Float or sink — answer key

1. DQ16 · Practice

Model answer. a, b and d. Cork (0.24), candle wax (0.90) and oak (0.75 g/cm³) are less dense than water, so they float. Glass (2.5) and aluminium (2.7 g/cm³) are denser, so they sink.

A full answer includes

• I chose a, b and d: cork, candle wax and oak, each less dense than water.
• I left out glass and aluminium, which are denser than water.

Also accept

• a, b, d.

Watch for

• “The small aluminium washer is light, so it floats.” — A small piece of aluminium is light, but every cubic centimetre of it has 2.7 g: more than water’s 1.00 g. It sinks.
• “Candle wax at 0.90 is too close to 1.00 to float.” — Any density below water’s floats. Wax floats low in the water, but it floats.

2. DQ17 · Practice

Options as numbered on the pupil sheet: 1 — liquid P; 2 — water; 3 — liquid Q.

Model answer. Top: Q (0.80 g/cm³); middle: water (1.00 g/cm³); bottom: P (1.60 g/cm³). Liquids that do not mix settle with the least dense on top.

A full answer includes

• Bottom: P (the densest).
• Middle: water.
• Top: Q (the least dense).

Also accept

• top Q, middle water, bottom P.

Watch for

• “They settle in the order they are poured.” — Whatever the order of pouring, the denser liquid sinks through the less dense one until the layers are in order of density.
• “P floats on top because its number is biggest.” — A bigger density means more mass in each cubic centimetre, so P sinks to the bottom.

3. DQ18 · Practice

Model answer. (a) ρ = 120 g ÷ 150 cm³ = 0.80 g/cm³. (b) It floats: its density is less than water’s 1.00 g/cm³.

Checked automatically

• (a) Density of the toy: 0.80 g/cm³ (2 significant figures)
  • Common wrong answer 1.25 : You divided the volume by the mass. Density = mass ÷ volume: 120 ÷ 150.

A full answer includes

• (a) 120 g ÷ 150 cm³ = 0.80 g/cm³.
• (b) It floats, because 0.80 g/cm³ is less than water’s 1.00 g/cm³.

Also accept

• (a) 0.80 g/cm³; (b) floats, less dense than water.

Watch for

• “It sinks because 120 g is heavy.” — Mass alone doesn’t decide. Its density, 0.80 g/cm³, is less than water’s, so it floats.
• “Density = 150 ÷ 120 = 1.25, so it sinks.” — That is volume ÷ mass. Density = mass ÷ volume = 0.80 g/cm³.

4. DQ19 · Practice

Model answer. a. It floats on the mercury, because its density, 7.9 g/cm³, is less than mercury’s, 13.6 g/cm³. Steel sinks in water but floats in mercury: what matters is the comparison with the liquid it is in.

A full answer includes

• I chose a: it floats.
• I explained that steel (7.9 g/cm³) is less dense than mercury (13.6 g/cm³).

Also accept

• a; steel is less dense than mercury.

Watch for

• “It sinks, because steel always sinks.” — Steel sinks in water because water is less dense than steel. Mercury is denser than steel.
• “It sinks, because a metal can’t float on a metal.” — Floating depends only on the densities: 7.9 is less than 13.6.

5. DQ20 · Practice

Model answer. c. At 0.95 g/cm³ the bead is denser than the oil (0.92), so it sinks through the oil; it is less dense than the water (1.00), so it floats on the water. It stops at the boundary between them.

A full answer includes

• I chose c: at the boundary between the oil and the water.
• I explained that the bead is denser than oil, so it sinks through the oil, but less dense than water, so it floats on the water.

Also accept

• c; denser than oil, less dense than water.

Watch for

• “It floats on top of the oil because it is plastic.” — Its density, 0.95 g/cm³, is more than the oil’s 0.92 g/cm³, so it sinks through the oil.
• “It sinks to the bottom because it sank through the oil.” — In the water the comparison changes: 0.95 is less than 1.00, so it floats on the water.

6. DQ21 · Practice

Model answer. Oil and sea water do not mix (they are immiscible), so they stay as separate liquids. The oil is less dense (0.88 g/cm³) than sea water (1.03 g/cm³), so it floats on top and spreads out as a layer.

A full answer includes

• I said the oil is less dense than sea water (0.88 < 1.03 g/cm³).
• I said oil and water do not mix (they are immiscible), so the less dense oil forms a layer on top.

Also accept

• less dense than sea water, and does not mix.

Watch for

• “The oil floats because there is less of it than sea.” — The amount doesn’t decide it: oil floats because each cubic centimetre of it has less mass than a cubic centimetre of sea water.
• “It floats because oil is lighter.” — Say what is compared: the density, mass per cubic centimetre. And add that the two liquids do not mix.

7. DT5 · Apply

Model answer. (a) The hull and tanks enclose a large volume of air. The whole submarine’s average density, its total mass ÷ its total volume, is less than the density of sea water, so it floats. (b) Sea water fills the tanks: the mass goes up but the outside volume does not change, so the average density becomes greater than the sea water’s and the submarine sinks. (c) Compressed air pushes the water out, the mass falls, the average density drops below the sea water’s and it rises.

A full answer includes

• (a) I said the submarine’s average density (total mass ÷ total volume) is less than the sea water’s, because most of its volume is air.
• (b) I said the water adds mass but the volume of the hull stays the same, so the average density rises above the sea water’s and it sinks.
• (c) I said that pushing the water out lowers its mass, so its average density falls below the sea water’s again and it rises.

Also accept

• (a) average density less than sea water’s; (b) more mass, same volume: denser, sinks; (c) less mass: less dense, rises.

Watch for

• “The submarine sinks because the water in its tanks is heavy.” — Mass alone does not decide. The water raises the submarine’s mass while its volume stays the same, so its average density rises above the sea water’s.
• “Steel always sinks, so a submarine needs engines to stay up.” — A submarine floats at the surface with its engines off. It is mostly air inside, so its average density is less than the sea water’s.

8. DT6 · Apply

Model answer. (a) Olive oil, at 0.91 g/cm³, is less dense than vinegar at 1.01 g/cm³. Shaking only breaks the oil into drops; because the liquids are immiscible, the drops rise and join into a layer on top. (b) Milk mixes with water. The density rule only predicts layers for liquids that do not mix; liquids that mix spread through each other instead.

A full answer includes

• (a) I said olive oil is on top, because it is less dense than vinegar and the two do not mix.
• (b) I said milk mixes with water, so they do not form separate layers; the rule only works for liquids that do not mix.

Also accept

• (a) olive oil on top; (b) milk and water mix.

Watch for

• “After shaking they stay mixed for good.” — Oil and vinegar do not mix: shaking makes drops, but the drops separate again and the oil rises.
• “Milk must sink because 1.03 is more than 1.00.” — The rule needs liquids that do not mix. Milk mixes with water, so it doesn’t settle as a layer.