Determine the centroid of the wire shown in Fig.

1.	Determine the centroid of the wire shown in Fig.
Answer» The wire is divided into three segments AB, BC and CD. Taking A as origin the coordinates of the centroids of AB, BC and CD are G₁(300, 0); G₂(600, 100) and G₃ (600 – 150 cos 45°, 200 + 150 sin 45°) i.e., G₃ (493.93, 306.07) L₁ = 600 mm, L₂ = 200 mm, L₃ = 300 mm ∴ Total length L = 600 + 200 + 300 = 1100 mm ∴ From the eqn. Lx_c = ΣL_i x_i , we get 1100 x_c = L₁x₁ + L₂x₂ + L₃x₃ = 600 × 300 + 200 × 600 + 300 × 493.93 ∴ x_c = 407.44 mm Ly_c = ΣL_i y_i 1100 y_c= 600 × 0 + 200 × 100 + 300 × 306.07 ∴ y_c = 101.66 mm

Answer»

The wire is divided into three segments AB, BC and CD.

Taking A as origin the coordinates of the centroids of AB, BC and CD are

G₁(300, 0); G₂(600, 100) and G₃ (600 – 150 cos 45°, 200 + 150 sin 45°)

i.e., G₃ (493.93, 306.07)

L₁ = 600 mm, L₂ = 200 mm, L₃ = 300 mm

∴ Total length L = 600 + 200 + 300 = 1100 mm

∴ From the eqn. Lx_c = ΣL_i x_i , we get

1100 x_c = L₁x₁ + L₂x₂ + L₃x₃

= 600 × 300 + 200 × 600 + 300 × 493.93

∴ x_c = 407.44 mm

Ly_c = ΣL_i y_i

1100 y_c= 600 × 0 + 200 × 100 + 300 × 306.07

∴ y_c = 101.66 mm

Discussion

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