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A-LEVEL 9702 · AS · TOPIC 4
Forces, density and pressure
The chain of the topic: a force acting off-axis gives a turning moment, balanced moments and balanced forces define equilibrium, and a force shared over an area becomes pressure, which in a fluid grows with depth and pushes back as upthrust. Around the hexagon are the three syllabus ideas; above is what it builds on, below is where it leads.
TOPIC 4: FORCES, DENSITY AND PRESSURE
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T1 Units & vectors T2 Kinematics T3 Dynamics: F = ma 4.1
4.2
4.3
4.3
TOPIC 4
FORCES &
PRESSURE
1 · TURNING EFFECTS OF FORCES
A force off the pivot tends to rotate a body.
Centre of gravity: the single point where weight acts.
Moment = force × perpendicular distance to the pivot.
A couple: two equal, opposite, parallel forces.
moment = F d
torque of couple = F × s
d
F
pivot
F at distance d gives a moment about the pivot
2 · EQUILIBRIUM OF FORCES
Balanced forces and balanced moments.
Principle of moments: about any point,
sum of clockwise = sum of anticlockwise.
Equilibrium: no resultant force and no resultant torque.
Three coplanar forces close into a vector triangle.
ΣF = 0 Σ(moments) = 0
F1
F2
F3
three forces in equilibrium form a closed triangle
3 · DENSITY AND PRESSURE
Force per unit area; deeper means more.
Density ρ = m / V; pressure p = F / A (force normal to area).
A fluid column of height h presses by its own weight.
Hydrostatic pressure rises in proportion to depth h.
ρ = m / V p = F / A
Δp = ρ g Δh
h
p grows with depth
deeper down, the wall feels more pressure
4 · UPTHRUST & ARCHIMEDES
A pressure difference lifts a submerged body.
The bottom face is deeper, so pushed up harder than down.
Net upward force = upthrust = weight of fluid displaced.
A body floats when upthrust balances weight (equilibrium).
F = ρ g V
(Archimedes' principle)
fluid surface
W
F
deeper bottom pushed up more than top pushed down
LEADS TO
T5 Energy: work done by a force, W = F s T6 Deformation: stress as force per unit area T15 Ideal gases: pressure of a gas, pV = nRT Each reuses one idea: a force, or a force shared over an area as pressure, set equal and opposite so a body stays in equilibrium.
← Builds on IGCSE: Forces