Is Work Path Dependent with a Zero Total Displacement?

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SUMMARY

Work is path dependent, contrary to the initial assumption that it is a state function like energy. In scenarios where an object returns to its original position, such as dragging a block across a rough surface and back, work is still performed due to the force exerted against friction. Therefore, even with zero total displacement, work is done when a force acts on a moving object. This highlights the importance of considering the path taken when evaluating work done in physics.

PREREQUISITES
  • Understanding of basic physics concepts, specifically work and energy.
  • Familiarity with the definition of displacement in physics.
  • Knowledge of forces and friction in mechanical systems.
  • Basic grasp of state functions in thermodynamics.
NEXT STEPS
  • Research the mathematical definition of work in physics, including the formula W = F · d · cos(θ).
  • Explore the concept of path independence in conservative forces.
  • Study examples of work done against friction in real-world applications.
  • Learn about energy conservation principles related to work and displacement.
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of work and energy in physical systems.

fiziksfun
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Is work done if the total displacement is 0?

It doesn't matter what path the object took to get from A back to A, right? As long as it ends at A, then its zero work, correct?

So work IS NOT path dependent, it's a state function, like energy, right ?
 
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fiziksfun said:
Is work done if the total displacement is 0?
In general, yes.
fiziksfun said:
It doesn't matter what path the object took to get from A back to A, right? As long as it ends at A, then its zero work, correct?
No. In general even if the displacement is zero when a force acts on a moving object, work is done.
fiziksfun said:
So work IS NOT path dependent, it's a state function, like energy, right ?
Nope, work is path dependent.

For example, consider dragging a block across a rough surface for a distance of ten meters and then dragging it back to the same place you started. Did you do work on that block?
 

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