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- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/07%3A_Work_and_Energy/7.15%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/PHY_1030%3A_General_Physics_I/06%3A_Work_and_Energy/6.5%3A_Potential_Energy_and_Conservation_of_EnergyConservative force—a force with the property that the work done in moving a particle between two points is independent of the path it takes.
- https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/08%3A_Potential_Energy_and_Conservation_of_Energy/8.01%3A_Conservative_Forces\[\begin{aligned} \frac{\partial F_{z}}{\partial y}-\frac{\partial F_{y}}{\partial z} &= \frac{\partial }{\partial y}\left(\frac{-kz}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\partial}{\partial z}\left...\[\begin{aligned} \frac{\partial F_{z}}{\partial y}-\frac{\partial F_{y}}{\partial z} &= \frac{\partial }{\partial y}\left(\frac{-kz}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\partial}{\partial z}\left( \frac{-ky}{(x^2+y^2+z^2)^\frac{3}{2}}\right)\\ &=\frac{3kz(2y)}{2(x^2+y^2+z^2)^\frac{5}{2}}-\frac{3ky(2z)}{2(x^2+y^2+z^2)^\frac{5}{2}} = 0\\ \frac{\partial F_{x}}{\partial z}-\frac{\partial F_{z}}{\partial x} &= \frac{\partial}{\partial z}\left(\frac{-kx}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\…
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/08%3A_Work_and_Energy/8.15%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/09%3A_Work_Power_and_Energy/9.09%3A_Conservative_and_Non-Conservative_ForcesIf the derivative of the y-component of the force with respect to x is equal to the derivative of the x-component of the force with respect to y, the force is a conservative force, which means the pat...If the derivative of the y-component of the force with respect to x is equal to the derivative of the x-component of the force with respect to y, the force is a conservative force, which means the path taken for potential energy or work calculations always yields the same results.
- https://phys.libretexts.org/Courses/Tuskegee_University/Algebra_Based_Physics_I/06%3A_Work_Energy_and_Energy_Resources/6.05%3A_Conservative_Forces_and_Potential_EnergyA conservative force is one for which work depends only on the starting and ending points of a motion, not on the path taken. We can define potential energy (PE for any conservative force, just as...A conservative force is one for which work depends only on the starting and ending points of a motion, not on the path taken. We can define potential energy (PE for any conservative force, just as we defined PEg for the gravitational force. The potential energy of a spring is PEs=12kx2, where k is the spring’s force constant and |(x\) is the displacement from its undeformed position. Mechanical energy is defined to be KE=PE for conservative force.
- https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/6%3A_Work_and_Energy/6.5%3A_Potential_Energy_and_Conservation_of_EnergyConservative force—a force with the property that the work done in moving a particle between two points is independent of the path it takes.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/08%3A_Work_and_Energy/8.21%3A_Potential_Energy_and_Conservation_of_EnergyConservative force—a force with the property that the work done in moving a particle between two points is independent of the path it takes.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/09%3A_Potential_Energy_and_Conservation_of_Energy/9.03%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/07%3A_Work_Energy_and_Energy_Resources/7.04%3A_Conservative_Forces_and_Potential_EnergyA conservative force is one for which work depends only on the starting and ending points of a motion, not on the path taken. We can define potential energy (PE for any conservative force, just as...A conservative force is one for which work depends only on the starting and ending points of a motion, not on the path taken. We can define potential energy (PE for any conservative force, just as we defined PEg for the gravitational force. The potential energy of a spring is PEs=12kx2, where k is the spring’s force constant and |(x\) is the displacement from its undeformed position. Mechanical energy is defined to be KE=PE for conservative force.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/08%3A_Potential_Energy_and_Conservation_of_Energy/8.03%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
