W5.4 - February 5, 2008 Physics for...

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Unformatted text preview: February 5, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2008 Lecture 19 February 5, 2008 Physics for Scientists&Engineers 1 2 Yesterday Yesterday ’ ’ s Main results: s Main results: Work done by a variable force, 1d case: Most general 3d case W = F ( x ') dx x x ! ' W = ! F ! r ' ( ) • d ! r ' ! r ! r ! February 5, 2008 Physics for Scientists&Engineers 1 3 Integration Refresher (1) Integration Refresher (1) All indefinite integrals have an additive constant, c Definite integrals are taken by inserting upper and lower limits into the result from the indefinite integral, and taking the difference Integration is the inverse process to differentiation Some integrals • Polynomials x n dx ! = 1 n + 1 x n + 1 + c for all n " 1 x ! 1 dx " = ln x + c February 5, 2008 Physics for Scientists&Engineers 1 4 Integration Refresher (2) Integration Refresher (2) • Trigonometric functions: • Exponentials: • For more integrals, please see the “Math Primer” sin ax ( ) dx ! = " 1 a cos ax ( ) + c cos ax ( ) dx ! = 1 a sin ax ( ) + c e ax dx ! = 1 a e ax + c February 5, 2008 Physics for Scientists&Engineers 1 5 Clicker Quiz Clicker Quiz I pull a 2.0 kg mass and move it 2.0 m in the positive x- direction starting from x = 0. The force I exert is How much work have I done on the mass? • A) 0 J • B) 4.0 J • C) 6.0 J • D) 8.0 J • E) 16.0 J F x ( ) = 3.0 N/m 2 ( ) x 2 February 5, 2008 Physics for Scientists&Engineers 1 6 Clicker Quiz Solution Clicker Quiz Solution W = !...
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This note was uploaded on 04/06/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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W5.4 - February 5, 2008 Physics for...

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