Mass and weight — answer key

1. DQ1 · Practice

Options as numbered on the pupil sheet: 1 — the amount of matter in the object; 2 — the gravitational force on the object; 3 — kilogram (kg); 4 — newton (N); 5 — metre (m).

Model answer. Mass → the amount of matter in the object; weight → the gravitational force on the object; unit of mass → kilogram (kg); unit of weight → newton (N).

A full answer includes

• Mass: the amount of matter in an object, measured in kilograms (kg).
• Weight: the gravitational force on an object, measured in newtons (N).

Also accept

• mass – amount of matter – kg; weight – gravitational force – N.

Watch for

• “Weight is measured in kilograms.” — In everyday speech, yes. In physics weight is a force, so it is measured in newtons; kilograms measure mass.
• “Mass is how heavy something feels.” — How heavy something feels is the pull on it, its weight. Mass is the amount of matter, which stays the same on the Moon.

2. DQ2 · Practice

Model answer. W = m × g = 2.4 kg × 9.8 N/kg = 23.52 N, so 24 N to 2 significant figures.

Checked automatically

• Weight of the bag on Earth: 24 N (2 significant figures)
  • Common wrong answer 0.24 : You divided the mass by g. Each kilogram is pulled with 9.8 N, so multiply: 2.4 × 9.8.
  • Common wrong answer 4.1 : You divided g by the mass. Weight = mass × g: 2.4 × 9.8.
  • Common wrong answer 2.4 : That is the mass in kilograms. Weight is a force: multiply by g = 9.8 N/kg.

A full answer includes

• I used W = m × g: 2.4 kg × 9.8 N/kg.
• I gave 24 N, with the unit newtons.

Also accept

• 24 N (23.5 N before rounding).

Watch for

• “The weight is 2.4 kg.” — 2.4 kg is the mass. Weight is a force: multiply the mass by g to get newtons.
• “Divide: 2.4 ÷ 9.8 = 0.24 N.” — Each kilogram is pulled with 9.8 N, so 2.4 kg is pulled with 2.4 times as much: multiply.

3. DQ3 · Practice

Model answer. a. On the Moon the sugar and the 1 kg mass are both pulled about six times less strongly. Their weights are still equal, so the beam stays level. The balance compares masses the same way on any world.

A full answer includes

• I chose a: it still balances.
• I explained that both weights fall by the same amount, because both pans are in the same gravitational field, so the beam stays level.

Also accept

• a; both weights change by the same factor, so it still balances.

Watch for

• “The sugar side rises, because things weigh less on the Moon.” — Things weigh less on the Moon, but the 1 kg mass on the other pan weighs less too, by the same amount. The weights stay equal.
• “A balance cannot work without Earth’s gravity.” — The Moon has a gravitational field too. A balance needs a pull on both pans; it does not need it to be Earth’s.

4. DQ7 · Practice

Model answer. (1) field; (2) weight; (3) field strength; (4) weight. A gravitational field pulls on any mass in it; that pull is the weight, and the pull per kilogram is the field strength g.

A full answer includes

• (1) field
• (2) weight
• (3) field strength
• (4) weight

Also accept

• field; weight; field strength; weight.

Watch for

• “(4) mass” — The mass stays the same in a weaker field. What becomes smaller is the pull on it, the weight.
• “(1) force” — The region round the Earth is a field. The force is what a mass feels in that field.

5. DQ4 · Practice

Model answer. (a) 75 kg: the amount of matter is the same. (b) W = m × g = 75 kg × 1.6 N/kg = 120 N. The mass stays because nothing is added or removed; the weight is smaller because the Moon’s gravitational field pulls each kilogram with only 1.6 N.

Checked automatically

• (a) Mass on the Moon: 75 kg (within ±0.5 kg)
  • Common wrong answer 12.5 : Mass does not change on the Moon: the same matter makes up the astronaut and suit.
• (b) Weight on the Moon: 120 N (within ±2%)
  • Common wrong answer 735 : That is the weight on Earth (g = 9.8 N/kg). Use the Moon’s g, 1.6 N/kg.
  • Common wrong answer 47 : You divided the mass by g. Multiply: W = m × g.

A full answer includes

• (a) I gave the mass as 75 kg, the same as on Earth.
• (b) I calculated W = 75 kg × 1.6 N/kg = 120 N.
• I explained that mass is the amount of matter, which does not change, while weight is the pull of the gravitational field, which is weaker on the Moon.

Also accept

• (a) 75 kg; (b) 120 N; mass is unchanged, weight depends on the field.

Watch for

• “The mass on the Moon is 75 ÷ 6 = 12.5 kg.” — The astronaut is made of the same matter on the Moon. It is the weight that becomes about a sixth.
• “The weight on the Moon is 75 × 9.8 = 735 N.” — 735 N is the weight on Earth. On the Moon use the Moon’s g, 1.6 N/kg.

6. DQ5 · Practice

Model answer. b. Falling freely, it gains 9.8 m/s of speed every second: its acceleration is 9.8 m/s². This is the same number as g = 9.8 N/kg, because the gravitational field strength equals the acceleration of free fall.

