ST02: Solution for Exercise Problem 1

Summary

In this physics problem, a particle is in equilibrium with three cable forces acting on it. The particle is suspended by a 5 kN tension in cable A-D, while tensions in cables A-B and A-C need to be determined. By analyzing the forces and applying trigonometry, equilibrium equations are used to solve for the tensions in cables A-B (5.12 kN) and A-C (0.34 kN). The process demonstrates the application of static equilibrium principles and force resolution to solve for unknown forces acting on a particle.

Takeaways

• 😀 Point A lies at the intersection of three cable forces, and we treat it as a particle in equilibrium.
• 😀 A 5 kN pipe is suspended from cable AD, resulting in a tension force of 5 kN in the cable.
• 😀 The force diagram for the particle includes a downward 5 kN force, and two tension forces in cables AB and AC.
• 😀 The coordinate system is defined with the x-axis positive to the right and the y-axis positive upward.
• 😀 The angle between cable AC and the x-axis is 20 degrees, and we define the angle alpha for cable AB with respect to the x-axis.
• 😀 Alpha (the angle that cable AB makes with the x-axis) can be determined using trigonometry.
• 😀 Particle A must be in equilibrium, meaning the net force in both the x and y directions must be zero.
• 😀 The equilibrium conditions give us two equations: one for the sum of forces in the x-direction and one for the sum in the y-direction.
• 😀 Solving the two simultaneous equations results in the tension in cable AB being 5.12 kN.
• 😀 The tension in cable AC is determined to be 0.34 kN based on the equilibrium equations.

Q & A

What is the main purpose of analyzing point A in this script?

The main purpose is to analyze the forces acting on point A, which lies at the intersection of three cable forces, and to determine the tension forces in the cables supporting the five-kilonewton pipe.

How is the five-kilonewton pipe suspended?

The five-kilonewton pipe is suspended from cable AD, which results in a tension force of 5 kilonewtons in the cable.

What forces are acting on the particle at point A?

The forces acting on the particle at point A include the downward force of 5 kilonewtons (due to the weight of the pipe), a tension force in cable AB, and a tension force in cable AC.

How is the coordinate system defined in this analysis?

The coordinate system is defined with the x-axis as positive to the right and the y-axis as positive upward.

What is the significance of the angle that cable AC makes with the x-axis?

The angle that cable AC makes with the x-axis, labeled as 'fac', is used to resolve the tension forces into components along the x and y axes.

How do we refer to the angle that cable AB makes with the x-axis?

The angle that cable AB makes with the x-axis is referred to as alpha (α).

What method is used to determine the angle alpha?

The angle alpha is determined using simple trigonometry.

What is the equilibrium condition for the particle at point A?

The particle at point A must be in equilibrium, meaning the net force in the x direction and the net force in the y direction must both be zero.

How many unknown forces are involved in solving the equilibrium equations?

There are two unknown forces (the tensions in cables AB and AC) involved in solving the equilibrium equations.

What are the results of solving the simultaneous equations for the tensions in cables AB and AC?

Solving the simultaneous equations gives a tension of 5.12 kilonewtons in cable AB and a tension of 0.34 kilonewtons in cable AC.