smaller force (can be 0), this is just transferred to the ground and the object does not move. If the force is too large, only this maximal amount is transferred and the object gets accelerated.
This is ignoring the difference between static and dynamic friction here.

kperry1408

Yeah I agree that static friction behaves this way. I guess I should have been more specific but kinetic friction is primarily what I'm interested in for this case. Kinetic friction does rely on velocity because it opposes the velocity vector, whereas static friction just opposes the net force vector.

mfb

This is the part about kinetic friction. It is always there if the object is moving, it is antiparallel to the velocity and with the same magnitude (independent of the velocity !=0), neglecting nonlinear effects.