Physics / AS level
Analyse equilibrium, turning effects and fluid forces.
Equilibrium requires both zero resultant force and zero resultant moment. A moment depends on the perpendicular distance from the pivot to the force’s line of action, not simply the distance to where it is applied.
Pressure is normal force per unit area. In a stationary fluid of uniform density, pressure difference increases with vertical depth. Upthrust arises from the difference in pressure forces and equals the weight of displaced fluid.
Zero resultant force prevents translational acceleration, but a pair of equal opposite forces can still form a turning couple. Static equilibrium also needs zero resultant moment about any chosen pivot. A moment uses perpendicular distance to the force’s line of action. Choosing a pivot through an unknown support force can simplify a calculation because that force then has zero moment about the pivot.
For ordinary near-Earth problems, weight acts through the centre of gravity. An object becomes liable to topple when the weight’s line of action moves outside its support base. A wider base or lower centre of gravity can improve stability. This is separate from sliding: friction determines whether an object slips before it tips, and a realistic explanation should identify which type of motion is being considered.
Density is mass per unit volume. In a stationary uniform-density liquid, the pressure increase over vertical depth h is ρgh. At 0.50 m depth in water, using g = 10 N/kg, the increase is about 5000 Pa. That is a pressure difference, not automatically absolute pressure: add the surface pressure when required. Width and sloping path length do not replace the vertical depth.
Pressure on a submerged object’s lower surface exceeds that on its upper surface, producing an upward resultant. Upthrust equals the weight of displaced fluid. A floating object displaces fluid of weight equal to its own, while a fully submerged object may rise or sink according to its weight and upthrust. Increasing the object’s mass does not by itself increase upthrust when its submerged volume is unchanged.
The ship’s shape allows it to displace enough water for upthrust to balance its weight. The bolt’s fully submerged volume may displace too little water to support its weight.
Perpendicular force distance from a pivot.
Here p is pressure in Pa, not momentum; the fluid has uniform density.
Find the pressure difference across 2.0 m of water, using ρ = 1000 kg/m³ and g = 10 m/s².
Δp = 1000 × 10 × 2.0 = 20000 Pa.
Balance a ruler using small known masses and compare clockwise with anticlockwise moments. Secure the apparatus against falling.
Compare moments, pressure at equal depths and displaced volumes in separate models. Do not infer absolute pressure from a gauge without checking its reference level.
Perpendicular distance to the force’s line of action
Only the perpendicular lever arm determines the turning effect.
20000 Pa
Δp = 1000 × 10 × 2.0 = 20000 Pa.
Zero resultant force and zero resultant moment
Both translational and rotational balance are necessary.