4 questions, one for each idea where we can. Answer them, then see which ideas to fix.
Question 1 of 4
A block of ice keeps its own shape, but the water it melts into takes the shape of whatever holds it. Which explanation, in terms of the water molecules, accounts for this difference?
Answer and reasoning
AThe molecules in the ice are themselves hard and rigid, while the molecules in liquid water are soft and able to change their shape. A student who gives the particles the properties of the bulk material picks this. The molecules are the same H₂O molecules in ice and in liquid water; what differs is how they are arranged and how freely they can move.
BIn the ice the molecules are packed tightly together; in the liquid they are several times farther apart, so they are free to move. A student who pictures a liquid's particles as widely spaced picks this. Ice (917 kg/m³) and liquid water (1000 kg/m³) have almost the same density, so the molecules are about equally close in both; the liquid flows because its molecules can move past one another.
CThe molecules in the ice do not move at all, while the molecules in the liquid are constantly moving around one another. A student who thinks the particles of a solid are motionless picks this. The molecules in ice vibrate continually; the difference is that interactions hold each one near a fixed place, whereas in the liquid they can change places.
DInteractions keep each molecule near one place in the ice; in the liquid, molecules stay close but can move past each other.Correct The shape of a solid is fixed because interactions with its neighbors keep each molecule near one position, about which it vibrates. In the liquid the molecules are still close together and still interact, but they are not held in place, so they can slide past one another and the liquid takes the shape of its container.
Which property is shared by every fluid, whether it is a liquid or a gas?
Answer and reasoning
AA sample of it fills the same volume in whatever container it is poured into. A student who thinks 'fluid' means 'liquid' picks this. A fixed volume is a property of liquids only: a gas spreads out to fill any container, yet it is still a fluid.
BIts particles are far apart from one another, with empty space between them. A student who pictures the particles of every fluid as widely spaced picks this. That is true of a gas, but in a liquid the particles are about as close together as in a solid; liquids flow because their particles can move past one another.
CA sample has no shape of its own, so it takes the shape of its container.Correct A fluid is a substance with no fixed shape. A liquid takes the shape of the part of the container it fills, and a gas spreads to fill the whole container, but neither keeps a shape of its own, so both are fluids.
DIt flows without any resistance at all, however thick or sticky it may appear. A student who takes the ideal-fluid model as a description of every fluid picks this. Real fluids have viscosity, a resistance to flowing, and some, such as honey, have a lot; 'no viscosity' describes only the ideal model.
A student pours a liquid into a beaker in steps. After each step she records the volume V of liquid in the beaker and the total mass m of the beaker and liquid. The graph shows her results. What is the mass of 400 cm³ of this liquid?
Answer and reasoning
A440 g A student who extends the line to V = 400 cm³ and reads off the value picks this. The graph shows the total mass of beaker and liquid, so the reading includes the 120 g beaker; the liquid alone is 440 − 120 = 320 g.
B320 gCorrect The slope of the graph is the liquid's density, (280 − 120) g ÷ 200 cm³ = 0.80 g/cm³; the intercept, 120 g, is the beaker. So 400 cm³ of liquid has mass m = ρV = 0.80 × 400 = 320 g.
C560 g A student who treats the straight line as a proportional relationship scales from the last point: 280 g × (400/200) = 560 g. The line does not pass through the origin, because the 120 g beaker is included, so doubling V does not double m.
D500 g A student who finds the density correctly, 0.80 g/cm³, but rearranges ρ = m/V as m = V/ρ gets 400 ÷ 0.80 = 500 g. Multiplying both sides of ρ = m/V by V gives m = ρV = 0.80 × 400 = 320 g.
Working The intercept, 120 g, is the mass of the empty beaker. The slope is the liquid's density: (280 g − 120 g)/(200 cm³ − 0) = 0.80 g/cm³ (800 kg/m³). Mass of 400 cm³ of liquid: m = ρV = (0.80 g/cm³)(400 cm³) = 320 g.
Honey poured from a jar flows much more slowly than water. A student models the honey as an ideal fluid. Which property of real honey does this model leave out?
