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Unformatted text preview: Page 1 Physics 207 – Lecture 12 Physics 207: Lecture 12, Pg 1 Physics 207, Physics 207, Lecture 13, Oct. 15 Lecture 13, Oct. 15 Agenda: Finish Chapter 10, start Chapter 11 Agenda: Finish Chapter 10, start Chapter 11 Assignment: Assignment: c HW5 due tonight HW5 due tonight c HW6 available today HW6 available today c Monday, finish reading chapter 11 Monday, finish reading chapter 11 • Chapter 10: Energy Chapter 10: Energy x Potential Energy (gravity, springs) x Kinetic energy x Mechanical Energy x Conservation of Energy x Start Chapter 11, Work Physics 207: Lecture 12, Pg 2 Chapter 10: Energy Chapter 10: Energy c Rearranging Newton’s Laws gives (Fd vs . ½ mv 2 relationship)2mg (y f – y i ) = m (v yf 2  v yi 2 ) c or b ½ m v yi 2 + mgy i = ½ m v yf 2 + mgy f c and adding ½ m v xi 2 + ½ m v zi 2 and ½ m v xf 2 + ½ m v zf 2 ½ m v i 2 + mgy i = ½ m v f 2 + mgy f c where v i 2 = v xi 2 +v yi 2 + v zi 2 ½ m v 2 terms are referred to as kinetic energy Physics 207: Lecture 12, Pg 3 Energy Energy c If only If only “conservative conservative ” forces are present, the total energy forces are present, the total energy (sum of potential, U, and kinetic energies, K sum of potential, U, and kinetic energies, K ) of a system ) of a system is is conserved conserved . K ½ mv 2 U mgy c K and U may change, but E = K + U mech remains constant. E mech = K + U = constant constant E mech is called “mechanical energy” K i + U i = K f + U f Physics 207: Lecture 12, Pg 4 Another example of a conservative system: Another example of a conservative system: The simple pendulum. The simple pendulum. c Suppose we release a mass m from rest a distance h 1 above its lowest possible point. x What is the maximum speed of the mass and where does this happen ? x To what height h 2 does it rise on the other side ? v h 1 h 2 m Physics 207: Lecture 12, Pg 5 Example: The simple pendulum. Example: The simple pendulum. y y=0 y=h 1 x What is the maximum speed of the mass and where does this happen ? E = K + U = constant and so K is maximum when U is a minimum. Physics 207: Lecture 12, Pg 6 Example: The simple pendulum. Example: The simple pendulum. v h 1 y y=h 1 y=0 x What is the maximum speed of the mass and where does this happen ? E = K + U = constant and so K is maximum when U is a minimum E = mgh 1 at top E = mgh 1 = ½ mv 2 at bottom of the swing Page 2 Physics 207 – Lecture 12 Physics 207: Lecture 12, Pg 7 Example: The simple pendulum. Example: The simple pendulum....
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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 Wisconsin.
 Spring '06
 Winnokur
 Physics, Energy, Gravity, Potential Energy

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