3 m 47 B FIGURE P6-10 6-10.A carport roof is supported as shown in Figure P6-10. If the roof has a mass of 200 kg, determine the load on each support. -3 m Am/- C 3 m
3 m 47 B FIGURE P6-10 6-10.A carport roof is supported as shown in Figure P6-10. If the roof has a mass of 200 kg, determine the load on each support. -3 m Am/- C 3 m
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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![### Load Distribution on a Carport Roof
#### Problem Description
A carport roof is supported as shown in **Figure P6-10**. If the roof has a mass of 200 kg, determine the load on each support.
#### Diagram Explanation
**Figure P6-10** illustrates a carport roof supported at three points: A, B, and C. The structure is depicted in a simplified diagram with the following dimensions:
- The distance between supports A and B is 3 meters.
- The distance between supports A and C is 3 meters.
- The horizontal projection from support A to the end of the roof (along the left side) is 3 meters.
- The horizontal projection from support A to the edge of the roof at B is 3 meters.
- The distance between the vertical line from support B to the perpendicular projection of the support at C is 3 meters.
- From support C to the right edge of the roof is an additional 1 meter.
The entire roof structure is symmetric with respect to the central support at A. The goal is to determine how the total mass of the roof (200 kg) is distributed as a load on each of the supports.
#### Load Calculation
Given that the mass of the roof is 200 kg, we need to consider the gravitational force acting on it. The gravitational force (weight) can be calculated by multiplying the mass by the acceleration due to gravity (g = 9.81 m/s²).
\[ \text{Weight (W)} = \text{mass} \times g = 200 \text{ kg} \times 9.81 \text{ m/s}^2 = 1962 \text{ N} \]
The weight is distributed among the supports A, B, and C. The symmetry of the design implies that the loads on supports A and C will be equal. Using principles of static equilibrium and considering moments about the central support, the load distribution can be determined.
### Key Points to Determine:
1. **Symmetry and Even Load Distribution:** Given the symmetrical placement of the supports and equal dimensions on either side, the load on supports A and C should be equal.
2. **Moment Calculations:** Using moments about point B or other supports to find individual forces.
This problem involves applying principles of static equilibrium to solve for the individual loads on each support. Detailed steps would include summing forces in vertical directions and taking moments about strategically chosen points to solve](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a2e60b5-531b-408d-ad87-91178dbcae31%2Feec7775a-1fbf-4b3b-a311-8a1e8e0d2ff0%2Fjmlrmc_processed.gif&w=3840&q=75)
Transcribed Image Text:### Load Distribution on a Carport Roof
#### Problem Description
A carport roof is supported as shown in **Figure P6-10**. If the roof has a mass of 200 kg, determine the load on each support.
#### Diagram Explanation
**Figure P6-10** illustrates a carport roof supported at three points: A, B, and C. The structure is depicted in a simplified diagram with the following dimensions:
- The distance between supports A and B is 3 meters.
- The distance between supports A and C is 3 meters.
- The horizontal projection from support A to the end of the roof (along the left side) is 3 meters.
- The horizontal projection from support A to the edge of the roof at B is 3 meters.
- The distance between the vertical line from support B to the perpendicular projection of the support at C is 3 meters.
- From support C to the right edge of the roof is an additional 1 meter.
The entire roof structure is symmetric with respect to the central support at A. The goal is to determine how the total mass of the roof (200 kg) is distributed as a load on each of the supports.
#### Load Calculation
Given that the mass of the roof is 200 kg, we need to consider the gravitational force acting on it. The gravitational force (weight) can be calculated by multiplying the mass by the acceleration due to gravity (g = 9.81 m/s²).
\[ \text{Weight (W)} = \text{mass} \times g = 200 \text{ kg} \times 9.81 \text{ m/s}^2 = 1962 \text{ N} \]
The weight is distributed among the supports A, B, and C. The symmetry of the design implies that the loads on supports A and C will be equal. Using principles of static equilibrium and considering moments about the central support, the load distribution can be determined.
### Key Points to Determine:
1. **Symmetry and Even Load Distribution:** Given the symmetrical placement of the supports and equal dimensions on either side, the load on supports A and C should be equal.
2. **Moment Calculations:** Using moments about point B or other supports to find individual forces.
This problem involves applying principles of static equilibrium to solve for the individual loads on each support. Detailed steps would include summing forces in vertical directions and taking moments about strategically chosen points to solve
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