2 Recap – Work & Energy The total work done on a particle is equal to the change in itskinetic energy
3 Potential EnergyThe total work done on an object equals the change in its kinetic energyBut the total work done on a system of objects may or may not change its total kinetic energy. The energy may be stored as potential energy.
4 Potential Energy – A Spring Both forces do work on the spring. Butthe kinetic energy of the spring isunchanged. The energy is stored aspotential energy
5 Conservative Forces If the ski lift takes you up a displacement h, the work done on you, bygravity, is –mgh. But when you ski downhillthe work done by gravityis +mgh, independent of thepath you take
6 Conservative Forces The work done on a particle by a conservative force is independent of the path takenbetween any twopoints
7 Potential-Energy Function If a force is conservative, then we candefine a potential-energy function as thenegative of the work done on the particle
8 Potential-Energy Function potential-energy function associatedwith gravity (taking +y to be up)The valueofU0 = U(y0)can be setto anyconvenientvalue
9 Potential-Energy Function of a Spring By convention,one choosesU0 =U(0) = 0
10 Force & Potential-Energy Function In 1-D, given the potential energy functionassociated with a force one can computethe latter using:Example:
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