FIGURE 11.1 below shows a square-to-square hopper (off-centre). Calculate the true length of the following: 11.1.1 A–2 11.1.2 B–3 11.1.3 C–4 FIGURE 11.2 below shows a top view of a square-to-round transformer. Calculate the true lengths of the following: 11.2.1 5–6 11.2.2 3–6 11.2.3 B–6

NSC Mechanical Technology Welding and Metalwork Basic calculations: FIGURE 11.1 below shows a square

FIGURE 11.1 below shows a square-to-square hopper (off-centre) - NSC Mechanical Technology Welding and Metalwork - Question 11 - 2023 - Paper 1

Question 11

FIGURE 11.1 below shows a square-to-square hopper (off-centre). Calculate the true length of the following: 11.1.1 A–2 11.1.2 B–3 11.1.3 C–4 FIGURE 11.2 below s... show full transcript

Worked Solution & Example Answer:FIGURE 11.1 below shows a square-to-square hopper (off-centre) - NSC Mechanical Technology Welding and Metalwork - Question 11 - 2023 - Paper 1

Step 1

A–2

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Answer

To find the true length A–2, we will use the Pythagorean theorem to calculate the diagonal distance.

Given:

Vertical height = 400 mm
Horizontal displacements from point A to D and C respectively.

The length A–2 can be calculated as:

A–2 = \\sqrt{(180^2 + 350^2 + 400^2)}

Calculating the values:

A–2 = \\sqrt{32400 + 122500 + 160000} \\approx 561.16 \, \text{mm}

Step 2

B–3

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Answer

For the true length B–3, again we apply the Pythagorean theorem:

Given:

Vertical height = 400 mm

The length B–3 can be derived as:

B–3 = \\sqrt{(410^2 + 150^2 + 400^2)}

Calculating the values:

B–3 = \\sqrt{68100 + 22500 + 160000} \\approx 592.11 \, \text{mm}

Step 3

C–4

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Answer

To find the length C–4, we again use the Pythagorean theorem:

The length C–4 can be expressed as:

C–4 = \\sqrt{(380^2 + 90^2 + 400^2)}

Calculating:

C–4 = \\sqrt{14400 + 8100 + 160000} \\approx 559.02 \, \text{mm}

Step 4

5–6

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Answer

To calculate the true length 5–6:

We use the formula:

5–6 = \frac{\pi \times D}{12}

Given:

D = 500 mm

So:

5–6 = \frac{\pi \times 500}{12} \approx 130.90 \, \text{mm}

Step 5

3–6

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Answer

Next, for the true length 3–6:

This length can be derived using:

3–6 = \frac{3 \times D}{12}

Calculating:

Given the diameter D = 500 mm,

3–6 = \frac{3 \times 500}{12} \approx 392.70 \, \text{mm}

Step 6

B–6

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Answer

Finally, the true length B–6:

Using the formula:

B–6 = \sqrt{(300^2 + 500^2 + 400^2)}

Calculating:

B–6 = \sqrt{90000 + 250000 + 160000} \approx 502.49 \, \text{mm}

FIGURE 11.1 below shows a square-to-square hopper (off-centre) - NSC Mechanical Technology Welding and Metalwork - Question 11 - 2023 - Paper 1

Worked Solution & Example Answer:FIGURE 11.1 below shows a square-to-square hopper (off-centre) - NSC Mechanical Technology Welding and Metalwork - Question 11 - 2023 - Paper 1

A–2

B–3

C–4

5–6

3–6

B–6

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