Physical intuition physics help

[yxgao]

Consider a horizontal string. There are SMALL vertical displacements. One is is fixed. The other is attached to a ring that slides on a frictionless pole.


No calculation required. Initially, there is gravity. Using physical intuition, describe rougly what the equilibrium position looks like. Suddenly turn off gravity. Again using physical tuition, describe what happens as a result.

 

[HallsofIvy]

Looks pretty easy to me. You could actually do the first part as an experiment. You would of course, see that the ring slips down the pole until the string is in a straight line. When gravity is "turned off", the tension in the string will (that was previously keeping the ring from sliding further) cause the ring to move upward. Since there is no friction, the ring will rise until the string is horizontal.

OOPs, just occurred to me this is a "string", presumably non-elastic.
In that case, there is no upward force and the ring stays where it is. If the string is elastic the ring will rise until the string reaches it natural, unstretched length or until it is horizontal, which ever comes first.

 

[yxgao]

Thanks for your reply!
Does it also matter whether the ring is massless or not?
The length of the string is L which is just the distance between the left and right pole. The string is elastic for SMALL displacements.

 

[HallsofIvy]

As long as the string has mass, the mass of the ring can be incorporated into that.

Since the "rest" length of the string is exactly the distance between "right and left poles" (actually your original post only mentioned one pole. I assume this means the horizontal distance from the point at which one end of the string is fixed to the pole at the other end.) the only way the end of the string can move is if the string stretches.

The ring slides down the pole until the vertical component of tension in the string is equal to the weight of the string (and ring).

If gravity is "turned off" the ring will rise above the horizontal the same distance it was below and then oscillate around the horizontal- sort of like a pendulum.