Unit 8 practice test: Fluids

F_b = ρ_water V_displaced g. Z displaces its whole volume, Y three quarters, X one half. The blocks have equal volumes, so Z > Y > X.

• Correct: Z, then Y, then X: Right: more displaced water, larger buoyant force.
• X, then Y, then Z: This reverses the ranking; floating higher means less water displaced.
• X, Y and Z are equal: Equal volumes are not equal displaced volumes: X and Y are only partly under water.
• Y, then X, then Z: Z, fully under water, displaces the most.

Y is at rest with only two forces on it, so they balance: F_b = F_g. Floating means the buoyant force equals the weight, not that it exceeds it.

• Correct: They are equal, because Y is floating at rest: Right: equilibrium of a floating object.
• The buoyant force is larger, because Y floats: If F_b were larger, Y would accelerate upward until it displaced less water.
• The buoyant force is smaller, because Y is partly above the water: Being partly out of the water lowers F_b only until it matches the weight.
• The buoyant force is larger, because Y is denser than X: Y is denser than X, which is why it sits lower; it still floats with F_b = F_g.

Z displaces its full volume, so it does feel a buoyant force, but Z is denser than water, so F_b < F_g. At rest, F_b + F_N = F_g.

• Correct: F_b is less than Z's weight; the floor's normal force makes up the rest: Right: three forces balance on the sunk block.
• There is no buoyant force on Z, because water is not pushing up from under it: The model treats the water as pushing up on Z, giving a buoyant force ρVg; the floor adds a normal force.
• The buoyant force equals Z's weight, because Z is at rest: At rest the net force is zero, but the normal force is part of the balance.
• The buoyant force on Z is smaller than on X, because Z is denser: The buoyant force depends on the displaced volume, not the block's density: Z displaces the most.

Floating, X displaced half its volume; fully under, it displaces all of it. F_b ∝ V_displaced, so it doubles. The extra push comes from the hand.

• Correct: Twice as large: Right: twice the displaced volume, twice the buoyant force.
• The same: The buoyant force depends on how much water is displaced, which doubled.
• Half as large: Pushing it deeper displaces more water, not less.
• Four times as large: The displaced volume doubled, so the force doubles, not quadruples.

Squeezing changed the air's volume noticeably but not the water's. Liquids are close to incompressible because their particles are already touching; gas particles are far apart.

• Correct: Water is nearly incompressible; air is easily compressed: Right: water's volume hardly changes under the push.
• Both fluids are incompressible, since neither leaks out: Not leaking does not make a fluid incompressible; the air's volume clearly shrank.
• The air is nearly incompressible, but the water is compressed: This reverses the observations: the air plunger moved in.
• Neither is a fluid, because they are trapped in the syringe: A fluid is defined by flowing and taking its container's shape, which both do.

The blocked tip keeps the mass of air fixed, while the volume shrinks. ρ = m/V, so the density rises. A compressible fluid's density can change.

• Correct: It increases, because the same mass occupies a smaller volume: Right: same m, smaller V, larger ρ.
• It stays the same, because no air leaves the syringe: The mass stays the same, but density is mass per volume and the volume shrank.
• It decreases, because the particles are pushed apart: Pushing the plunger in squeezes the particles closer together, not farther apart.
• It stays the same, because density is a property of the material: For an incompressible fluid density is fixed, but air is compressible.

An ideal fluid is incompressible (constant density) and nonviscous (no internal friction), and its flow is smooth and steady.

• Correct: Its density stays the same as it flows and is squeezed: Right: incompressible means constant density.
• The fluid sticks to the walls of its container: Sticking to walls is a sign of viscosity, which an ideal fluid lacks.
• The fluid has no mass, so it exerts no forces: An ideal fluid has mass and weight; only its friction is ignored.
• The fluid keeps its shape when it is poured: No fluid keeps its shape; that is the difference between a fluid and a solid.

In a liquid the particles touch and slide past each other; there is little empty space to squeeze out. In a gas most of the volume is empty space between particles.

• Correct: Water particles already touch; air particles are far apart: Right: the spacing of the particles decides how compressible the fluid is.
• Water particles are locked in fixed places, as in a solid: Water particles can slide past each other; that is why water flows.
• Water has a larger mass than air, so it is harder to move: The two syringes hold the same volume; the difference is in particle spacing, not mass.
• Air particles attract each other more strongly than water particles do: In a gas the attractions between particles are weak, which is why they spread out.