PHY183-Lecture19 - Midterm 1 ! The average for Midterm 1...

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February 20, 2006 1 Engineers 1 Engineers 1 Spring Semester 2006 Lecture 19 February 20, 2006 2 Midterm 1 Midterm 1 ! The average for Midterm 1 was 5.11/8 (64%) ! You should do all 8 problems in Corrections Set 1 ! We will calculate your grade as 0.3*(Corrections Set 1 - Midterm 1) + Midterm 1 Don’t just do the problems you missed, do them all! ! If the average student did all the corrections, he/she would get 5.98/8 (75%) February 20, 2006 3 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 0 x ! ' W = r F r r ' ( )• d r r ' r r 0 r r ! February 20, 2006 4 Integration Refresher (1) Integration Refresher (1) ! Indefinite integrals have an additive constant, c ! Definite integrals are taken by inserting upper and lower bounds 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
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February 20, 2006 5 Integration Refresher (2) Integration Refresher (2) Trigonometric functions: Exponentials: For more integrals, please see “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 20, 2006 6 Quiz 19.1 Quiz 19.1 Three identical balls are thrown from the top of a building with the same initial speed. Initially, Ball 1 moves horizontally. Ball 2 moves upward. Ball 3 moves downward. Neglecting air resistance, which ball has the fastest speed when it hits the ground? A) Ball 1 B) Ball 2 C) Ball 3 D) All have the same speed. February 20, 2006 7 Quiz 19.1 Quiz 19.1 Three identical balls are thrown from the top of a building with the same initial speed. Initially, Ball 1 moves horizontally. Ball 2 moves upward. Ball 3 moves downward.
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PHY183-Lecture19 - Midterm 1 ! The average for Midterm 1...

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