SOL22 - Thevalingam Donald – Homework 22 – Due midnight...

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Unformatted text preview: Thevalingam, Donald – Homework 22 – Due: Mar 19 2007, midnight – Inst: Eslami 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A uniform flat plate of metal with a circular hole is situated in the reference frame shown in the figure below.- 10- 8- 6- 4- 2 2 4 6 8 10- 10- 8- 6- 4- 2 2 4 6 8 10 Calculate the x-coordinate of the center of mass x cm of the metal plate. Correct answer: 1 . 53215 . Explanation: Basic Concept: The center of mass coor- dinate is x cm ≡ ∑ x i m i ∑ m i ≡ Z xdm M , (1) where M ≡ Z dm, dm = σ y dx, and σ is the areal density ‡ mass area · of the plate. Solution: Let : y = ± 8 , Δ y = 2 y = 2 (8) = 16 , x 1 =- 5 , x 2 = 8 , A r = [ x 2- x 1 ] (Δ y ) = [(8)- (- 5)] (16) = 208 x r = [ x 2 + x 1 ] 2 = [(8) + (- 5)] 2 = 1 . 5 A c = π r 2 = π (2) 2 = 12 . 5664 x c = 1 , and r = 2 , Since the plate is symmetry about the x- axis, the y-coordinate of the center of mass must fall on the x-axis, y cm = 0 . Using the definition of x cm from Eq. 1, we have x cm = A r x r- A c x c A r- A c = (208) (1 . 5) + (12 . 5664) (1) (208)- (12 . 5664) = 1 . 53215 ....
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SOL22 - Thevalingam Donald – Homework 22 – Due midnight...

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