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Unformatted text preview: reddy (ar38357) – Center of Mass – clancy – (SCI4112) 1 This printout should have 8 questions. Multiplechoice 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 xcoordinate 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 ycoordinate of the center of mass must fall on the xaxis, 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 xaxis is horizontal and to the right. The yaxis 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 – (SCI4112) 2 D E B C What is the xcoordinate of the center of gravity?...
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 Fall '10
 Sontar
 Physics, Center Of Mass, Mass

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