Answer and reasoning
AIts resistance to flowing, which slows layers of honey that slide past one another.Correct An ideal fluid has no viscosity. Honey's viscosity, the internal friction between layers of honey sliding past one another, is exactly what makes it pour slowly, and it is the property the ideal-fluid model ignores.
BIts large density, which is the property that makes honey thick and slow to pour. A student who confuses density with viscosity picks this. An ideal fluid still has a density, so the model keeps honey's density; honey pours slowly because of its viscosity, which is a separate property.
CIts ability to change shape, which an incompressible fluid does not have. A student who thinks 'incompressible' means 'rigid' picks this. An incompressible fluid keeps its volume but still flows and takes the shape of its container, so the model does not remove honey's ability to change shape.
DIts liquid state, since the ideal-fluid model applies only to gases. A student who mixes up the ideal fluid with the 'ideal gas' of chemistry picks this. The ideal-fluid model (incompressible, no viscosity) is used mostly for liquids, which are nearly incompressible.
In preparation: 0 of 4 sections compiled and reviewed. The rest show key terms and common mistakes from our question bank until they are.
8.1.A.1 Solid (particle model) Fix
Solid (particle model)
A state of matter in which attractive interactions between neighboring atoms or molecules hold each particle near a fixed position, about which it vibrates. As a result a solid has a fixed shape and a fixed volume.
Liquid (particle model)
A state of matter in which the particles are about as close together as in the solid, and their interactions keep them together, but they are not held in fixed positions and can move past one another. A liquid has a fixed volume but no fixed shape.
Gas (particle model)
A state of matter in which the particles are, on average, far apart compared with their size and interact significantly only when they collide. A gas has neither a fixed shape nor a fixed volume: it spreads out to fill its container.
Students often think The particles of a solid are themselves hard and rigid, the particles of a liquid are soft, and the particles of a substance change their size or mass when it melts, boils, expands or shrinks. In fact No. The particles of water are the same molecules, of the same size and mass, in ice, liquid water and steam. The properties of a solid, liquid or gas come from how the particles are arranged, how they move and how strongly they interact, not from the particles being hard, soft, large or small.
Students often think In a liquid the particles are several times farther apart than in the solid, roughly halfway between their spacing in a solid and in a gas, and this gap is what lets a liquid flow. In fact No. For most substances the densities of the solid and the liquid differ by only a few percent, so the particles are about as closely spaced in both. The large change in spacing comes on boiling: a gas is typically about a thousand times less dense than its liquid.
8.1.A.2 Fluid Fix
Fluid
A substance that has no fixed shape, so that a sample takes the shape of the container that holds it. Both liquids and gases are fluids.
Students often think 'Fluid' means 'liquid': a fluid keeps a fixed volume while taking the shape of its container, so a gas, which spreads out and can be squeezed, is not a fluid. In fact No. A fluid is any substance with no fixed shape. Liquids and gases are both fluids. A liquid happens to keep a nearly fixed volume; a gas does not, but it is still a fluid.
8.1.A.3 Density Fix
Density
The ratio of the mass of a sample to its volume, ρ = m/V. It characterizes the material, not the size of the sample: any piece of a uniform material has the same density. SI unit: kg/m³ (1 g/cm³ = 1000 kg/m³).
Mass and volume of a fluid sample
Mass m is the amount of matter in the sample (unit: kg). Volume V is the space the sample occupies (unit: m³; 1 cm³ = 10⁻⁶ m³ and 1 L = 10⁻³ m³). When a fluid is weighed in a container, the container's mass must be subtracted to find the fluid's mass.
Students often think Density means how heavy something is, so the object with more mass is the denser one, and objects of equal mass have equal densities. In fact No. Density is mass per unit volume, ρ = m/V. A large object of a low-density material can have more mass than a small object of a high-density material, and two objects with equal masses can have very different densities.
Students often think Enlarging an object so that each side is twice as long doubles its volume. In fact No. Volume depends on the product of three lengths, so doubling every side multiplies the volume by 2 × 2 × 2 = 8. (The area of each face is multiplied by 4.)
8.1.A.4 Ideal fluid Fix
Ideal fluid
A model of a fluid that is incompressible and has no viscosity. Real liquids are often close to incompressible, and the model is used whenever compression and internal friction are small enough to ignore.
