https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/a/potential-energy-and-conservative-forces 2026-05-01T14:10:52.97313295Z Learn and try: Potential energy and conservative forces Learn how to model the potential energies associated with gravitational and spring force interactions. Explore the special energy properties associated with the work done by conservative forces. article https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/e/gravitational-potential-energy-ap-physics-1 2026-06-19T17:56:42.733541135Z Potential energy Check your understanding of potential energy in this set of free practice questions. Sean Boston exercise https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/v/potential-energy-and-conservative-forces-part-1 2026-03-26T20:17:16.460726625Z Potential energy and conservative forces (part 1) Potential energies are only associated with conservative forces. The change in potential energy between two configurations of a system is the negative of the work done by the conservative force during the change. Because the gravitational field near the surface of a planet is nearly constant, the change in gravitational potential energy of a system containing an object and a planet when the object is near the surface of the planet can be approximated by ΔU_g = mgΔy. Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/edfc8a28-7018-45dd-9ce6-993ede90c0fa_1280_720_base.png Potential energy and conservative forces (part 1) Potential energies are only associated with conservative forces. The change in potential energy between two configurations of a system is the negative of the work done by the conservative force during the change. Because the gravitational field near the surface of a planet is nearly constant, the change in gravitational potential energy of a system containing an object and a planet when the object is near the surface of the planet can be approximated by ΔU_g = mgΔy. https://cdn.kastatic.org/ka-youtube-converted/1eooA5q9GCs.mp4/1eooA5q9GCs.mp4 1026 Potential energy https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/v/potential-energy-and-conservative-forces-part-2 2026-03-26T20:17:16.460726625Z Potential energy and conservative forces (part 2) The general form for the gravitational potential energy of a system consisting of two approximately spherical distributions of mass is given by the equation U_g = -GMm/r. The gravitational energy is negative because the zero reference configuration is chosen as the two masses being infinitely far away from each other (r = infinity). Therefore, the gravitational potential energy for any closer configuration is less than zero. Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/5d0f63a9-26d7-479d-b59a-41b68c8022c2_1280_720_base.png Potential energy and conservative forces (part 2) The general form for the gravitational potential energy of a system consisting of two approximately spherical distributions of mass is given by the equation U_g = -GMm/r. The gravitational energy is negative because the zero reference configuration is chosen as the two masses being infinitely far away from each other (r = infinity). Therefore, the gravitational potential energy for any closer configuration is less than zero. https://cdn.kastatic.org/ka-youtube-converted/9o1WbcK7_-g.mp4/9o1WbcK7_-g.mp4 853 Potential energy https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/v/potential-energy-and-conservative-forces-part-3 2026-03-26T21:24:35.431306416Z Potential energy and conservative forces (part 3) The force exerted by an ideal spring is a conservative and obeys Hooke’s law. Applying the general equation for change in potential energy reveals that the elastic potential energy of a system containing an ideal spring is given by the following equation, where Δx is the distance the spring has been stretched or compressed from its equilibrium length: ΔU_s = ½k(Δx)^2. The elastic potential energy is zero when the spring is at its relaxed length. Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/6f7520d4-369a-4c74-965d-51861414a9f4_1280_720_base.png Potential energy and conservative forces (part 3) The force exerted by an ideal spring is a conservative and obeys Hooke’s law. Applying the general equation for change in potential energy reveals that the elastic potential energy of a system containing an ideal spring is given by the following equation, where Δx is the distance the spring has been stretched or compressed from its equilibrium length: ΔU_s = ½k(Δx)^2. The elastic potential energy is zero when the spring is at its relaxed length. https://cdn.kastatic.org/ka-youtube-converted/Q6EgiGx7EUQ.mp4/Q6EgiGx7EUQ.mp4 693 Potential energy https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/v/potential-energy-and-conservative-forces-part-4 2026-03-26T21:24:35.431306416Z Potential energy and conservative forces (part 4) A conservative force exerted on a system in a single dimension is equal to the negative derivative of the system’s potential energy with respect to position in that dimension. The force points in the direction of decreasing potential energy. The relationship is represented by the following equation: F_x = -dU(x)/dx Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/08c08345-1d90-4633-98a8-dffe921406db_1280_720_base.png Potential energy and conservative forces (part 4) A conservative force exerted on a system in a single dimension is equal to the negative derivative of the system’s potential energy with respect to position in that dimension. The force points in the direction of decreasing potential energy. The relationship is represented by the following equation: F_x = -dU(x)/dx https://cdn.kastatic.org/ka-youtube-converted/qKTBVL5jBIA.mp4/qKTBVL5jBIA.mp4 760 Potential energy https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/v/potential-energy-and-conservative-forces-part-5 2026-03-26T21:24:35.431306416Z Potential energy and conservative forces (part 5) Graphs of a system’s potential energy as a function of position can be useful in determining properties of that system. Stable equilibrium is a location at which a small displacement results in a force opposite the direction of the displacement, accelerating the object back toward the equilibrium position. Stable equilibrium positions exist where the potential energy as a function of position has a local minimum. Unstable equilibrium is a location at which a small displacement results in a force in the same direction as the displacement, accelerating the object away from the equilibrium position. Unstable equilibrium positions exist where the potential energy as a function of position has a local maximum. Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/ae149018-473d-49b1-b244-32ddf234c586_1280_720_base.png Potential energy and conservative forces (part 5) Graphs of a system’s potential energy as a function of position can be useful in determining properties of that system. Stable equilibrium is a location at which a small displacement results in a force opposite the direction of the displacement, accelerating the object back toward the equilibrium position. Stable equilibrium positions exist where the potential energy as a function of position has a local minimum. Unstable equilibrium is a location at which a small displacement results in a force in the same direction as the displacement, accelerating the object away from the equilibrium position. Unstable equilibrium positions exist where the potential energy as a function of position has a local maximum. https://cdn.kastatic.org/ka-youtube-converted/gY8sqnmju-0.mp4/gY8sqnmju-0.mp4 816 Potential energy https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:work-energy-and-power/x077f5683c1428fac:potential-energy/e/potential-energy-and-conservative-forces 2026-06-13T13:40:49.567900266Z Potential energy and conservative forces Apply your knowledge of potential energy and conservative forces in this set of free practice questions. Emily Cizmas exercise