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5.1 FIGURE 5.1 below shows a shaped lamina - NSC Civil Technology Woodworking - Question 5 - 2017 - Paper 1
Question 5
5.1 FIGURE 5.1 below shows a shaped lamina. All dimensions are in millimetres. Study the lamina and calculate the centroid of the lamina from A-A. Round off your an... show full transcript
Worked Solution & Example Answer:5.1 FIGURE 5.1 below shows a shaped lamina - NSC Civil Technology Woodworking - Question 5 - 2017 - Paper 1
Step 1
Calculate the Areas of the Sections
Answer
To find the centroid, start by identifying two main sections of the lamina: section 1 (the rectangle) and section 2 (the triangle).
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Calculate the area for section 1 (rectangle):
Area of rectangle = width × height = 60 mm × 45 mm = 2700 mm².
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Calculate the area for section 2 (triangle):
Area of triangle = (1/2) × base × height = (1/2) × 30 mm × 45 mm = 675 mm².
Step 2
Determine the Centroid of Each Section
Answer
Next, find the centroid for each section, which is located at:
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Section 1 (rectangle) centroid position from A-A:
x1 = 30 mm (width/2) and y1 = 22.5 mm (height/2)
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Section 2 (triangle) centroid position from A-A:
x2 = 15 mm (width/2 from A) and y2 = 45 mm (height from A to the apex divided by 3, thus 15 mm).
Step 3
Calculate the Overall Centroid
Answer
Finally, use the area-weighted average to find the overall centroid:
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Sum of the areas:
A_total = A1 + A2 = 2700 mm² + 675 mm² = 3375 mm². -
Calculate the x-coordinate:
x_c = (A1 × x1 + A2 × x2) / A_total = (2700 mm² × 30 mm + 675 mm² × 15 mm) / 3375 mm².
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Calculate the y-coordinate:
y_c = (A1 × y1 + A2 × y2) / A_total = (2700 mm² × 22.5 mm + 675 mm² × 15 mm) / 3375 mm².
Round off the final coordinates to two decimal places.