Explanation Section 1: To determine : The x -coordinate of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed. Answer : The x -coordinate of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed is 3.33 ft . Explanation : Given info : The area of the part A 1 of the plywood is 16.0 ft 2 , the area of the part A 2 is 8.00 ft 2 , and x coordinates of the center of gravity of parts of the plywood A 1 , A 2 are 2.00 ft and 6.00 ft . Assume the remaining parts of plywood as two parts A 1 with an area of 4.00 ft by 4.00 ft and its center of gravity is located at ( 2.00 ft, 2 .00 ft ) . Similarly, another part of the plywood is A 2 with area of 2.00 ft by 4.00 ft and the location of the center of gravity of this part is ( 6.00 ft, 1 .00 ft ) . The mass of the plywood is proportion to its area; its mass is defined as m = σ A where σ is proportionality constant. In this way, the masses of each part can be determined. The formula for the x co-ordinate of the center of gravity is, x cm = ρ A 1 x 1 + ρ A 2 x 2 ρ A 1 + ρ A 2 ρ is proportionality constant. A 1 and A 2 are areas of the plywood respectively. x 1 and x 2 are the x -coordinates of the center of gravity of the parts of plywood. Substitute 16.0 ft 2 for A 1 , 8.00 ft 2 for A 2 , 2.00 ft for x 1 , and 6.00 ft for x 2 to find x cm . x cm = ρ ( 16.0 ft 2 ) ( 2.00 ft ) + ρ ( 8.00 ft 2 ) ( 6.00 ft ) ρ ( 16.0 ft 2 ) + ρ ( 8.00 ft 2 ) = 3.33 ft Thus, the x -coordinate of the center of gravity of a 4

10th Edition

ISBN: 9781285737027

Author: Raymond A. Serway, Chris Vuille

Publisher: Cengage Learning

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Concept explainers

Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.

Question

Chapter 8, Problem 11P

To determine

The x -and y -coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed.

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Chapter 8 Solutions

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The x -and y -coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed.

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The x -and y -coordinates of the center of gravity of a 4.00 ft by 8.00 ft uniform sheet of plywood with the upper right quadrant removed.

Chapter 8 Solutions