Weight, Mass and Gravity — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions

Section 1 of 11Mass and inertia

1Mass2 points

• the amount of matter in an object, measured in kilograms.
• It is a scalar and it stays the same on the Earth, on the Moon or in space.

2Inertia2 points

• the tendency of an object to stay at rest or to continue in uniform motion in a straight line unless a force acts.
• Mass is a measure of inertia, so a larger mass is harder to accelerate or to stop.

3Everyday examples of inertia2 points

• passengers lurch forward when a bus brakes suddenly because their bodies tend to keep moving.
• A heavy lorry needs a larger force and a longer distance to stop than a small car at the same speed.

4Resistance to change in motion2 points

• the greater the mass, the smaller the acceleration produced by the same force.
• This is the link to the equation F = ma used in the forces topic.

Section 2 of 11Weight and gravitational field strength

• Weight
  • the force of gravity acting on an object's mass, measured in newtons.
  • It is a vector that points downward toward the centre of the Earth.
• Gravitational field
  • a region in which a mass experiences a force because of another mass.
• Gravitational field strength g
  • the force per unit mass on an object in a gravitational field, in newtons per kilogram (N/kg).
  • On the Earth's surface g is about 9.8 N/kg, which is the same as an acceleration of free fall of 9.8 m/s².
  • g is larger near massive bodies and smaller near light bodies.
• Equation
  • weight = mass × gravitational field strength, or W = mg.
• Linking the units
  • N/kg and m/s² are equivalent because 1 N = 1 kg m/s².

Place	Approximate g (N/kg)
Earth	9.8
Moon	1.6
Mars	3.7
Jupiter	25

Section 3 of 11Mass compared with weight

Mass	Weight
Amount of matter in an object	Force of gravity on the object
Scalar quantity	Vector quantity, directed downward
Unit: kilogram (kg)	Unit: newton (N)
Does not change with location	Changes with the gravitational field strength
Measured with a balance	Measured with a newtonmeter (spring balance)

• Astronaut example
  • an astronaut of mass 80 kg has a weight of 784 N on Earth and about 128 N on the Moon.
  • The mass is still 80 kg on the Moon, but the downward pull is much weaker.
• Weightlessness
  • in orbit the astronaut seems weightless because the astronaut and the spacecraft are both in free fall, not because gravity is absent.
• Dependence on distance
  • g falls as the distance from the centre of the Earth increases, so weight is slightly smaller at the top of a mountain.

Section 4 of 11Measuring mass and weight

• Top-pan balance
  • it measures mass by comparing the pull of gravity on the object with an internal force,
  • so it gives the same reading anywhere in the same field.
• Beam balance
  • it compares the mass of an object with known masses; it would balance on the Moon as well as on the Earth.
• Newtonmeter (spring balance)
  • it measures the weight of an object by the extension of a spring.
  • On the Moon it would show a smaller reading for the same object.
• Finding weight experimentally
  • hang masses from a newtonmeter and plot a graph of weight against mass.

1. Hang a 100 g mass on the newtonmeter and record the reading in newtons.
2. Add further masses in steps of 100 g and record each reading.
3. Plot weight (vertical) against mass (horizontal).
4. Draw a straight line through the origin, and find its gradient.
5. The gradient is the gravitational field strength, about 9.8 N/kg.

• Comparing masses
  • a balance is used to compare masses because the effect of gravity cancels out on each side.

Section 5 of 11Centre of gravity and gravity's effects

• Centre of gravity
  • the point at which the whole weight of an object seems to act.
  • For a uniform regular object it is at the geometric centre.
• Finding the centre of gravity of a flat lamina
  • use a plumb line.

1. Make three small holes near the edge of the card.
2. Hang the card from a pin through one hole so it swings freely.
3. Hang a plumb line from the same pin and draw the vertical line on the card.
4. Repeat from the other holes.
5. The lines cross at the centre of gravity.

• Falling objects
  • gravity gives all objects the same acceleration in the absence of air, even though heavier objects have larger weights.
  • A heavier object has more inertia, which cancels the larger weight, so both fall at 9.8 m/s².
• Projectiles and planets
  • gravity is the force that keeps the Moon in orbit and gives weight to everything on a planet.

Section 6 of 11Using W = mg in calculations

• Finding weight
  • multiply the mass in kg by g in N/kg.
• Finding mass
  • divide the weight by g, m = W ÷ g.
• Finding g
  • divide the weight by the mass, g = W ÷ m.

