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- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/08%3A_Work_and_Energy/8.16%3A_Conservation_of_EnergyA conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particl...A conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/04%3A_Electric_Potential_Energy_Electrical_Potential_or_Voltage_and_Capacitance/4.02%3A_Electric_Potential_Energy_and_Electrical_Potential_DifferenceA convenient choice of reference that relies on our common sense is that when the two charges are infinitely far apart, there is no interaction between them. (Recall the discussion of reference potent...A convenient choice of reference that relies on our common sense is that when the two charges are infinitely far apart, there is no interaction between them. (Recall the discussion of reference potential energy in Potential Energy and Conservation of Energy.) Taking the potential energy of this state to be zero removes the term \(U_{ref}\) from the equation (just like when we say the ground is zero potential energy in a gravitational potential energy problem), and the potential energy of Q when…
- 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/8.03%3A_Mechanical_Energy_and_Conservation_of_EnergyThe mechanical energy of the block at position \(A\) is thus: \[\begin{aligned} K_A&=0\\[4pt] U_A&=\frac{1}{2}kD^2\\[4pt] \therefore E_A &= U_A + K_A = \frac{1}{2}kD^2\end{aligned}\] At position \(B\)...The mechanical energy of the block at position \(A\) is thus: \[\begin{aligned} K_A&=0\\[4pt] U_A&=\frac{1}{2}kD^2\\[4pt] \therefore E_A &= U_A + K_A = \frac{1}{2}kD^2\end{aligned}\] At position \(B\), the spring potential energy of the block is zero (since the spring is at rest), and all of the energy is kinetic: \[\begin{aligned} K_B&=\frac{1}{2}mv_B^2\\[4pt] U_B&=0\\[4pt] \therefore E_B &= U_B+K_B=\frac{1}{2}mv_B^2\end{aligned}\] Since there are no non-conservative forces doing work on the b…
- 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 \(PE_g\) for the gravitational force. The potential energy of a spring is \(PE_s = \frac{1}{2}kx^2\), 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/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/09%3A_Work_Power_and_Energy/9.12%3A_Conservation_of_EnergyFigure \(\PageIndex{2}\): Bar graphs representing the total energy (E), potential energy (U), and kinetic energy (K) of the particle in different positions. (a) The total energy of the system equals t...Figure \(\PageIndex{2}\): Bar graphs representing the total energy (E), potential energy (U), and kinetic energy (K) of the particle in different positions. (a) The total energy of the system equals the potential energy and the kinetic energy is zero, which is found at the highest point the particle reaches. (b) The particle is midway between the highest and lowest point, so the kinetic energy plus potential energy bar graphs equal the total energy. (c) The particle is at the lowest point of th…
- 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 \(PE_g\) for the gravitational force. The potential energy of a spring is \(PE_s = \frac{1}{2}kx^2\), 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/Workbench/PH_245_Textbook_V2/04%3A_Module_3_-_Conservation_Laws/4.01%3A_Objective_3.a./4.1.08%3A_Conservation_of_EnergyA conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particl...A conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/07%3A_Work_and_Energy/7.16%3A_Conservation_of_EnergyA conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particl...A conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/09%3A_Potential_Energy_and_Conservation_of_Energy/9.04%3A_Conservation_of_EnergyA conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particl...A conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.
- 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/8.04%3A_Conservation_of_EnergyA conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particl...A conserved quantity is a physical property that stays constant regardless of the path taken. If non-conservative forces do no work and there are no external forces, the mechanical energy of a particle stays constant. For one-dimensional particle motion, in which the mechanical energy is constant and the potential energy is known, the particle’s position, as a function of time, can be found by evaluating an integral that is derived from the conservation of mechanical energy.
- https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/08%3A_Potential_Energy_and_Conservation_of_Energy/8.03%3A_Mechanical_Energy_and_Conservation_of_EnergyThe mechanical energy of the block at position \(A\) is thus: \[\begin{aligned} K_A&=0\\ U_A&=\frac{1}{2}kD^2\\ \therefore E_A &= U_A + K_A = \frac{1}{2}kD^2\end{aligned}\] At position \(B\), the spri...The mechanical energy of the block at position \(A\) is thus: \[\begin{aligned} K_A&=0\\ U_A&=\frac{1}{2}kD^2\\ \therefore E_A &= U_A + K_A = \frac{1}{2}kD^2\end{aligned}\] At position \(B\), the spring potential energy of the block is zero (since the spring is at rest), and all of the energy is kinetic: \[\begin{aligned} K_B&=\frac{1}{2}mv_B^2\\ U_B&=0\\ \therefore E_B &= U_B+K_B=\frac{1}{2}mv_B^2\end{aligned}\] Since there are no non-conservative forces doing work on the block, the mechanical…
