Answer: the equilibrium point or center of mass is (4, 7.33)
Explanation:
1) Physicial principles:
- The equilibrium point is the center of mass.
- Call Xc and Yc the coordinates of the center of mass (Xc, Yc), then:
- Xc is given by the equation Xc = (m₁X₁ + m₂X₂) / (m₁ + m₂)
- Yx is given by the equation Yc = (m₁Y₁ + m₂Y₂) / (m₁ + m₂)
2) Data:
- m₁ = 24 kg
- X₁ = 2
- Y₁ = 5
- m₂ = 12 kg
- X₂ = 8
- Y₂ = 12
3) Solution:
- Xc = (m₁X₁ + m₂X₂) / (m₁ + m₂) = (24×2 + 12×8) / (24 + 12) = 4
- Yc = (m₁Y₁ + m₂Y₂) / (m₁ + m₂) = (24×5 + 12×12) / (24 + 12) = 7.33
Answer: the equilibrium point or center of mass is (4, 7.33)
