Adoniram said:Homework Statement
Does there exist a 1-dimensional non-conservative force that depends on POSITION (not velocity)?
Homework Equations
N/A
The Attempt at a Solution
I've given this a lot of thought, and I can't come up with anything! Friction doesn't work, etc...
Any help would be greatly appreciated! :)
Adoniram said:Friction doesn't fit the definition because it is not dependent on position. Hysteresis... not sure. That seems more dependent on tension, but if it can be quantified in terms of position, that might work. What do you think?
berkeman said:I think friction can work if you put one condition on it. Can you think of that condition?
Adoniram said:Are you referring to static vs kinetic? As far as I can tell, friction depends on some velocity being present (kinetic), or not present at all (static). As far as I can imagine, it doesn't depend on position, but I would love to hear which condition you refer to :)
Adoniram said:Ok, so say you have a block sliding along a surface. The only way I can think of making the force of friction dependent on position is if the coefficient of friction changes along the surface. For example, if you have sand paper on the surface with changing grit values from left to right, then yes, the force of friction would absolutely depend on position.
I'm not sure if that's what my prof is going for, but I'll give it a whirl... I can't think of any others!
A 1-dimensional non-conservative force is a type of force that acts on an object along a single dimension, such as in the horizontal or vertical direction. This force is not conservative, meaning that it does not conserve mechanical energy, and its magnitude and direction can change as the position of the object changes.
A 1-dimensional non-conservative force depends on position because its magnitude and direction change as the position of the object changes. This means that the force may be different at different points along the object's path, and it is not constant like a conservative force.
Friction is a common example of a 1-dimensional non-conservative force. As an object moves along a surface, the force of friction acting on it changes depending on its position. For example, as a block slides down a ramp, the force of friction decreases as it moves further down the ramp.
The work done by a 1-dimensional non-conservative force is calculated by integrating the force over the object's path. This takes into account the changing magnitude and direction of the force at different positions along the path.
1-dimensional non-conservative forces do not conserve mechanical energy, as their magnitude and direction can change along the object's path. This means that work must be done to overcome these forces, resulting in a change in the object's kinetic or potential energy.