Mass and weight

Key points

Mass

• Mass measures how much matter an object contains: its quantity of matter.
• The definition has a condition: the mass is measured with the object at rest relative to the observer (not moving compared with the person measuring it). Learn this condition as part of the definition.
• The unit of mass is the kilogram (kg).
• The mass of an object does not change when you take it to a different place. A 5 kg bag has a mass of 5 kg on the Earth and on the Moon.

Weight

• Weight is the gravitational force that acts on an object because it has mass.
• Weight is a force, so its unit is the newton (N).
• On the Earth, weight acts downwards, towards the centre of the Earth.
• The weight of an object does change from place to place, because the strength of gravity changes. On the Moon, a bag has the same mass as on the Earth, but a smaller weight.

Gravitational field strength, g

• Gravitational field strength, g, is the force per unit mass. It is the gravitational force on each kilogram.
• g = W / m. Rearranged: W = mg.
• The unit of g is N/kg.
• Near the Earth’s surface, g is about 9.8 N/kg. So each kilogram has a weight of about 9.8 N.
• Gravitational field strength is equivalent to the acceleration of free fall. The two have the same value: g = 9.8 N/kg and g = 9.8 m/s² near the Earth’s surface. 1 N/kg is the same as 1 m/s².

Comparing masses and weights

• A balance can compare the weights of two objects. A beam balance has two pans. The beam is level when the objects on the two pans have equal weights.
• Both pans are in the same place, so g is the same for both objects. Equal weights therefore mean equal masses. So a balance compares masses as well as weights.
• To measure a mass, balance the object against standard masses whose values are known.
• A newton meter (a spring balance marked in newtons) measures weight directly.

Weight and the gravitational field Extended

• A gravitational field is a region where a mass feels a force. Extended
• A gravitational field acts on any mass that is in it. The force that the field produces on the mass is its weight. So weight is how a gravitational field affects a mass. Extended
• The stronger the field, the bigger the weight of the same mass. The bigger the mass, the bigger its weight in the same field. Extended
• Why g is also the acceleration of free fall: if weight is the only force on an object, the resultant force F = W = mg. From F = ma (see 1.5), ma = mg, so a = g. Extended
• This is why all objects in free fall at the same place have the same acceleration, whatever their mass. A bigger mass has a bigger weight, but it also needs a bigger force for the same acceleration. Extended

Common mistakes

• Students give a weight in kilograms, for example “the bag weighs 8 kg”. / The mark scheme wants: weight is a force in newtons; mass is in kilograms.
• Students write that an object’s mass is smaller on the Moon. / The mark scheme wants: the mass stays the same; the weight is smaller because g is smaller on the Moon.
• Students define mass as “how heavy something is”. / The mark scheme wants: how much matter the object contains (its quantity of matter), measured with the object at rest relative to the observer.
• Students define gravitational field strength as “the pull of gravity”. / The mark scheme wants: force per unit mass.
• Students write that a beam balance gives a different mass on the Moon. / The mark scheme wants: both pans are in the same gravitational field, so the balance still compares masses correctly.
• Students write that heavier objects fall faster when there is no air resistance. / The mark scheme wants: all objects in free fall at the same place have the same acceleration, g. Extended

Exam tips

• State the definitions in a few words: mass = quantity of matter; weight = gravitational force on a mass; g = force per unit mass.
• Calculate with W = mg. Check that the mass is in kg before you start. Change grams to kilograms by dividing by 1000.
• When a question says “use g = 9.8 N/kg”, use that value. Show the substitution and give the unit.
• Explain a difference between the Earth and the Moon: say what stays the same (mass) and what changes (weight), and give the reason (g is different).
• Describe weight using the field: “weight is the force on a mass due to a gravitational field”. Extended
• A typical 1-mark answer: “Weight is the gravitational force acting on a mass.”
• A typical 2-mark answer to “An astronaut has a mass of 70 kg. What is the mass on the Moon, and why?”: “70 kg (1). Mass is the quantity of matter, which does not depend on where the astronaut is (1).”
• A typical 2-mark answer to “Why can a balance be used to compare masses?”: “The balance compares the weights of the two objects (1). g is the same for both, so equal weights mean equal masses (1).”
• A typical 2-mark answer to “Explain why g is the acceleration of free fall”: “In free fall, the only force is the weight, mg (1). F = ma, so ma = mg and a = g (1).” Extended