1. Write the known values with units.
2. Convert grams into kilograms before calculating.
3. Substitute into W = mg.
4. Give the answer in newtons, kilograms or N/kg.

• Link with other topics
  • weight is the force used in work done lifting and in gravitational potential energy mgh.

Section 7 of 11Gravity on other bodies and in orbit

1Why g differs between bodies2 points

• g depends on the mass of the body and its radius, so a small, low-mass body has a weak field.
• The Moon has about one-sixth of the Earth's gravitational field strength, so a person could jump about six times higher there.

2Weight in different places2 points

• the same mass has different weights on different planets, found by multiplying by the local g.
• A 50 kg student weighs 490 N on Earth, 80 N on the Moon and 1250 N on Jupiter.

3Orbits2 points

• gravity provides the pull that keeps the Moon moving around the Earth and the planets moving around the Sun.
• Without gravity these bodies would move off in straight lines because of their inertia.

4Apparent weight2 points

• a lift accelerating upward makes a scale read more than mg, while free fall makes the reading drop to zero.
• True weight, the force of gravity, has not changed in either case.

5Measuring mass in space2 points

• astronauts use a spring-and-oscillation method because a weighing scale would read zero.
• A larger mass oscillates more slowly on the same spring, showing mass is linked to inertia.

Section 8 of 11Comparing masses and measuring with balances and force meters

• Mass of an object at rest
  • mass is a measure of the quantity of matter in the object, measured when the object is at rest relative to the observer.
• Inertia
  • an object's mass resists any change from its state of rest or motion.
  • This resistance is why a heavier trolley is harder to start and harder to stop.
• Beam or equal-arm balance
  • it compares the weights of two objects, and because the same g acts on both pans, it also compares their masses.
  • When the beam is level, the unknown mass equals the standard masses on the other pan.
• Electronic balance
  • follow the steps to find a mass.

1. Place the balance on a level surface and switch it on.
2. Press the zero (tare) button so it reads 0.00 g with the container on it.
3. Place the object on the pan and wait for a steady reading.
4. Record the reading with its unit.

• Force meter
  • hang the object from the hook and read the scale where the pointer stops, which gives the weight in newtons.
  • Hold the force meter vertically and read it with your eye level with the pointer to avoid parallax.
• Gravitational field as a vector
  • g has a direction, toward the centre of the planet, so it is a vector like weight.

Section 9 of 11Worked examples

1. Calculate the weight on Earth of a 6.5 kg bag of sugar (g = 9.8 N/kg). [2]2 marks

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2. An astronaut has a weight of 980 N on Earth. Find her mass, and her weight on the Moon where g = 1.6 N/kg. [4]4 marks

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3. A newtonmeter reads 4.5 N when a block is hung from it on a planet where g = 3.0 N/kg. Calculate the mass of the block. [3]3 marks

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4. A student plots weight against mass and finds a straight line through (0.20 kg, 1.96 N) and (0.50 kg, 4.90 N). Find the gradient and say what it represents. [3]3 marks

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5. Explain why a beam balance gives the same mass reading on the Moon but a newtonmeter does not. [3]3 marks

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6. An equal-arm balance is level when a stone is on one pan and 250 g and 50 g masses are on the other pan. State the mass and the weight of the stone on Earth (g = 9.8 N/kg). [3]3 marks

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Section 10 of 11Key terms

Term	Meaning
Mass	The amount of matter in an object, measured in kg.
Weight	The force of gravity on an object, W = mg, in newtons.
Gravitational field strength	The force per unit mass in a gravitational field, in N/kg.
Inertia	The resistance of an object to a change in its state of motion.
Centre of gravity	The point where the whole weight of an object appears to act.
Newtonmeter	A spring balance used to measure force or weight in newtons.
Free fall	Falling with gravity as the only force acting on the object.

Section 11 of 11Exam technique

1. Using the words mass and weight interchangeably — mass is in kg and does not change, weight is a force in N.
2. Saying an astronaut in orbit has no weight — gravity still acts, but both astronaut and craft are in free fall.
3. Forgetting to convert grams to kilograms in W = mg — 250 g is 0.25 kg, giving a weight of about 2.5 N.
4. Thinking heavier objects always fall faster — without air resistance they all accelerate at 9.8 m/s².
5. Quoting g only as m/s² — it is also N/kg, which shows it is force per unit mass.