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5.1 FIGURE 1 below shows a shaped lamina - NSC Civil Technology Civil Services - Question 5 - 2017 - Paper 1
Question 5
5.1 FIGURE 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 answ... show full transcript
Worked Solution & Example Answer:5.1 FIGURE 1 below shows a shaped lamina - NSC Civil Technology Civil Services - Question 5 - 2017 - Paper 1
Step 1
Calculate Total Area
Answer
To find the centroid, we first calculate the total area of the lamina.
The lamina consists of two rectangles:
- Rectangle 1: Base = 60 mm, Height = 45 mm
- Rectangle 2: Base = 30 mm, Height = 15 mm
We calculate the areas:
- Area 1 (A1) = Base × Height = 60 mm × 45 mm = 2700 mm²
- Area 2 (A2) = Base × Height = 30 mm × 15 mm = 450 mm²
Now, the total area (A) is:
Step 2
Calculate Centroid Coordinates
Answer
Next, we calculate the coordinates of the centroid (x̄, ȳ).
The x-coordinate of the centroid (x̄) is calculated using the formula:
x̄ = rac{Σ(A_i × x_i)}{A}
where:
- For Rectangle 1 (A1): x1 = 30 mm (center of base)
- For Rectangle 2 (A2): x2 = 105 mm (from left end)
Thus:
x̄ = rac{(A1 × x1) + (A2 × x2)}{A} = rac{(2700 ext{ mm}^2 × 30 ext{ mm}) + (450 ext{ mm}^2 × 105 ext{ mm})}{3150 ext{ mm}^2}
Calculating gives:
x̄ = rac{81000 + 47250}{3150} = rac{128250}{3150} ≈ 40.71 ext{ mm}
Step 3
Calculate the Y-coordinate of the Centroid
Answer
The y-coordinate of the centroid (ȳ) is calculated similarly:
ȳ = rac{Σ(A_i × y_i)}{A}
For y-coordinates:
- For Rectangle 1 (A1): y1 = 22.5 mm (half of height)
- For Rectangle 2 (A2): y2 = 52.5 mm (15 mm + half of 15 mm)
Hence:
ȳ = rac{(2700 ext{ mm}^2 × 22.5 ext{ mm}) + (450 ext{ mm}^2 × 52.5 ext{ mm})}{3150 ext{ mm}^2}
Calculating gives:
ȳ = rac{60750 + 23625}{3150} = rac{84375}{3150} ≈ 26.88 ext{ mm}
Step 4