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Unformatted text preview: reddy (ar38357) – Center of Mass – clancy – (SCI411-2) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 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 0 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: 3 . 74228. Explanation: Basic Concept: The center of mass coor- dinate is x cm ≡ ∑ x i m i ∑ m i ≡ integraldisplay xdm M , (1) where M ≡ integraldisplay dm, dm = σ y dx, and σ is the areal density parenleftBig mass area parenrightBig of the plate. Solution: Let : y = ± 7 , Δ y = 2 y = 2 (7) = 14 , x 1 =- 2 , x 2 = 9 , A r = [ x 2- x 1 ] (Δ y ) = [(9)- (- 2)] (14) = 154 x r = [ x 2 + x 1 ] 2 = [(9) + (- 2)] 2 = 3 . 5 A c = π r 2 = π (4) 2 = 50 . 2655 x c = 3 , and r = 4 , 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 = (154) (3 . 5) + (50 . 2655) (3) (154)- (50 . 2655) = 3 . 74228 . Note: This problem has a different plate for each student. 002 (part 1 of 2) 10.0 points A carpenter’s square of uniform density has the shape of an L, as shown in the figure. Assume: A ( x,y ) coordinate frame with the origin at the lower left corner of the car- penter’s square. The x-axis is horizontal and to the right. The y-axis is vertically upward. Given: In the figure, B = 13 cm, C = 4 . 4 cm, D = 5 . 3 cm, E = 20 cm. Because the square is uniform in thickness and has a small thickness, we can assume that the weight of each segment of the square is proportional to its area. reddy (ar38357) – Center of Mass – clancy – (SCI411-2) 2 D E B C What is the x-coordinate of the center of gravity?...
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solution_pdf16 - reddy(ar38357 – Center of Mass –...

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