Floating Equilibrium and Layered Liquids
Static floating equilibrium requires zero net force and, when orientation matters, zero net torque; buoyant contributions from distinct immiscible fluids are summed over their displaced volumes.
Why this shows up in the exam
Hydrometers and density floats · Ice, boats, and cargo loading · Bodies resting at immiscible-liquid interfaces
Learn the idea
A floating body displaces enough total fluid weight to balance its weight, possibly across several liquid layers. A floater settles until the upward contributions from every immersed region add to its weight. Denser layers need less displaced volume to provide the same support.
🧠 Memory hook: Float by adding the weights of every displaced liquid layer.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- mg = sum(rho_i g V_i) — vertical force balance for a freely floating body spanning one or more static fluids
- V_sub/V = rho_body/rho_fluid — fraction submerged for a homogeneous body floating in one fluid
- sum(tau) = 0 — rotational equilibrium when centres of gravity and buoyancy or attachment forces matter
How to approach it
- 1Split the immersed body volume by liquid
- 2Sum buoyant forces and external loads
- 3Use geometry only after writing equilibrium
Common slip-ups that cost marks
- •Averaging liquid densities without volume weighting
- •Assuming half-submerged means half the density
- •Ignoring a coin, cavity, spring, or attached body's weight
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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