Hydrostatics
High-Yield Summary
- Pascal's Principle: pressure applied to an incompressible fluid transmits undiminished throughout the fluid and to its container's walls.
- Hydraulic lifts exploit this: F1/A1 = F2/A2 — force is amplified but distance traveled shrinks proportionally, so energy is conserved.
- Archimedes' Principle: a submerged object feels an upward buoyant force equal to the weight of fluid it displaces (Fb = ρfluid·Vdisplaced·g).
- Object density < fluid density → floats; object density > fluid density → sinks. Submerged fraction (floating) = object density / fluid density.
- Surface tension arises from unbalanced intermolecular forces at a liquid's surface. Capillary action results from cohesion (same-substance attraction) vs. adhesion (different-substance attraction).
Hydraulic Lift and Buoyant Force
F1/A1 = F2/A2 | Fb = ρfluid · Vdisplaced · g
- F1, A1 = Force and area at the small piston
- F2, A2 = Force and area at the large piston
- Fb = Buoyant force
- ρfluid = Density of the fluid
- Vdisplaced = Volume of fluid displaced by the submerged object
- Hydraulic lifts don't violate energy conservation: the small piston moves a large distance for a small force; the large piston moves a small distance for a large force.
Meniscus: Cohesion vs. Adhesion
| Meniscus Type | Dominant Force / Example |
|---|---|
| Concave (curves up at edges) | Adhesion > cohesion — e.g., water in a glass tube |
| Convex (curves down at edges) | Cohesion > adhesion — e.g., mercury in glass |
Must Know
- Floating fraction shortcut: an ice cube (ρ = 0.92 g/cm³) floats in water with ~92% of its volume submerged, since its density is 92% of water's.
- Surface tension is why water droplets are spherical (minimum surface area for a given volume) and why a needle can float on water.
- Capillary action (xylem in plants, a paper towel absorbing a spill) requires adhesion to exceed cohesion.
Common MCAT Trap
- A hydraulic lift's force amplification isn't 'free energy' — always check whether the question is asking about force (amplified) or work/energy (conserved, since distance shrinks proportionally).
- Don't confuse cohesion (same substance) with adhesion (different substances) — capillary action needs adhesion > cohesion, not the reverse.
Quick Recall
Why doesn't a hydraulic lift violate conservation of energy?
What determines whether an object floats or sinks in a fluid?