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9-74. Determine the location (x, y) of the center of gravity of the three-wheeler. The location of the center of gravity of each component and its weight are tabulated in the figure. If the three-wheeler is symmetrical with respect to the x-y plane, determine the normal reaction each of its wheels exerts on the ground.

9-74. Determine the location (x, y) of the center of gravity of the three-wheeler. The location of the center of gravity of each component and its weight are tabulated in the figure. If the three-wheeler is symmetrical with respect to the x-y plane, determine the normal reaction each of its wheels exerts on the ground.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter9: Mass And Mass-related Variables In Engineering
Section: Chapter Questions
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**Problem 9-74**: Determine the location \((\bar{x}, \bar{y})\) of the center of gravity of the three-wheeler. The location of the center of gravity of each component and its weight are tabulated in the figure. If the three-wheeler is symmetrical with respect to the \(x-y\) plane, determine the normal reaction each of its wheels exerts on the ground. **Diagram Explanation:** The diagram displays a three-wheeler with various components marked for analysis: 1. **Rear Wheels (18 lb)**: Positioned 1.30 ft from the \(x\)-axis. 2. **Mechanical Components (85 lb)**: Located in the center and positioned below the seat, 1.50 ft from the front wheel vertically. 3. **Frame (120 lb)**: Significantly affects the center of gravity due to its central position and substantial weight. 4. **Front Wheel (8 lb)**: Situated 1 ft from the \(x\)-axis and acts as a pivotal point for calculating equilibrium. **Dimensions:** - Horizontal distances between centers: - From rear wheel to mechanical components: 2.30 ft - Between mechanical components: 0.80 ft - From mechanical components to front wheel: 1.40 ft **Coordinates (A to B):** - \(A\) to the rear wheel center is 1 ft vertically. - \(B\) measures the horizontal axis, indicating the bike's length and is crucial for calculating the torques around various points. By using the given weights and measurements, one can calculate the location of the center of gravity and determine the normal reaction at each wheel by applying static equilibrium equations.
Transcribed Image Text:**Problem 9-74**: Determine the location \((\bar{x}, \bar{y})\) of the center of gravity of the three-wheeler. The location of the center of gravity of each component and its weight are tabulated in the figure. If the three-wheeler is symmetrical with respect to the \(x-y\) plane, determine the normal reaction each of its wheels exerts on the ground. **Diagram Explanation:** The diagram displays a three-wheeler with various components marked for analysis: 1. **Rear Wheels (18 lb)**: Positioned 1.30 ft from the \(x\)-axis. 2. **Mechanical Components (85 lb)**: Located in the center and positioned below the seat, 1.50 ft from the front wheel vertically. 3. **Frame (120 lb)**: Significantly affects the center of gravity due to its central position and substantial weight. 4. **Front Wheel (8 lb)**: Situated 1 ft from the \(x\)-axis and acts as a pivotal point for calculating equilibrium. **Dimensions:** - Horizontal distances between centers: - From rear wheel to mechanical components: 2.30 ft - Between mechanical components: 0.80 ft - From mechanical components to front wheel: 1.40 ft **Coordinates (A to B):** - \(A\) to the rear wheel center is 1 ft vertically. - \(B\) measures the horizontal axis, indicating the bike's length and is crucial for calculating the torques around various points. By using the given weights and measurements, one can calculate the location of the center of gravity and determine the normal reaction at each wheel by applying static equilibrium equations.
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