Incompressible
Describes a fluid whose volume, and so density, does not change when the pressure on it changes. An incompressible fluid can still change shape freely; it simply cannot be squeezed into a smaller volume.
Viscosity
A fluid's internal resistance to flowing: the friction-like interaction between neighboring layers of fluid that slide past one another at different speeds. Honey has a much larger viscosity than water. An ideal fluid has none.
Students often think Every fluid flows with no resistance and cannot be compressed; this is part of what being a fluid means. In fact No. The ideal fluid is a model. Real fluids have some viscosity (honey has a lot) and can be compressed to some degree (gases easily). The model is useful when these effects are small enough to ignore.
Students often think An incompressible substance is rigid, like a solid, so a fluid whose volume does not change when it is pushed is behaving as a solid. In fact No. Incompressible means that the volume, and so the density, does not change when the fluid is pushed on. An incompressible liquid still flows and takes the shape of its container.
5 more questions. Every wrong answer here is a real mistake students make, and you see why it is wrong as soon as you answer.
Question 1 of 5
The table shows the densities of water in its three states, each measured at atmospheric pressure. Which claim about the water molecules is best supported by the data?
Answer and reasoning
AThe spacing of the molecules in the liquid is roughly halfway between their spacing in the solid and in the gas. A student who expects the spacing to increase in even steps from solid to liquid to gas picks this. The data show the liquid's density is almost the same as the solid's, not intermediate: the big change comes between liquid and gas.
BThe molecules are about as closely spaced in the liquid as in the solid, but much farther apart in the gas.Correct The same molecules are present in every state, so density shows how closely they are packed. The solid (917 kg/m³) and the liquid (1000 kg/m³) have nearly equal densities, so the spacing is similar; the gas (0.60 kg/m³) is about 1700 times less dense, so its molecules are, on average, about 12 times farther apart.
CThe molecules are packed more closely together in the solid than they are in the liquid. A student who assumes a solid is always the most closely packed state picks this. The table shows the opposite for water: ice (917 kg/m³) is less dense than liquid water (1000 kg/m³), so its molecules are, on average, slightly farther apart.
DEach molecule in the gas is much smaller and lighter than each molecule in the liquid or the solid. A student who explains a change in the substance by a change in its particles picks this. Steam, liquid water and ice are all made of the same H₂O molecules; the gas is less dense because the molecules are farther apart, not because they are smaller or lighter.
Working Density is mass per volume, and the molecules are the same in every state, so density shows how closely they are packed. Solid 917 and liquid 1000 kg/m³ differ by under 10%, so the spacing is about the same (cube root of 1000/917 ≈ 1.03). Gas 0.60 kg/m³ is about 1700 times less dense than the liquid, so the average spacing is about (1700)1/3 ≈ 12 times larger.
Cube X is made of a uniform material. Cube Y is made of a different uniform material, has the same mass as cube X, and has sides twice as long as those of cube X. The density of cube Y is how many times the density of cube X?
Answer and reasoning
A0.125Correct Density is ρ = m/V. Doubling every side multiplies the volume by 2³ = 8, and the mass is the same, so cube Y's density is 1/8 = 0.125 times cube X's.
B0.500 A student who thinks that doubling the sides doubles the volume gets 1/2. Volume depends on three lengths, so it grows by 2 × 2 × 2 = 8, and the density is 1/8 as large.
C1.000 A student who judges density by mass alone reasons that equal masses mean equal densities. Density is mass per unit volume; cube Y spreads the same mass over 8 times the volume, so it is much less dense.
D8.000 A student who takes density to be volume divided by mass finds that cube Y's 'density' is 8 times larger. Density is mass divided by volume, so a larger volume for the same mass means a smaller density: 1/8, not 8.
Working ρ = m/V. Same mass; VY = (2s)³ = 8s³ = 8VX. So ρY/ρX = (m/8VX)/(m/VX) = 1/8 = 0.125.
Three solid blocks have these masses and volumes. Block A: 6.0 kg and 2.0 × 10⁻³ m³. Block B: 4.0 kg and 4.0 × 10⁻³ m³. Block C: 3.0 kg and 1.5 × 10⁻³ m³. Which ranks the densities of the blocks from greatest to least?
