sy14_oct22_07hc - Physics 207, Lecture 14, Oct. 22 Physics...

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Physics 207: Lecture 14, Pg 1 Physics 207, Physics 207, Lecture 14, Oct. 22 Lecture 14, Oct. 22 Agenda: Finish Chapter 10, Chapter 11 Agenda: Finish Chapter 10, Chapter 11 Assignment: Assignment: HW6 due Wednesday HW6 due Wednesday HW7 available soon HW7 available soon Wednesday, Read Chapter 11 Wednesday, Read Chapter 11 Chapter 10: Energy Chapter 10: Energy Energy diagrams Springs Chapter 11: Work Chapter 11: Work Work and Net Work Work and Kinetic Energy Work and Potential Energy Conservative and Non-conservative forces
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Physics 207: Lecture 14, Pg 2 Force vs. Energy for a Hooke’s Law spring Force vs. Energy for a Hooke’s Law spring F = - k (x – x equilibrium ) F = ma = m dv/dt = m (dv/dx dx/dt) = m dv/dx v = mv dv/dx So - k (x – x equilibrium ) dx = mv dv Let u = x – x eq. m = - f i f i v v x x dv mv du ku f i f i v v x x mv ku | | 2 2 1 2 2 1 = - 2 2 1 2 2 1 2 2 1 2 2 1 i f i f mv mv kx kx - - = + 2 2 1 2 2 1 2 2 1 2 2 1 f f i i mv kx mv kx + = +
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Physics 207: Lecture 14, Pg 3 Energy for a Hooke’s Law spring Energy for a Hooke’s Law spring Associate ½ kx 2 with the “potential energy” of the spring m 2 2 1 2 2 1 2 2 1 2 2 1 f f i i mv kx mv kx + = + f sf i si U K U K + = + Perfect Hooke’s Law springs are “conservative” so the mechanical energy is constant
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Physics 207: Lecture 14, Pg 4 Energy diagrams Energy diagrams In general: Energy K y U E mech K x U E mech Spring/Mass system Ball falling
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Physics 207: Lecture 14, Pg 5 Energy diagrams Energy diagrams Spring/Mass/Gravity system Force y -mg K Energy K y U g E mech U s U Total Notice: mass has maximum kinetic energy when the net force is zero (acceleration changes sign) m net spring
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Physics 207: Lecture 14, Pg 6 Equilibrium Equilibrium Example Spring: F x = 0 => dU / dx = 0 for x=0 The spring is in equilibrium position In general: dU / dx = 0 for ANY function establishes equilibrium stable equilibrium unstable equilibrium U U
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Physics 207: Lecture 14, Pg 7 Comment on Energy Conservation Comment on Energy Conservation We have seen that the total kinetic energy of a system undergoing an inelastic collision is not conserved. Mechanical energy is lost: Heat (friction) Bending of metal and deformation Kinetic energy is not conserved by these non-conservative forces occurring during the collision ! Momentum along a specific direction is conserved when there are no external forces acting in this direction. In general, easier to satisfy conservation of momentum than energy conservation.
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Physics 207: Lecture 14, Pg 8 Chapter 11, Work Chapter 11, Work Potential Energy (U) Kinetic Energy (K) Thermal Energy (E th , new) where E sys = E mech + E th = K + U + E th Any process which changes the potential or kinetic energy of a system is said to have done work W on that system E sys = W W can be positive or negative depending on the direction of energy transfer Net work reflects changes in the kinetic energy W = K
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This note was uploaded on 04/12/2011 for the course PHYS 204 taught by Professor Winoker during the Spring '11 term at University of Wisconsin - Fond du Lac.

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sy14_oct22_07hc - Physics 207, Lecture 14, Oct. 22 Physics...

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