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Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadrant removed. Assume the plywood is uniform and determine the x and y coordinates of the center of gravity. Hint: The Earth's gravitational field is also uniform for the entire sheet of plywood.

Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadrant removed. Assume the plywood is uniform and determine the x and y coordinates of the center of gravity. Hint: The Earth's gravitational field is also uniform for the entire sheet of plywood.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Shown below is a 4.00-ft by 8.00-ft sheet of plywood with the upper left quadrant removed. Assume the plywood is uniform and determine the x and y coordinates of the center of gravity. Hint: The Earth's gravitational field is also uniform for the entire sheet of plywood.

 

### Analysis of Composite Rectangular Shape The image presents a piecewise rectangular shape laid out on an \( x \)- and \( y \)-axis grid, scaled in feet, which is useful for calculating areas and understanding the geometric properties of combined rectangular regions. **Graph Description:** - **Axes:** - The vertical axis (y-axis) measures height in feet (ft) ranging from 0 to 4.00 ft. - The horizontal axis (x-axis) measures length in feet (ft), ranging from 0 to 8.00 ft. **Detailed Description of the Shape:** - The shape consists of two rectangles: 1. A smaller rectangle occupying an area from (0,0) to approximately (4,2). 2. A larger rectangle appended to the right of the smaller one, extending from (4,2) to (8,4). **Key Points of the Shape:** - The lower base starts at the origin (0,0), extends horizontally rightwards to the coordinate (8,0). - From (8,0), the side extends vertically upwards to (8,2). - At (8,2), the horizontal boundary extends leftwards to (4,2). - From (4,2), it extends upwards vertically to (4,4). - Finally, it extends horizontally rightwards from (4,4) to (8,4), completing the shape back at (8,2). The bottom rectangle has dimensions 4 ft in width and 2 ft in height. The upper rectangle lies above it, with a height from y=2 ft to y=4 ft, and a length from x=4 ft to x=8 ft. --- This shape can be analyzed further for properties like the total area, perimeters, or centroid, which are common topics in geometric and spatial studies. For example, calculating the total area would involve adding the areas of the two constituent rectangles.
Transcribed Image Text:### Analysis of Composite Rectangular Shape The image presents a piecewise rectangular shape laid out on an \( x \)- and \( y \)-axis grid, scaled in feet, which is useful for calculating areas and understanding the geometric properties of combined rectangular regions. **Graph Description:** - **Axes:** - The vertical axis (y-axis) measures height in feet (ft) ranging from 0 to 4.00 ft. - The horizontal axis (x-axis) measures length in feet (ft), ranging from 0 to 8.00 ft. **Detailed Description of the Shape:** - The shape consists of two rectangles: 1. A smaller rectangle occupying an area from (0,0) to approximately (4,2). 2. A larger rectangle appended to the right of the smaller one, extending from (4,2) to (8,4). **Key Points of the Shape:** - The lower base starts at the origin (0,0), extends horizontally rightwards to the coordinate (8,0). - From (8,0), the side extends vertically upwards to (8,2). - At (8,2), the horizontal boundary extends leftwards to (4,2). - From (4,2), it extends upwards vertically to (4,4). - Finally, it extends horizontally rightwards from (4,4) to (8,4), completing the shape back at (8,2). The bottom rectangle has dimensions 4 ft in width and 2 ft in height. The upper rectangle lies above it, with a height from y=2 ft to y=4 ft, and a length from x=4 ft to x=8 ft. --- This shape can be analyzed further for properties like the total area, perimeters, or centroid, which are common topics in geometric and spatial studies. For example, calculating the total area would involve adding the areas of the two constituent rectangles.
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