Three forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140o from the positive x-axis, and force C acts at 15o from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. Using your FBD from problem 1) substitute the known weight and angles α and β into your equations, then solve them simultaneously to find the tensions in cables AC and BC . Fb= 117.92kn Fc= 93.507kn
Three forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140o from the positive x-axis, and force C acts at 15o from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. Using your FBD from problem 1) substitute the known weight and angles α and β into your equations, then solve them simultaneously to find the tensions in cables AC and BC . Fb= 117.92kn Fc= 93.507kn
Related questions
Question
Three forces act on particle A located at the origin of an x-y coordinate system. Force B acts at 140o from the positive x-axis, and force C acts at 15o from the positive x-axis. The weight acts down with a magnitude of W = 100 kN. Use the equations of equilibrium to determine the magnitudes of B and C such that particle A is in equilibrium. Using your FBD from problem 1) substitute the known weight and angles α and β into your equations, then solve them simultaneously to find the tensions in cables AC and BC . Fb= 117.92kn Fc= 93.507kn
![**Equilibrium of a Particle**
### Concept
When dealing with the equilibrium of a particle, the sum of all forces acting on the particle must equal zero. This is expressed mathematically as:
\[ \sum F = 0 \]
which can be broken down into:
\[ \sum F_x = 0 \]
\[ \sum F_y = 0 \]
### Problem Statement
Given a system in equilibrium, the dimensions provided are:
- \( h = 2.5 \, \text{ft} \)
- \( d_1 = 4.75 \, \text{ft} \)
- \( d_2 = 3 \, \text{ft} \)
- The load (\( W \)) acting on the system is \( 50 \, \text{lb} \).
You are required to find the numeric answers with three significant figures.
### Diagram Explanation
The provided diagram shows the system consisting of two points, \( A \) and \( B \), connected to point \( C \) by two members. The load \( W \) is hanging down from point \( C \).
Key elements in the diagram include:
- \( h \): Vertical distance from the horizontal bar to point \( C \).
- \( d_1 \): Horizontal distance from point \( A \) to point \( C \).
- \( d_2 \): Horizontal distance from point \( B \) to point \( C \).
- \( \alpha \): Angle between member \( AC \) and the horizontal.
- \( \beta \): Angle between member \( BC \) and the horizontal.
The members \( AC \) and \( BC \) form right triangles with the vertical line through point \( C \). The horizontal distances \( d_1 \) and \( d_2 \) span along the horizontal bar from points \( A \) to \( C \) and \( B \) to \( C \), respectively.
### Steps to Find the Values
To solve for the numeric values:
1. **Resolve the forces in the horizontal and vertical directions:**
\[
\sum F_x = T_{AC} \cos(\alpha) - T_{BC} \cos(\beta) = 0
\]
\[
\sum F_y = T_{AC} \sin(\alpha) + T_{BC} \sin(\beta) - W = 0
\]
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff12ec146-5781-453b-8388-2e7cc9921f6c%2Fdb3509ad-8048-4d87-8fa6-02cb1bb30862%2Fylyed8t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equilibrium of a Particle**
### Concept
When dealing with the equilibrium of a particle, the sum of all forces acting on the particle must equal zero. This is expressed mathematically as:
\[ \sum F = 0 \]
which can be broken down into:
\[ \sum F_x = 0 \]
\[ \sum F_y = 0 \]
### Problem Statement
Given a system in equilibrium, the dimensions provided are:
- \( h = 2.5 \, \text{ft} \)
- \( d_1 = 4.75 \, \text{ft} \)
- \( d_2 = 3 \, \text{ft} \)
- The load (\( W \)) acting on the system is \( 50 \, \text{lb} \).
You are required to find the numeric answers with three significant figures.
### Diagram Explanation
The provided diagram shows the system consisting of two points, \( A \) and \( B \), connected to point \( C \) by two members. The load \( W \) is hanging down from point \( C \).
Key elements in the diagram include:
- \( h \): Vertical distance from the horizontal bar to point \( C \).
- \( d_1 \): Horizontal distance from point \( A \) to point \( C \).
- \( d_2 \): Horizontal distance from point \( B \) to point \( C \).
- \( \alpha \): Angle between member \( AC \) and the horizontal.
- \( \beta \): Angle between member \( BC \) and the horizontal.
The members \( AC \) and \( BC \) form right triangles with the vertical line through point \( C \). The horizontal distances \( d_1 \) and \( d_2 \) span along the horizontal bar from points \( A \) to \( C \) and \( B \) to \( C \), respectively.
### Steps to Find the Values
To solve for the numeric values:
1. **Resolve the forces in the horizontal and vertical directions:**
\[
\sum F_x = T_{AC} \cos(\alpha) - T_{BC} \cos(\beta) = 0
\]
\[
\sum F_y = T_{AC} \sin(\alpha) + T_{BC} \sin(\beta) - W = 0
\]
2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
