FIGURE 8.1 below shows a system of four forces acting on the same point. Calculate the magnitude and direction of the resultant for this system of forces. HINT: Draw and complete the diagram in FIGURE 8.1. Show ALL the horizontal and vertical components before doing the calculations.

NSC Mechanical Technology Fitting and Machining Basic calculations on forces, moments and stress and strain: FIGURE 8.1 below shows a system

FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Question 8

FIGURE 8.1 below shows a system of four forces acting on the same point. Calculate the magnitude and direction of the resultant for this system of forces. HINT: Dra... show full transcript

Worked Solution & Example Answer:FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Step 1

Calculate the horizontal components

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Answer

To find the horizontal components, we can use:

$\sum H_C = 50 \cos(30^\circ) - 85 + 75 \cos(70^\circ)$

Calculating each term gives:

$50 \cos(30^\circ) = 43.30 \ N$
$75 \cos(70^\circ) = 25.65 \ N$

Thus, we get: $\sum H_C = 43.30 - 85 + 25.65 = -16.05 \ N$

Step 2

Calculate the vertical components

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Answer

For the vertical components, we use:

$\sum V_C = 50 \sin(30^\circ) + 25 - 75 \sin(70^\circ)$

Calculating the terms:

$50 \sin(30^\circ) = 25 \ N$
$75 \sin(70^\circ) = 70.48 \ N$

Therefore, we have: $\sum V_C = 25 - 75 \sin(70^\circ) = 25 - 70.48 = -45.48 \ N$

Step 3

Determine the magnitude and direction of the resultant

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Answer

Now, we find the resultant force using:

$R = \sqrt{(\sum V_C)^2 + (\sum H_C)^2}$

Substituting the values gives: $R = \sqrt{(-70.48)^2 + (-16.05)^2} = \sqrt{5225.033} \approx 72.28 \ N$

To find the angle, we use:

$\tan(\theta) = \frac{\sum V_C}{\sum H_C} \implies \theta = \tan^{-1}\left(\frac{-70.48}{-16.05}\right) \approx 77.17^\circ$

This angle can be expressed as $77^\circ 10' 12'$ West from South.

FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Worked Solution & Example Answer:FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Calculate the horizontal components

Calculate the vertical components

Determine the magnitude and direction of the resultant

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