Cambridge IGCSE0625

Mass and weight

Physics 0625 Chapter Notes

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Mass and weight
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In this chapter

  1. 1What is Mass?
  2. 2The Concept of Weight
  3. 3The Mass-Weight Relationship
  4. 4Mass vs. Weight: A Comparison

1. What is Mass?

Mass is the measure of the amount of 'stuff' or matter an object contains. It's a fundamental property of an object that has two important effects. Firstly, it's what causes the force of gravity – all objects with mass attract each other. Secondly, mass is a measure of an object's inertia, which is its resistance to changing its state of motion. The more mass an object has, the harder it is to start it moving, stop it, or change its direction. The SI unit for mass is the kilogram (kg). Crucially, an object's mass is the same everywhere in the universe.

Key term

Mass: The measure of the amount of matter in an object, which also determines its inertia and the strength of the gravitational force it experiences.

Examiner insight

Examiners reward students who can clearly define mass as the 'quantity of matter' and correctly state its SI unit, the kilogram (kg).

Common pitfall

Stating that mass is measured in grams in an exam. While grams are commonly used, the base SI unit for physics calculations is the kilogram (kg).

Fun fact

The official definition of a kilogram is no longer based on a physical block of metal in Paris; it's now defined by a fundamental constant of nature called the Planck constant.

Worked example 13 marks

An astronaut is floating in the zero-gravity environment of space. She pushes a large satellite and a small toolkit with an identical force. Which object accelerates more, and why?

  1. 1

    The toolkit will accelerate more.

  2. 2

    According to Newton's second law (F=ma), acceleration is inversely proportional to mass (a = F/m) for a constant force.

  3. 3

    The toolkit has a much smaller mass than the satellite.

  4. 4

    Therefore, for the same applied force, the object with the smaller mass (the toolkit) will experience a greater acceleration.

Recap

  • Mass is the amount of matter in an object.
  • The SI unit for mass is the kilogram (kg).
  • Mass is a measure of inertia, an object's resistance to changing its motion.
  • An object's mass is constant and does not change with location.

Quick check

  1. What is the SI base unit for mass?1 mark
  2. Which property of an object describes its resistance to a change in its state of motion?1 mark

2. The Concept of Weight

Weight is the force of gravity acting on a mass. It is not the same as mass. Because it is a force, it is measured in newtons (N). Your weight is the result of the Earth's gravitational field pulling down on the mass of your body. If you were on the Moon, which has a weaker gravitational field, your weight would be less, even though your mass remains unchanged. Weight is a vector quantity, meaning it has both a magnitude (how strong the force is) and a direction (always acting towards the centre of the planet or moon).

Key term

Weight: The gravitational force exerted on an object due to its mass, measured in newtons (N).

Examiner insight

Marks are often awarded for clearly identifying weight as a type of force and stating its unit as the newton (N).

Common pitfall

Using 'grams' or 'kilograms' as the unit for weight. This is a very common mistake and will always lose marks in an exam.

Fun fact

You are technically lighter at the top of a tall mountain than at sea level because you are slightly further from the Earth's centre, which weakens the gravitational pull.

Worked example 12 marks

A student says, 'I weigh 60 kilograms'. Explain why this statement is scientifically incorrect.

  1. 1

    The statement is incorrect because it confuses weight with mass.

  2. 2

    Kilograms (kg) are the unit of mass, which is the amount of matter in an object.

  3. 3

    Weight is a force, caused by gravity, and is measured in newtons (N).

  4. 4

    The correct statement would be 'I have a mass of 60 kilograms'.

Recap

  • Weight is the force of gravity acting on an object.
  • The unit for weight (and all forces) is the newton (N).
  • Weight is a vector quantity that always acts towards the centre of a large mass like a planet.
  • An object's weight depends on its location in a gravitational field.

Quick check

  1. What is the name of the force caused by gravity acting on a mass?1 mark
  2. What is the correct scientific unit of weight?1 mark

3. The Mass-Weight Relationship

The weight of an object is directly proportional to its mass. This relationship is defined by the gravitational field strength of the location. Gravitational field strength, represented by the symbol 'g', is the force experienced per unit mass. On Earth, its value is approximately 10 newtons per kilogram (10 N/kg). This means that for every 1 kg of mass, the Earth pulls on it with a force of 10 N. The relationship is summarised by the crucial formula: Weight = mass × gravitational field strength.

W = m × g

Key term

Gravitational Field Strength (g): The force exerted per unit mass on an object placed in a gravitational field, measured in newtons per kilogram (N/kg).

Examiner insight

Examiners expect you to write down the formula (W=mg), show your substitution, and give a final answer with the correct unit (N) to secure all marks in a calculation.

Common pitfall

Forgetting to convert mass from grams to kilograms before using the W = mg formula. For example, using '500' for 500g instead of '0.5' for 0.5 kg.

Worked example 12 marks

A bag of flour has a mass of 1.5 kg. Calculate its weight on Earth, where the gravitational field strength(g) is 10 N/kg.

  1. 1

    State the formula: W = m × g

  2. 2

    Substitute the known values: W = 1.5 kg × 10 N/kg

  3. 3

    Calculate the result: W = 15 N

Worked example 23 marks

An object has a weight of 120 N on a planet where the gravitational field strength is 8 N/kg. What is the mass of the object?

