Path-dependent Forces
Path-dependent Forces - Related Videos
01:22
Mean free path and Mean free time
0 Views •
2025
Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path." The mean free path varies inversely with the density of the molecules because when there are more molecules inside a volume, they have a greater chance of colliding with each other, thus reducing the mean free path. Additionally, the mean free path is inversely related to...
01:21
Path Between Thermodynamics States
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2023
Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1: In the first process for path A to C, the gas is kept at constant temperature T. It undergoes an expansion from volume V1 to V2. The work done by an ideal gas is expressed as Substituting for pressure as nRT/V from the ideal gas equation and integrating the terms, the work done by an ideal gas at constant temperature is obtained as In the second process, for path A to B, the...
07:26
Foraging Path-length Protocol for Drosophila melanogaster Larvae
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Cited by 18 •
2016
We provide a detailed protocol for a Drosophila melanogaster foraging path-length assay. We discuss the preparation and handling of test animals, how to perform the assay and analyze the data.
03:48
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion
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2020
Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
01:10
Interference: Path Lengths
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2023
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same. Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
FAQs
Path-dependent Forces require evaluating work along the trajectory, using the force’s component in the direction of each infinitesimal displacement. This calculation is represented by the line integral of F dot dr. Therefore, two routes connecting the same endpoints can yield different work values when the traveled path or the force encountered along it changes.
A nonzero closed-path result shows that returning to the starting position does not restore the original mechanical-energy balance. Friction, drag, or deformation can transfer energy away from mechanical motion or otherwise dissipate it during the circuit. The closed-path calculation therefore exposes effects that endpoint positions alone cannot describe.
Conservative forces can be represented through a potential-energy change because their work depends only on the endpoints. Path-dependent Forces do not generally permit that shortcut: route-specific work must be evaluated directly, and energy transferred through resistance or deformation must be included separately. This distinction prevents potential-energy methods from hiding mechanical-energy losses.
To analyze one of these interactions, first specify the object’s actual trajectory and the force acting along it. Then evaluate the force-displacement integral over that route, rather than using only the endpoint coordinates. Finally, include the resulting work when accounting for changes in the object’s mechanical energy. This workflow connects geometry, force, and energy.
Vehicles moving through air, objects sliding across surfaces, and machines experiencing resistance are direct applications. In each case, the relevant motion follows a physical route, while drag, friction, or deformation can alter the mechanical-energy balance. Modeling the actual trajectory and associated work helps describe energy losses that an endpoint-only treatment would omit.
They make motion models more realistic by requiring resistance and energy transfer to be included. A model that tracks only positions and conservative potential energy may fail to represent work done by friction, drag, or deformation. Incorporating route-dependent work allows the analysis to connect the modeled motion with changes in mechanical energy.