A full answer includes

• I chose b: its speed increases by 9.8 m/s every second.
• I linked this to g: the gravitational field strength, 9.8 N/kg, equals the acceleration of free fall, 9.8 m/s².

Also accept

• b; acceleration of free fall = g = 9.8 m/s².

Watch for

• “It falls at a steady speed.” — A falling stone speeds up. Only air resistance, which we are ignoring here, could stop it gaining speed.
• “A heavier stone speeds up faster.” — Without air resistance every object falls with the same acceleration, 9.8 m/s², whatever its mass.

7. DQ6 · Practice

Model answer. g = W ÷ m = 18.5 N ÷ 5.0 kg = 3.7 N/kg.

Checked automatically

• Gravitational field strength on Mars: 3.7 N/kg (2 significant figures)
  • Common wrong answer 0.27 : You divided the mass by the weight. g = W ÷ m: 18.5 ÷ 5.0.
  • Common wrong answer 92.5 : You multiplied. g is force per kilogram: 18.5 N ÷ 5.0 kg.

A full answer includes

• I used g = W ÷ m = 18.5 N ÷ 5.0 kg.
• I gave 3.7 N/kg, with the unit newtons per kilogram (3.7 m/s² is the same quantity).

Also accept

• 3.7 N/kg.

Watch for

• “g = 5.0 ÷ 18.5 = 0.27.” — That is mass ÷ weight. Gravitational field strength is force per unit mass: weight ÷ mass.
• “g = 18.5 × 5.0 = 92.5 N/kg.” — Multiplying gives a far stronger field than Earth’s. Share the 18.5 N between the 5.0 kg: divide.

8. DQ8 · Practice

Model answer. c. The pan with X is pulled down harder, so X has the bigger weight. Both pans are in the same field, where weight = mass × the same g, so X also has the bigger mass.

A full answer includes

• I chose c: X has the bigger weight and the bigger mass.
• I explained that both parcels are in the same gravitational field, so the bigger weight belongs to the bigger mass.

Also accept

• c; same g on both pans, so bigger weight means bigger mass.

Watch for

• “X has the bigger weight but you cannot tell about mass.” — Both parcels are in the same field with the same g. Weight = mass × g, so the bigger weight must come with the bigger mass.
• “X is bigger in size.” — A balance compares weights, not sizes. A small lump of lead can outweigh a big box of feathers.

9. DT1 · Apply

Model answer. (a) 800 kg. (b) g = W ÷ m = 19 800 N ÷ 800 kg = 24.75 N/kg, so 25 N/kg. Every kilogram of the probe is pulled with about 25 N, about 2.5 times the pull on Earth (9.8 N/kg). (c) About 25 m/s², because the acceleration of free fall is equal to g there.

Checked automatically

• (a) Mass near Jupiter: 800 kg (within ±1 kg)
  • Common wrong answer 2020 : The probe’s mass does not change near Jupiter. 2020 is what a balance calibrated for Earth would show.
• (b) Gravitational field strength near Jupiter: 25 N/kg (2 significant figures)
  • Common wrong answer 0.040 : You divided the mass by the force. g = W ÷ m.
• (c) Acceleration of the falling part: 25 m/s2 (2 significant figures)
  • Common wrong answer 9.8 : 9.8 m/s² is the acceleration of free fall on Earth. Near Jupiter it equals g there, the value you found in (b).

A full answer includes

• (a) I gave 800 kg: the mass is the same.
• (b) I calculated g = 19 800 N ÷ 800 kg = 24.75, so 25 N/kg.
• I said that each kilogram is pulled with about 25 N, about two and a half times as hard as on Earth.
• (c) About 25 m/s²: the acceleration of free fall equals the gravitational field strength there.

Also accept

• (a) 800 kg; (b) 25 N/kg; each kg pulled with 25 N; (c) 25 m/s².

Watch for

• “The probe’s mass near Jupiter is 19 800 ÷ 9.8 = 2020 kg.” — Dividing by Earth’s g gives what a balance set up for Earth would wrongly show. The mass is still 800 kg; the field is stronger.
• “g = 800 ÷ 19 800 = 0.040.” — That is mass ÷ force. Field strength is force per kilogram: 19 800 ÷ 800.

10. DT2 · Apply

Model answer. (a) Yes. On Mars the rice and the standard masses are both pulled with 3.7 N/kg, so the beam is level only when their masses are equal. (b) No. The spring stretches by the weight, which on Mars is about 0.38 of its Earth value, so a scale marked on Earth shows about 0.38 of the true mass: customers would be given far too much rice.

A full answer includes

• (a) I said yes: the rice and the standard masses are in the same field, so equal weights still mean equal masses.
• (b) I said no: the spring balance measures the weight, which on Mars is only about 3.7/9.8 of Earth’s, so its kilogram scale shows too little.
• I gave the reason in terms of the gravitational field being weaker on Mars.

Also accept

• (a) yes, same g on both sides; (b) no, it shows about 0.38 of the mass.

Watch for

• “Neither works on Mars because gravity is different.” — The equal-arm balance compares two things in the same field, so the different g affects both pans equally.
• “The spring balance shows too much on Mars.” — The pull on Mars is weaker, so the spring stretches less and the reading is too small.