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Unformatted text preview: Page 1 Physics 207 – Lecture 12 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: c HW6 due Wednesday HW6 due Wednesday c HW7 available soon HW7 available soon c Wednesday, Read Chapter 11 Wednesday, Read Chapter 11 • Chapter 10: Energy Chapter 10: Energy x Energy diagrams x Springs c Chapter 11: Work Chapter 11: Work x Work and Net Work x Work and Kinetic Energy x Work and Potential Energy x Conservative and Nonconservative forces Physics 207: Lecture 14, Pg 2 Force vs. Energy for a Force vs. Energy for a Hooke Hooke ’s Law spring Law spring c F =  k (x – x equilibrium ) c F = ma = m dv/dt = m (dv/dx dx/dt) = m dv/dx v = mv dv/dx c So  k (x – x equilibrium ) dx = mv dv c Let u = x – x eq. b 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 + = + Physics 207: Lecture 14, Pg 3 Energy for a Energy for a Hooke Hooke ’s Law spring Law spring c 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 + = + c Perfect Hooke’s Law springs are “conservative” so the mechanical energy is constant Physics 207: Lecture 14, Pg 4 Energy diagrams Energy diagrams c In general: Energy K y U E mech Energy K x U E mech Spring/Mass system Ball falling Physics 207: Lecture 14, Pg 5 Energy diagrams Energy diagrams Spring/Mass/Gravity system Force ymg 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 Physics 207: Lecture 14, Pg 6 Equilibrium Equilibrium c Example x Spring: F x = 0 => dU / dx = 0 for x=0 The spring is in equilibrium position c In general: dU / dx = 0 b for ANY function establishes equilibrium stable equilibrium unstable equilibrium U U Page 2 Physics 207 – Lecture 12 Physics 207: Lecture 14, Pg 7 Comment on Energy Conservation Comment on Energy Conservation c We have seen that the total kinetic energy of a system undergoing an inelastic collision is not conserved. x Mechanical energy is lost: h Heat (friction) h Bending of metal and deformation c Kinetic energy is not conserved by these nonconservative forces occurring during the collision ! c Momentum along a specific direction is conserved when there are no external forces acting in this direction. x In general, easier to satisfy conservation of momentum than energy conservation. Physics 207: Lecture 14, Pg 8 Chapter 11, Work Chapter 11, Work c Potential Energy (U) c Kinetic Energy (K) c Thermal Energy (E th , new) where E sys = E mech + E th = K + U + E th c 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...
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This note was uploaded on 10/30/2011 for the course PHYS 207 taught by Professor Winnokur during the Spring '06 term at University of Wisconsin.
 Spring '06
 Winnokur
 Physics, Energy, Kinetic Energy, Work

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