Mass and weight Revision Notes

Mass is a measure of the amount of matter contained in an object. It quantifies how much substance the object has, regardless of its shape or volume.

Mass is a scalar quantity, meaning it has magnitude only and no direction. This contrasts with vector quantities like force, which have both magnitude and direction.

Mass remains constant for an object regardless of its location or motion relative to an observer. For example, an object’s mass is the same on Earth, in space, or on the Moon, and whether it is stationary or moving.

• Mass measures the amount of matter in an object.
• Mass is a scalar quantity (magnitude only).
• Mass is invariant with respect to the observer’s frame of reference.

The standard unit of mass in the International System of Units (SI) is the kilogram (kg). Other units such as grams (g) are also used, where 1 kg = 1000 g.

Mass can be measured using a balance scale, which compares an unknown mass to known standard masses. This method relies on comparing matter rather than forces, so it directly measures mass rather than weight.

Balances are designed so that the measurement is independent of local gravitational field strength, making them reliable for measuring mass anywhere.

• SI unit of mass: kilogram (kg).
• Mass measurement uses balance scales comparing matter.
• Mass measurement is independent of gravity.

Mass should not be confused with weight. Weight is the force exerted on a mass by gravity and depends on the local gravitational field strength.

Weight is a vector quantity measured in newtons (N) and calculated by the equation W = mg, where g is the gravitational field strength (approximately 9.8 m/s² near Earth's surface).

Mass remains constant regardless of location, but weight varies with gravitational field strength. For example, an object’s weight on the Moon is about one-sixth of its weight on Earth, but its mass is unchanged.

• Weight is a force, mass is amount of matter.
• Weight depends on gravitational field strength; mass does not.
• Weight units: newtons (N); mass units: kilograms (kg).

Mass is fundamental in physics because it determines an object's resistance to changes in motion (inertia) and its gravitational interaction with other masses.

In Newton’s second law, F = ma, mass (m) relates force (F) to acceleration (a), showing that greater mass requires greater force to achieve the same acceleration.

Mass is also important in conservation laws, such as conservation of mass in chemical reactions and conservation of mass-energy in physics.

• Mass determines inertia and gravitational interaction.
• Mass appears in Newton’s second law: F = ma.
• Mass is conserved in isolated systems.

To illustrate mass, draw a simple labelled diagram of an object (e.g., a block) with the label 'Mass (m) – amount of matter in object'.

Next to it, draw a balance scale with two pans: one pan holds the object, the other holds standard masses. Label the scale 'Measures mass by comparison of matter, independent of gravity'.

This diagram helps visualise that mass is a measure of matter, not weight or force.

• Draw object labelled with mass (m).
• Draw balance scale comparing object to standard masses.
• Label to emphasise mass measurement independent of gravity.

Weight is the force exerted on an object by the gravitational field of a planet or other celestial body. It acts vertically downwards towards the centre of the Earth (or other body).

Weight depends on the mass of the object and the strength of the gravitational field at the object's location.

Weight is a vector quantity because it has both magnitude and direction (towards the centre of gravity).

• Weight is the gravitational force on an object.
• It acts vertically downwards.
• Weight depends on mass and gravitational field strength.

Mass is the amount of matter in an object and is a scalar quantity measured in kilograms (kg).

Weight is a force measured in newtons (N). It is the effect of gravity acting on the mass.

Mass remains constant regardless of location, but weight can change depending on the gravitational field strength (for example, on the Moon or other planets).

• Mass is measured in kilograms (kg).
• Weight is measured in newtons (N).
• Mass is constant; weight varies with location.

The weight (W) of an object can be calculated using the formula:

W = m × g, where: m is the mass in kilograms (kg), g is the gravitational field strength in newtons per kilogram (N/kg), and W is the weight in newtons (N).

On Earth, g is approximately 9.8 N/kg (sometimes rounded to 9.81 N/kg). This means each kilogram of mass experiences a force of about 9.8 newtons due to gravity.

• W = mg (weight equals mass times gravitational field strength).
• g ≈ 9.8 N/kg on Earth.
• Weight is proportional to mass.

Calculate the weight of a 5 kg object on Earth, where g = 9.8 N/kg.

Using the formula W = mg: Substitute m = 5 kg and g = 9.8 N/kg.

W = 5 kg × 9.8 N/kg = 49 N. The object’s weight is 49 newtons downward.

• Write down the formula: W = mg.
• Substitute values with correct units.
• Calculate and include units in the answer.
• Common error: forgetting to include units or mixing mass and weight units.

Weight changes if the gravitational field strength changes. For example, on the Moon, g is about 1.6 N/kg, so objects weigh less there than on Earth.

Mass remains the same regardless of location, but weight depends on the local gravitational field strength.

This explains why astronauts feel lighter on the Moon.

• Weight depends on local gravitational field strength.
• Mass is constant everywhere.
• Example: weight on Moon is less than on Earth.

Gravitational field strength (symbol g) at a point in a gravitational field is defined as the gravitational force acting on a unit mass placed at that point. It is a vector quantity, having both magnitude and direction, directed towards the source of the gravitational field (e.g., the centre of the Earth).

Mathematically, gravitational field strength is given by:

\[ g = \frac{F}{m} \] where F is the gravitational force (in newtons, N) acting on a mass m (in kilograms, kg). The unit of gravitational field strength is newtons per kilogram (N/kg).

• Gravitational field strength = force per unit mass.
• Unit: newtons per kilogram (N/kg).
• Direction: towards the mass creating the field.

