Overview
This lecture explains how to apply the principle of moments to solve equilibrium problems, using a seesaw example to illustrate the step-by-step mathematical method.
Principle of Moments
- A moment is the force applied multiplied by the perpendicular distance to the pivot.
- In equilibrium, the total clockwise moments equal the total anticlockwise moments.
- The principle of moments formula:
Clockwise moments = Anticlockwise moments.
- F1 x D1 = F2 x D2
Worked Example: Seesaw Problem
- A person weighing 500 N stands 1.5 m from the pivot, creating an anticlockwise moment.
- A second person weighs 600 N and stands on the opposite side at an unknown distance d.
- Set up the equation: 600 × d = 500 × 1.5.
- Calculate 500 × 1.5 = 750.
- Rearrange for d: d = 750 ÷ 600.
- Solve to get d = 1.25 m.
Problem-Solving Steps
- State the principle of moments at the start of the solution.
- Substitute known values (forces and distances) into the equation.
- Rearrange to make the unknown variable the subject.
- Solve for the unknown to find the required distance or force.
Key Terms & Definitions
- Moment — The turning effect of a force, calculated as force × perpendicular distance from the pivot.
- Pivot — The fixed point about which an object rotates.
- Equilibrium — The state where total clockwise and anticlockwise moments are equal.
Action Items / Next Steps
- Practice solving principle of moments problems using the outlined steps.
- Review key terms and ensure you can define and use them in context.