Lecture16

# Lecture16 - PHYSICS 149: Lecture 16 Chapter 6: Conservation...

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PHYSICS 149: Lecture 16 ±C h a p t e r 6 : C o n s e r v a t i o n o f E n e r g y ²6 .5 G rav i ta t iona l Po ten t ia l Ene rgy .6 Wo rk Done by Va r iab le Fo rces : Hooke ³s Law Lecture 16 Purdue University, Physics 149 1

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ILQ 1 A cart starts with velocity v and moves up the path shown At what point is the kinetic energy path shown. At what point is the kinetic energy greatest? A) 1 B) 2 B) 2 C) 3 D) 4 D) 4 Lecture 16 2 Purdue University, Physics 149
ILQ 2 A sleigh, initially at rest, moves down a frictionless hill and attains a speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the bottom, how many times higher must the hill be? A) half the height B) the same heigh B) the same height C) sqrt(2) times the height D) twice the height E) four times the height Lecture 16 3 Purdue University, Physics 149

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Energy and Work ±Work : Trans fer o f Energy by Force T W F = |F| |s| cos T ±K ine t ic (Energy o f Mo t ion) K = 1/2 mv 2 ±Work-K t Theorem : 6 W ' K W = Gravitational Potential Energy: Lecture 16 Purdue University, Physics 149 4 U grav = mgy = -W grav
Work - Kinetic Energy Theorem 1 1 2 2 2 2 i f i f mv mv K K ± ± ³ The work done on an object by the ±net² force (whether the net force is constant or variable) is equal to the change in the kinetic energy equal to the change in the kinetic energy. Or the ±total² work done on the object is equal to ³ Or, the total work done on the object is equal to the change in the kinetic energy. Lecture 16 5 Purdue University, Physics 149

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Work Done by Gravity ±Q u e s t i o n : D o e s t h e w o r k d o n e b y gravity depend on the path taken? mg T ' r Left Case: W grav = F ±' r ± cos = mg | ' y| cos0 = mg| ' y| Middle Case: W grav = F r cos = mg| ' y| (because ' r cos = | ' y| ) Right Case: W grav = mg| ' y| (because each segment can be mg| treated like the middle case) ±A n s w e r : T h e w o r k d o n e b y g r a v i t y i s i n d e p e n d e n t of path²that is, the work depends only on the initial and final positions ' y ) work depends only on the initial and final positions ( | y| ). ±T h i s k i n d o f f o r c e i s c a l l e d ³ c o n s e r v a t i v e f o r c e Lecture 16 6 Purdue University, Physics 149
Potential (stored) Energy ±² S t o r e d ³ g r a v i t a t i o n a l e n e r g y c a n b e c o n v e r t e d t o kinetic energy ± -m g ' y= ' K ± 0 = ' K + m g ' y define U g = mgy g ± 0 = ' K + ' U g ' U = -W C W = ' K ±W o r k s f o r a n y C O N S E R V A T I V E f o r c e ± Gravity U g = m g y ± Spring U s = 1/2 k x 2 ± NOT friction Lecture 16 Purdue University, Physics 149 7

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Work and Potential Energy ±W o r k d o n e b y g r a v i t y i n d e p e n d e n t o f p a t h ² W g = -mg (y f - y i ) ±D e f i n e U g = mgy o r k s f o r a n y C O N S E R V A T I V E f o r c e U K W ' ± ' ¦ ± Modify Work-Energy theorem nc Lecture 16 Purdue University, Physics 149 8
Conservative Force ±I f t h e w o r k d o n e b y a f o r c e i s independent of path (that is, depends only on the initial and final positions), the force is called ²conservative ´Examp le : g rav i ta t iona l fo rce , sp r ing , and electrical force ´No te tha t the wo rk done by conse rva t ive

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## This note was uploaded on 04/23/2011 for the course PHYS 149 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture16 - PHYSICS 149: Lecture 16 Chapter 6: Conservation...

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