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 Logic Question: 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. Solution Anticlockwise 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 N Experimental 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 Method By 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, F = 0) No resultant torque: (Rotational equilibrium, M = 0) Worked Example: Vertical Take-Off Jet 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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