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

icon
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
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
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer