Flashcards · 9702 · AS Topic 4

Forces, density and pressure (AS Level) flashcards

16 cards on AS Topic 4, subtopics 4.1 to 4.3. Pick a subtopic or study them all.

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Moment of a force: The force × the perpendicular distance from the pivot to the line of action of the force. Unit N m.
Couple: A pair of equal, opposite, parallel forces whose lines of action do not coincide. It produces rotation only: zero resultant force.
Torque of a couple: One of the forces × the perpendicular distance between their lines of action.
Centre of gravity: The single point where the whole weight of a body can be taken to act. For a uniform body it is at the geometric centre.
When does an object topple, and how is stability improved?: It topples when the line of action of its weight falls outside its base. A lower centre of gravity and a wider base make it more stable.

Principle of moments: For a body in rotational equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.
The two conditions for a body to be in equilibrium: 1. The resultant force is zero (no translational acceleration). 2. The resultant moment (torque) about any point is zero (no rotation).
Exam technique: about which point should you take moments?: About a point where an unknown force acts. Its moment there is zero, so it drops out of the equation.
A 30 N weight hangs 0.8 m from a pivot. Where must a 20 N weight hang on the other side to balance it?: 30 × 0.8 = 20 × d, so d = 24 ÷ 20 = 1.2 m.
How can three coplanar forces in equilibrium be represented?: As a closed vector triangle: the forces drawn tip-to-tail return to the starting point. Used to find an unknown force or angle.

Density and pressure: definitions and units: Density ρ = mass ÷ volume (kg m⁻³). Pressure p = normal force ÷ area (Pa = N m⁻²).
Derive Δp = ρgΔh: A column of fluid of height Δh and area A has volume AΔh, mass ρAΔh and weight ρAΔhg. Pressure = weight ÷ area = ρgΔh.
Does the pressure at a given depth depend on the shape of the container?: No. Δp = ρgΔh depends only on depth, density and g, not on the container’s width, shape or volume.
Where does upthrust come from?: Pressure increases with depth, so the upward pressure on the bottom of a submerged object is greater than the downward pressure on its top. The difference gives a net upward force.
Archimedes’ principle and the upthrust formula: Upthrust equals the weight of fluid displaced: F = ρgV, where ρ is the fluid’s density and V the volume of fluid displaced (only the submerged volume).
Why does a steel ship float?: Its average density, including the enclosed air, is less than that of water, so it displaces its own weight of water before it is fully submerged. Upthrust = weight.