Homework Help is Here – Start Your Trial Now!
Science
Physics
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.

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 68P
See similar textbooks
icon
Related questions
Question

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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Center of gravity of a system
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers with Modern …
Physics for Scientists and Engineers with Modern …
Physics
ISBN:
9781337553292
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers, Technology …
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
College Physics
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
SEE MORE TEXTBOOKS