  1. 1

    State the formula: W = m × g

  2. 2

    Rearrange the formula to make mass the subject: m = W / g

  3. 3

    Substitute the known values: m = 120 N / 8 N/kg

  4. 4

    Calculate the result: m = 15 kg

Recap

  • The formula linking weight and mass is W = m × g.
  • 'g' represents the gravitational field strength, measured in N/kg.
  • For calculations on Earth, use g = 10 N/kg unless told otherwise.
  • Always convert mass to kilograms (kg) before using the formula.
  • Always ensure weight is in newtons (N) when using the formula.

Quick check

  1. An apple has a mass of 200 g. What is its weight in newtons? (Use g = 10 N/kg)2 marks
  2. What does the symbol 'g' represent in the equation W = mg and what are its units?2 marks

4. Mass vs. Weight: A Comparison

It is vital to understand the differences between mass and weight. An object's mass is a measure of the matter within it and is constant everywhere. A 60 kg astronaut has a mass of 60 kg on Earth, on the Moon, and in deep space. However, weight is the force of gravity on that mass, so it changes with location. On Earth (g ≈ 10 N/kg), the astronaut's weight is 60 kg × 10 N/kg = 600 N. On the Moon (g ≈ 1.6 N/kg), their weight is only 60 kg × 1.6 N/kg = 96 N. In deep space, far from any gravitational field, their weight would be zero, but their mass would still be 60 kg. Mass is measured in kilograms (kg) using a beam balance or top-pan balance, which compares an unknown mass to known masses. Weight is measured in newtons (N) using a newton meter (or spring balance), which measures the extent a spring is stretched by a force.

W_Earth = m × g_Earth

W_Moon = m × g_Moon

Key term

Newton Meter: A device used to measure force, consisting of a spring of known stiffness which extends in proportion to the applied force; it is used to measure weight.

Examiner insight

Questions comparing mass and weight are very common. A full-mark answer will compare their definitions, units, the instruments used to measure them, and whether they are constant or variable.

Common pitfall

Thinking that an object becomes 'lighter' on the Moon because it loses mass. The mass is constant; only the gravitational force (weight) changes.

Fun fact

On Jupiter, where g ≈ 25 N/kg, a person with a mass of 70 kg would weigh 1750 N. On Earth, they only weigh 700 N. This is like having an extra one and a half of you sitting on your shoulders!

Worked example 13 marks

An astronaut has a total mass of 120 kg (including her suit). The gravitational field strength on Mars is 3.7 N/kg.(a) What is the astronaut's mass on Mars?(b) What is the astronaut's weight on Mars?

  1. 1

    (a) Mass is the amount of matter and is constant regardless of location. The astronaut's mass on Mars is still 120 kg.

  2. 2

    (b) State the formula for weight: W = m × g

  3. 3

    Substitute the values for Mars: W = 120 kg × 3.7 N/kg

  4. 4

    Calculate the result: W = 444 N

Worked example 22 marks

State two differences between mass and weight.

  1. 1

    Difference 1: Mass is the amount of matter in an object, measured in kg. Weight is the force of gravity on an object, measured in N.

  2. 2

    Difference 2: Mass is constant everywhere. Weight depends on the local gravitational field strength.

Recap

  • Mass is a scalar quantity (kg); weight is a vector quantity (N).
  • Mass is constant everywhere; weight changes with location.
  • Mass is measured with a balance; weight is measured with a newton meter.
  • An object in deep space has mass but has zero weight.

Quick check

  1. An object has a mass of 25 kg on Earth. What is its mass on Jupiter?1 mark
  2. Does a beam balance fundamentally measure mass or weight?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define mass and state its SI unit.2 marks
  2. A bowling ball has a mass of 7 kg. Calculate its weight on Earth. (Use g = 10 N/kg)2 marks
  3. Explain the key differences between mass and weight. You should refer to their definitions, units, and how they are affected by a change in location.4 marks
  4. A rock has a weight of 72 N on a planet where the gravitational field strength is 12 N/kg. (a) Calculate the mass of the rock. (b) The rock is taken to Earth (g = 10 N/kg). What is its new weight?4 marks
  5. A top-pan balance and a newton meter are taken to the Moon, where gravity is weaker. An object is placed on each instrument. Describe and explain what would be observed on the reading of each instrument compared to the readings for the same object on Earth.4 marks
  6. A block of aluminium has a volume of 0.05 m³ and a density of 2700 kg/m³. Calculate the weight of the block on Earth. (Use g = 10 N/kg)3 marks
  7. An astronaut has a mass of 80 kg. On a mission, she wears a spacesuit and backpack with a combined mass of 65 kg. The spacecraft lands on a moon where the gravitational field strength is 2.0 N/kg. Calculate the total weight of the fully-equipped astronaut on this moon.3 marks
  8. A space probe has a weight of 4900 N on Earth (g = 10 N/kg). It lands on an asteroid where its weight is measured to be only 9.8 N. (a) Calculate the mass of the probe. (b) Calculate the gravitational field strength on the surface of the asteroid.4 marks
  9. A person looking at their bathroom scales says, 'My weight is 75 kg'. (a) Correct this statement, explaining the scientific error. (b) Calculate the person's actual weight in newtons. (Use g = 10 N/kg)3 marks
  10. On Earth, a hammer falls to the ground much faster than a feather. On the Moon, where there is no air, they fall at the same rate. Explain these observations, referring to weight and one other force.3 marks

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