Mass and Weight

Section 1 of 11Mass and inertia

1Mass

• Mass 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.

2Inertia

• Inertia 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 inertia

• Everyday examples of inertia 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 motion

• Resistance to change in motion 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 and gravitational field strength

Weight

• 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

• Gravitational field a region in which a mass experiences a force because of another mass.

Gravitational field strength g

• 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

• 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

• 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

• 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

• 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

1Top-pan balance

• 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.

2Beam balance

• Beam balance it compares the mass of an object with known masses;
  • it would balance on the Moon as well as on the Earth.

3Newtonmeter (spring balance)

• 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.

4Finding weight experimentally

• 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

1Centre of gravity

• 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.

2Finding the centre of gravity of a flat lamina

• 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

• 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

• 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

• Finding weight multiply the mass in kg by g in N/kg.

Finding mass

• Finding mass divide the weight by g, m = W ÷ g.

Finding 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

Gravity on other bodies and in orbit

Why g differs between bodies

• Why g differs between bodies 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.

Weight in different places

• Weight in different places 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.

Orbits

• Orbits 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.

Apparent weight

• Apparent weight 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.

Measuring mass in space

• Measuring mass in space 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

1Mass of an object at rest

• 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.

2Inertia

• 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.

3Beam or equal-arm balance

• 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.

4Electronic balance

• 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.

1Force meter

• 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.

2Gravitational field as a vector

• 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.