NSC Mechanical Technology Automotive Basic calculations: 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 Automotive - 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 Automotive-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 Automotive - Question 7 - 2017 - Paper 1

Step 1

Calculate Horizontal and Vertical Components

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Answer

To find the resultant force, we need to determine the horizontal (HC) and vertical (VC) components of each force:

For $1.2 \, kN$ at $40^\circ$ :

HC = $1.2 \cdot \cos(40^\circ)$
VC = $1.2 \cdot \sin(40^\circ)$

For $2 \, kN$ at $50^\circ$ :

HC = $2 \cdot \cos(50^\circ)$
VC = $2 \cdot \sin(50^\circ)$

For $3.4 \, kN$ at $0^\circ$ :

HC = $3.4 \cdot \cos(0^\circ)$
VC = $3.4 \cdot \sin(0^\circ)$

For $1.8 \, kN$ at $70^\circ$ :

HC = $1.8 \cdot \cos(70^\circ)$
VC = $1.8 \cdot \sin(70^\circ)$

Calculating these gives:

HC = $1.2 \cdot 0.7660 - 2 \cdot 0.6428 + 3.4 - 1.8 \cdot 0.3420 = 4.39 \, kN$
VC = $1.2 \cdot 0.6428 + 2 \cdot 0.7660 + 0 - 1.8 \cdot 0.9397 = 0.61 \, kN$

Step 2

Determine the Resultant

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Answer

The magnitude of the resultant force (R) can be calculated using the Pythagorean theorem:

$R = \sqrt{HC^2 + VC^2}$
Substituting the values:
$R = \sqrt{(4.39)^2 + (0.61)^2} = 4.43 \, kN$

To find the direction (angle $\theta$ ) with respect to the horizontal:

$\tan(\theta) = \frac{VC}{HC}$
Substituting gives: $\theta = \tan^{-1}\left(\frac{0.61}{4.39}\right) = 7.91^\circ$
Thus, the resultant direction is $7.91^\circ$ north of east.

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 Automotive - 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 Automotive - Question 7 - 2017 - Paper 1

Calculate Horizontal and Vertical Components

Determine the Resultant

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