AP Physics 2:: Fluids

What is DENSITY, and what is the mathematical FORMULA relating an object's or fluid's density to its MASS and VOLUME?

- **A)** Density is a measure of how much mass is packed into a given volume; rho = m/V (mass divided by volume), measured in kg/m^3 -- a HIGHER density means MORE mass packed into the same volume
- **B)** Density is calculated as rho = m*V (mass multiplied by volume), rather than mass divided by volume
- **C)** This concept has no actual mathematical relationship between density, mass, and volume
- **D)** Density depends only on VOLUME, with no actual dependence on an object's or fluid's mass

What is PRESSURE, and what is the mathematical FORMULA relating pressure to a FORCE and the AREA over which that force is distributed?

- **A)** Pressure is the amount of force applied PER UNIT AREA; P = F/A (force divided by area), measured in PASCALS (Pa), where one pascal equals one newton per square meter
- **B)** This concept has no actual mathematical relationship between pressure, force, and area
- **C)** Pressure depends only on AREA, with no actual dependence on the applied force
- **D)** Pressure is calculated as P = F*A (force multiplied by area), rather than force divided by area

Why does a SHARP KNIFE cut through material MORE EASILY than a DULL knife, when BOTH are pushed with the SAME applied force, based on the pressure formula P=F/A?

- **A)** Cutting ability depends only on the applied FORCE, with no actual relationship to the knife's contact area or resulting pressure
- **B)** This concept has no actual relationship between a knife's sharpness (contact area) and the pressure it produces for a given applied force
- **C)** A sharp knife has a LARGER contact area than a dull knife, producing LESS pressure for the same force -- the reverse of the actual relationship
- **D)** A sharp knife has a MUCH SMALLER contact area (a thin edge) than a dull knife -- since pressure is INVERSELY proportional to area for a given force (P=F/A), the smaller area of a sharp edge produces a MUCH LARGER pressure, making it easier to cut through material

What is HYDROSTATIC PRESSURE, and what is the mathematical FORMULA for the pressure at a DEPTH h below the surface of a fluid, in terms of the fluid's density and local gravitational acceleration?

- **A)** This concept has no actual mathematical relationship between hydrostatic pressure, fluid density, gravitational acceleration, and depth
- **B)** Hydrostatic pressure is the pressure exerted by a fluid due to the WEIGHT of the fluid above a given point; P = rho*g*h (fluid density times gravitational acceleration times depth) -- pressure INCREASES linearly with depth
- **C)** Hydrostatic pressure is calculated as P = rho*g/h (density times gravitational acceleration DIVIDED by depth), rather than multiplied by depth
- **D)** Hydrostatic pressure DECREASES as depth increases, the reverse of the actual relationship

What is ABSOLUTE PRESSURE, and how does it relate to GAUGE PRESSURE and ATMOSPHERIC PRESSURE, based on the formula P_absolute = P_atmospheric + P_gauge?

- **A)** Absolute pressure and gauge pressure are IDENTICAL quantities, with no actual distinction between them
- **B)** Absolute pressure is the TOTAL pressure at a point (including atmospheric pressure); gauge pressure is the pressure DIFFERENCE relative to atmospheric pressure (what most pressure gauges actually measure) -- P_absolute = P_atmospheric + P_gauge
- **C)** This concept has no actual relationship between absolute pressure, gauge pressure, and atmospheric pressure
- **D)** Gauge pressure is always GREATER than absolute pressure, with atmospheric pressure being subtracted rather than added

What is PASCAL'S PRINCIPLE, and what does it state about how a change in pressure applied to an ENCLOSED, incompressible fluid is transmitted throughout that fluid?

- **A)** Pascal's Principle states that pressure changes DIMINISH significantly as they propagate through an enclosed fluid, rather than being transmitted undiminished
- **B)** Pascal's Principle states that a pressure change applied to an ENCLOSED fluid is transmitted UNDIMINISHED to EVERY point within that fluid and to the walls of its container -- this is the principle underlying hydraulic systems, which can multiply force
- **C)** This principle has no actual relationship to how pressure changes propagate through an enclosed fluid
- **D)** Pascal's Principle applies only to GASES, not to enclosed liquids

In a HYDRAULIC LIFT (two connected pistons of DIFFERENT areas, based on Pascal's Principle), how does the FORCE required on the SMALL piston compare to the FORCE produced at the LARGE piston, given that pressure is the SAME throughout the enclosed fluid?

- **A)** The force on the large piston is always EQUAL to the force on the small piston, regardless of their different areas
- **B)** Since pressure (P=F/A) is the SAME throughout the enclosed fluid, the force on the LARGE piston is GREATER than the force on the small piston, in direct proportion to the RATIO of their areas (F_large = F_small * (A_large/A_small)) -- allowing a small input force to lift a much heavier load
- **C)** The force on the large piston is SMALLER than the force on the small piston, the reverse of how a hydraulic lift actually provides mechanical advantage
- **D)** This concept has no actual relationship between piston area and the resulting force multiplication in a hydraulic lift

What is ARCHIMEDES' PRINCIPLE, and what does it state about the BUOYANT FORCE experienced by an object PARTIALLY OR FULLY submerged in a fluid?

- **A)** Archimedes' Principle applies only to objects that FLOAT, not to objects that are fully submerged and sink
- **B)** This principle has no actual relationship between buoyant force and the weight of fluid displaced by a submerged object
- **C)** Archimedes' Principle states that buoyant force depends only on the SUBMERGED OBJECT'S weight, with no actual relationship to the fluid displaced
- **D)** Archimedes' Principle states that the buoyant force on a submerged (or partially submerged) object is EQUAL to the WEIGHT of the fluid DISPLACED by that object -- F_buoyant = rho_fluid * g * V_displaced