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a. Find the (x, y)-coordinates of the center of mass of the plate. This "balance point" of the plate coincides with the center of mass of a system consisting of three 1-gram point masses located at the vertices of the plate. b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2, 2). [Hint: Let w, w2, and w3 denote the masses added at the three vertices, so that A thin triangular plate of uniform density and thickness has (0, 1), v2 = (8, 1), and v3 (2,4), as in the vertices at v= figure below, and the mass of the plate is 3 g. X2 4- Wi + w2 + uw3 = = 6.]

a. Find the (x, y)-coordinates of the center of mass of the plate. This "balance point" of the plate coincides with the center of mass of a system consisting of three 1-gram point masses located at the vertices of the plate. b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2, 2). [Hint: Let w, w2, and w3 denote the masses added at the three vertices, so that A thin triangular plate of uniform density and thickness has (0, 1), v2 = (8, 1), and v3 (2,4), as in the vertices at v= figure below, and the mass of the plate is 3 g. X2 4- Wi + w2 + uw3 = = 6.]

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Number 2 A thin triangular plate of uniform density and thickness has vertices at vi =(0, 1), v2 figure below, and the mass of the plate is 3 g. a. Find the (x, y)-coordinates of the center of mass of the plate. This "balance point" of the plate coincides with the center of mass of a system consisting of three 1-gram point masses located at the vertices of the plate. 3 (8, 1), and V3 = (2, 4), as in the b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2, 2). [Hint: Let w, w2, and w3 denote the masses added at the three vertices, so that 4 Wi+ w2 + w3 6.]
Transcribed Image Text:Number 2 A thin triangular plate of uniform density and thickness has vertices at vi =(0, 1), v2 figure below, and the mass of the plate is 3 g. a. Find the (x, y)-coordinates of the center of mass of the plate. This "balance point" of the plate coincides with the center of mass of a system consisting of three 1-gram point masses located at the vertices of the plate. 3 (8, 1), and V3 = (2, 4), as in the b. Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the balance point of the plate to (2, 2). [Hint: Let w, w2, and w3 denote the masses added at the three vertices, so that 4 Wi+ w2 + w3 6.]
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