Equilibrium of forces
Section: Forces, Density and Pressure | Syllabus: Cambridge AS Level Physics (9702)
The Principle of Moments
The principle of moments states that if there is no resultant torque on a body, then it is in rotational equilibrium.
Sum of Clockwise Moments = Sum of Anticlockwise Moments(About any point)
Figure 4.9: Balanced Beam
(Show a beam pivoted at its centre of gravity. Show force W_3 acting downwards at distance x (anticlockwise). Show forces W_1 and W_2 acting downwards at distances y and z respectively (clockwise).)
Worked Example: See-Saw LogicQuestion: A plank is not pivoted at its centre. A 400 N boy sits 2.5 m from the pivot. The plank's weight acts 0.25 m from the pivot on the same side. A 550 N force acts 2.0 m on the other side. Find the plank's weight.
SolutionAnticlockwise Moments: (400 × 2.5) + (W_plank × 0.25)
Clockwise Moments: 550 × 2.0
Equating them:
1000 + 0.25 W = 1100 0.25 W = 100 W = 400 NExperimental Skills: Finding Unknown Weight
You can use a metre ruler balanced on a pivot to find the mass of an unknown object.
Figure 4.12: Experiment Setup
(Ruler balanced on a pivot. Unknown mass on left at distance b. Known slotted masses on right at distance a.)
Analysis MethodBy varying the position (a) of the known mass (W) to balance the unknown weight (U) at fixed distance (b), we get:
W × a = U × b
If you plot W × a (y-axis) against b (x-axis), the gradient allows you to solve for U. This linear analysis minimizes experimental error compared to a single reading.
Equilibrium of Coplanar Forces
If an object is in equilibrium under the action of three coplanar forces, those forces can be represented by a closed vector triangle. This means there is no resultant force.
Figure 4.14: Forces on a Slope
(Show a resolved vector diagram for an object on a slope. Weight (W) acts down. Normal reaction (R) acts perpendicular to slope. Friction (F) acts up the slope. These three vectors form a closed right-angled triangle.)
Conditions for Complete Equilibrium- No resultant force: (Translational equilibrium, Σ F = 0)
- No resultant torque: (Rotational equilibrium, Σ M = 0)
A jet hovers horizontally. Identify the balance of forces and moments.
- Forces: Lift Fan Thrust + Engine Thrust = Weight.
- Moments: Taking moments about the Lift Fan, the moment from the Weight must equal the moment from the Engine Thrust to prevent rotation.
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