Chapter 2: Particles
2.4. Examples
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.
No examples submitted from students, yet. In the mean time, here are examples (P3.pdf, P5.pdf, P8.pdf) from Engineering Mechanics, Jacob Moore, et al. Mechanics Map – Equilibrium Analysis for Concurrent Force Systems
Example 2.4.1: Equilibrium Equation and Components of Vectors, Submitted by Analiya Benny
- Problem
A 280 lb Pipe is being lifted by a crane as shown in the figure. Find the magnitude of the tension on the cables, given that the forces on the cables are equal.
https://publicdomainvectors.org/en/free-clipart/Crane-with-a-pipeai/86375.html
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 TB 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]