Answer and reasoning
AρA > ρB > ρC A student who ranks the blocks by mass (6.0, 4.0, 3.0 kg) picks this. Block B has more mass than C but spreads it over more than twice the volume, so it is the least dense.
BρB > ρA > ρC A student who judges density by size ranks the blocks by volume (4.0, 2.0, 1.5 × 10⁻³ m³). The largest block, B, has the least mass per cubic meter: 1.0 × 10³ kg/m³.
CρA > ρC > ρBCorrect Dividing mass by volume: ρA = 3.0 × 10³ kg/m³, ρC = 2.0 × 10³ kg/m³ and ρB = 1.0 × 10³ kg/m³, so ρA > ρC > ρB.
DρB > ρC > ρA A student who divides volume by mass gets B highest and A lowest, the exact reverse of the correct order. Density is mass divided by volume, which puts A first.
Two identical syringes are sealed at the tip. One is completely filled with 20 cm³ of water and the other with 20 cm³ of air. A student pushes on each plunger with a force F and measures the volume V of the fluid inside. The graph shows the results. Which claim is supported by the graph?
Answer and reasoning
AOnly the water is a fluid, since a fluid must keep a fixed volume when it is pushed on. A student who thinks a fluid must have a fixed volume, as a liquid does, picks this. Air has no fixed shape and takes the shape of the syringe, so it is a fluid even though its volume changes.
BThe water is acting as a solid here, since its volume does not change when it is pushed. A student who thinks 'incompressible' means 'rigid' picks this. Keeping a constant volume under pressure does not make the water a solid: it still has no fixed shape and would flow out if the tip were opened.
CThe air's density decreases as it is pushed, since its volume decreases. A student who takes density to be volume divided by mass picks this. Density is mass divided by volume; the air's mass stays the same while its volume falls, so its density increases.
DOver this range the water can be modeled as incompressible, but the air cannot.Correct The water's volume stays at 20 cm³ however hard the plunger is pushed, so its volume and density do not change: it behaves as an incompressible fluid, as the ideal-fluid model assumes. The air's volume falls to about a third of its starting value, so air is clearly compressible.
Working Water: V stays at 20 cm³ for F from 0 to 40 N, so its volume (and hence its density m/V) does not change as it is pushed: incompressible over this range. Air: V falls from 20 cm³ to about 6.7 cm³, so it is compressed and its density m/V rises about threefold. Both are fluids (both take the shape of the syringe).
Equal masses of two liquids, one of density ρ and the other of density 3ρ, are poured into a container and mix completely. Assume that the volume of the mixture equals the sum of the volumes of the two liquids. Which expression gives the density of the mixture?
Answer and reasoning
A1.50ρCorrect With mass m of each liquid, the volumes are m/ρ and m/(3ρ), so the mixture has mass 2m and volume 4m/(3ρ). Its density is 2m ÷ 4m/(3ρ) = 1.50ρ, between the two densities and closer to ρ, because the less dense liquid takes up three-quarters of the volume.
B2.00ρ A student who averages the two densities picks this. The simple average is right only for equal volumes. Equal masses of the two liquids have different volumes: the less dense liquid takes up three times the space, so it counts for more, and the mixture's density is 1.50ρ.
C4.00ρ A student who treats density as an amount that adds up, like mass, picks this. The masses and the volumes add, and the density of the mixture, total mass over total volume, lies between ρ and 3ρ, not above both.
D0.75ρ A student who divides the mass of one liquid, m, by the combined volume, 4m/(3ρ), gets 0.75ρ, less than the density of either liquid. The mixture contains both liquids, so its mass is 2m; a density below that of both liquids is a sign that a mass has been left out. The mixture's density is 1.50ρ.
Working Let each liquid have mass m. Volumes: V₁ = m/ρ and V₂ = m/(3ρ). Mixture: mass 2m, volume m/ρ + m/(3ρ) = 4m/(3ρ). Density = 2m ÷ 4m/(3ρ) = (3/2)ρ = 1.50ρ.
Compiled from the AP Physics 1 Course and Exam Description (effective Fall 2024, 2026 reissue) and our question bank · Specialist review in progress. How these pages are made · Free, no account
