NSC Mechanical Technology Welding and Metalwork Effects of forces, moments, and torques: Four pulling forces of 1.2 kN, 2

Four pulling forces of 1.2 kN, 2 kN, 3.4 kN and 1.8 kN are acting on the same point, as shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2017 - Paper 1

Question 7

Four-pulling-forces-of-1.2-kN,-2-kN,-3.4-kN-and-1.8-kN-are-acting-on-the-same-point,-as-shown-in-FIGURE-7.1-below-NSC Mechanical Technology Welding and Metalwork-Question 7-2017-Paper 1.png

Four pulling forces of 1.2 kN, 2 kN, 3.4 kN and 1.8 kN are acting on the same point, as shown in FIGURE 7.1 below. Determine, by means of calculations, the magnitude... show full transcript

Worked Solution & Example Answer:Four pulling forces of 1.2 kN, 2 kN, 3.4 kN and 1.8 kN are acting on the same point, as shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2017 - Paper 1

Step 1

Calculate Horizontal and Vertical Components

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Answer

To find the resultant, we first need to calculate the horizontal and vertical components of each force:

Horizontal Components (HC):
- For 1.2 kN at 40°:
  
  $1.2 imes ext{cos}(40^ ext{o}) \approx 0.92 ext{ kN}$
- For 2 kN:
  
  $2 ext{ kN}$
- For 3.4 kN (straight to the right):
  
  $3.4 ext{ kN}$
- For 1.8 kN at 70°:
  
  $1.8 imes ext{cos}(70^ ext{o}) \approx 0.62 ext{ kN}$
- Total Horizontal Component (ΣHC):
  
  $ΣHC = 0.92 + 2 + 3.4 + 0.62 \approx 4.39 ext{ kN}$
Vertical Components (VC):
- For 1.2 kN at 40°:
  
  $1.2 imes ext{sin}(40^ ext{o}) \approx 0.77 ext{ kN}$
- For 2 kN:
  
  $0 ext{ kN}$
- For 3.4 kN:
  
  $0 ext{ kN}$
- For 1.8 kN at 70°:
  
  $1.8 imes ext{sin}(70^ ext{o}) \approx 1.69 ext{ kN}$
- Total Vertical Component (ΣVC):
  
  $ΣVC = 0.77 + 1.69 \approx 2.46 ext{ kN}$

Step 2

Calculate Resultant Magnitude and Direction

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Answer

Resultant Magnitude (R):

Using Pythagoras' theorem:

$R = \sqrt{(ΣHC)^2 + (ΣVC)^2} = \sqrt{(4.39)^2 + (0.61)^2} \approx 4.43 ext{ kN}$
Direction (θ):

The angle can be calculated using:

$\tan(θ) = \frac{ΣVC}{ΣHC}$ $θ = \text{tan}^{-1}\left(\frac{0.61}{4.39}\right) \approx 7.91^ ext{o}$

Four pulling forces of 1.2 kN, 2 kN, 3.4 kN and 1.8 kN are acting on the same point, as shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2017 - Paper 1

Worked Solution & Example Answer:Four pulling forces of 1.2 kN, 2 kN, 3.4 kN and 1.8 kN are acting on the same point, as shown in FIGURE 7.1 below - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2017 - Paper 1

Calculate Horizontal and Vertical Components

Calculate Resultant Magnitude and Direction

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