PHY 107 1st Edition Lecture 16 Outline of Last Lecture I. Work – Kinetic Energy TheoremII. PowerOutline of Current LectureIII. Potential EnergyIV. Conservative and Non-Conservative ForcesV. Mechanical Energy VI. Conservation of Mechanical EnergyCurrent LecturePotential Energy:- Change in potential energy, U: ∆U = -W - Consider an object of mass m:o The object is taken together with the earth as the systemo The object is thrown upwards with initial speed v0 at point Ao Gravitational force slows it down and it stops completely at point Bo The object falls back down and by the time it reaches point A, its speed has reached the original value of v0 From A to B, gravitational force does negative work (W1 = -mgh) – energy is transferred by Fg from the kinetic energy of the object to the gravitational potential energy U From B to A, the gravitational force does positive work (W2 = mgh) – gravitational force transfers energy from the gravitational potential energy U of the object-earth system to the kinetic energy of the object- Determining potential energy values:o W = ∫xixfF(x)dx → ∆U = Uf – Ui = -W → ∆U = Uf – Ui = - ∫xixfF(x)dx- Gravitational potential energy: These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o U(y) = mgy- Potential energy of a spring: o U = kx22Conservative and Non-Conservative Forces:- Conservative force – can transfer energy from the kinetic energy of part of the system to potential energy and vice versao E.g. gravitational force, spring force- Non-conservative force – energy transfer is irreversible o E.g. frictional force, drag force- Path independence of conservative forces: o A force is conservative if the net work done on a particle during a round trip is always equal to zero (Wnet = 0)o If a force is conservative then the work done on a particle between two points, a and b, does not depend on the pathWa1b = Wa2b (work done by a conservative force does not depend on the path taken but only on initial and final points) Mechanical Energy:- Sum of potential and kinetic energies: Emech = K + UConservation of Mechanical Energy: - ∆Emech = ∆K + ∆U = 0 - Mixture of conservative and non-conservative forces:o ∆Emech = ∆K + ∆U = Wnc (nc = non-conservative forces)- Mechanical energy conservation for projectile motion o K + Ug = K0 +
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