Parallel Forces Multiple Choice Question
(A) 15 N and 5 N
(B) 20 N and 5 N
(C) 15 N and 15 N
(D) None of the above
Explanation
Two like parallel forces (acting in the same direction) are separated by a distance of 24 mm, with a resultant force of 20 N. The line of action of the resultant is 6 mm from one of the forces. Using the Principle of Moments (Varignon’s Theorem), we can calculate the magnitudes of the two forces.
Calculation Steps
Let F₁ and F₂ be the two forces, with the resultant R = F₁ + F₂ = 20 N. The distance between the forces is 24 mm, and the resultant acts 6 mm from F₁, so it is 18 mm from F₂ (24 mm - 6 mm).
- F₁ × 6 = F₂ × 18
- ⇒ F₁ / F₂ = 18 / 6 = 3 ⇒ F₁ = 3F₂
- Using the resultant: F₁ + F₂ = 20 ⇒ 3F₂ + F₂ = 20 ⇒ 4F₂ = 20 ⇒ F₂ = 5 N
- ⇒ F₁ = 3 × 5 = 15 N
Thus, the two forces are 15 N and 5 N.
Key Notes
- The Principle of Moments ensures that the moments of individual forces about the resultant's line of action balance out.
- Like parallel forces have a resultant whose magnitude is the sum of the forces, and its position is determined by moment equilibrium.
- This concept is fundamental in statics and is widely applied in structural engineering for analyzing force systems.
- Accurate calculation of force magnitudes and positions is essential for designing stable structures in civil engineering.
Note: The Principle of Moments is critical for determining the magnitudes of parallel forces, ensuring accurate analysis in structural and civil engineering applications.
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