Here are examples from Chapter 2 to help you understand these concepts better. These were taken from the real world and supplied by FSDE students in Summer 2021. If you’d like to submit your own examples, please send them to the author eosgood@upei.ca.

Example 2.4.1: Equilibrium Equation and Components of Vectors, Submitted by Analiya Benny

2. Draw

3. Knowns and Unknowns

Knowns:

• F = 280 lb
• θ = 60° 

Unknown:

• [latex]\overrightarrow{T_{B}}[/latex]
• [latex]\overrightarrow{T_{A}}[/latex]

4. Approach

Applying the equilibrium equation and componentization of vectors to find [latex]T_{B}[/latex] and [latex]T_{A}[/latex].

Note: [latex]T_{B}[/latex] = [latex]T_{A}[/latex]

5. Analysis

Components of [latex]T_{B}[/latex]

[latex]T_{By} = T_{B} \sin {60}[/latex]

and, [latex]T_{Bx} = T_{B}\cos {60}[/latex]

Equilibrium equation in the y direction

[latex]\sum F_{y}= -T_{By} -T_{By}-280 lb = 0 \\ T_{By} = \dfrac{-280 lb}{2} = -140 lb[/latex]

Note that the -ve sign here means that the direction of vector T_B is opposite to that drawn in the FBD diagram. So now the FBD is as given below:

now,  [latex]T_{B} \sin {60} = 140 lb[/latex]

[latex]T_{B} = \dfrac{140 lb}{\sin{60}}[/latex]

Thus, [latex]T_{B} = T_{A} = 161.66 lb[/latex]

The magnitude of the tension carried by each of the cables is 161.66 lb.

6. Review

The results show that the x component does no essential contribution towards carrying the weight of the pipe because the sum of forces in the x direction just cancels out and equals 0lb.

[latex]\sum F_{x}= -T_{Bx} +T_{Bx}= 0[/latex]