Weight (symbol W) is the force exerted on an object due to the gravitational field acting on its mass. It is a vector quantity directed towards the centre of the Earth (or other gravitating body).

Weight depends on both the mass of the object and the gravitational field strength at its location. The relationship is:

\[ W = mg \] where W is weight in newtons (N), m is mass in kilograms (kg), and g is gravitational field strength in newtons per kilogram (N/kg).

• Weight is a force measured in newtons (N).
• Mass is measured in kilograms (kg).
• Weight depends on local gravitational field strength.

The gravitational field strength near the Earth's surface is approximately constant and is called the acceleration due to gravity, denoted by g. Its standard value is:

\[ g = 9.8\, \text{m/s}^2 \] This means that any object in free fall near the Earth's surface accelerates downwards at 9.8 m/s², ignoring air resistance.

Since gravitational field strength equals acceleration due to gravity, the units N/kg and m/s² are equivalent.

• g = 9.8 m/s² near Earth's surface.
• Gravitational field strength equals acceleration due to gravity.
• Units N/kg and m/s² are equivalent.

To calculate the weight of an object, multiply its mass by the gravitational field strength:

\[ W = mg \] For example, an object of mass 5.0 kg near Earth's surface has weight:

\[ W = 5.0\, \text{kg} \times 9.8\, \text{N/kg} = 49\, \text{N} \] The weight acts downwards towards the Earth’s centre.

• Formula: W = mg.
• Calculate weight by multiplying mass by g.
• Example: 5.0 kg mass → 49 N weight.

A common mistake is to confuse mass and weight. Mass is the amount of matter in an object and is constant everywhere, measured in kilograms (kg). Weight is a force that depends on gravitational field strength and is measured in newtons (N).

Another error is to use incorrect units or omit units in calculations. Always include units and convert where necessary.

Sometimes students forget that g varies slightly with location (altitude, planet), but for IGCSE problems, use g = 9.8 m/s² unless otherwise stated.

• Mass ≠ weight; mass in kg, weight in N.
• Always include units in calculations.
• Use g = 9.8 m/s² unless told otherwise.

Mass is the amount of matter in an object and is a scalar quantity measured in kilograms (kg). It does not change regardless of location.

Weight is the force exerted on a mass by gravity. It is a vector quantity measured in newtons (N). Weight depends on the gravitational field strength (g) and is calculated by the equation:

W = mg, where W is weight in newtons, m is mass in kilograms, and g is gravitational field strength in newtons per kilogram (N/kg) or metres per second squared (m/s²).

• Mass (kg) is constant for an object.
• Weight (N) varies with gravitational field strength.
• Weight is a force; mass is a measure of matter.

A balance scale consists of a beam pivoted at its centre with two pans suspended at equal distances from the pivot.

When objects are placed on both pans, the beam will tip towards the heavier side if the weights differ.

If the beam is horizontal and balanced, the moments about the pivot are equal, indicating the masses are equal under the same gravitational field.

• Balance scale compares moments (weight × distance from pivot).
• Equal moments mean equal weights on both sides.
• Since gravitational field strength is the same on both pans, equal weights mean equal masses.

To compare the mass of an unknown object, place it on one pan and standard masses on the other pan.

Add or remove standard masses until the beam is balanced horizontally.

At balance, the mass of the unknown object equals the total mass of the standard masses on the opposite pan.

• Place unknown mass on one pan.
• Add known masses to the other pan.
• Balance indicates equal mass, not just equal weight.

Weight depends on gravitational field strength, which can vary with location (e.g., Earth, Moon).

A balance scale compares the force on each side at the same location, so gravitational field strength cancels out.

Therefore, the balance scale effectively compares masses, not weights, because equal weights under the same gravity mean equal masses.

• Gravitational field strength cancels out in balance scale comparison.
• Balance scale reading is independent of location.
• Mass comparison is reliable even if gravity varies elsewhere.

Ensure the balance scale is level and the pivot is frictionless for accurate results.

Use standard masses with known mass values for comparison.

Repeat measurements to improve accuracy and reduce random errors.

• Level the balance scale before use.
• Use calibrated standard masses.
• Repeat and average results for precision.

Mass is a measure of the amount of matter in an object and is measured in kilograms (kg). It is a scalar quantity and does not change regardless of location.

Weight is the force exerted on a mass by the gravitational field of a planet or other celestial body. It is a vector quantity, having both magnitude and direction (towards the centre of the gravitational field).

Weight is measured in newtons (N), the SI unit of force.

• Mass (m) is measured in kilograms (kg).
• Weight (W) is a force measured in newtons (N).
• Weight acts vertically downwards towards the centre of the gravitational field.

The gravitational field strength (g) at a point is defined as the force per unit mass experienced by a small test mass placed at that point.

It is measured in newtons per kilogram (N/kg), which is equivalent to metres per second squared (m/s²).

Near the Earth's surface, the gravitational field strength is approximately 9.8 N/kg (often rounded to 9.81 N/kg). This means a 1 kg mass experiences a force of about 9.8 N due to gravity.

• Gravitational field strength (g) = force per unit mass (N/kg).
• On Earth, g ≈ 9.8 N/kg.
• Gravitational field strength varies with location (e.g., altitude, planet).

Weight is directly proportional to both the mass of the object and the gravitational field strength acting on it.

The formula linking these quantities is: W = mg, where W is weight in newtons, m is mass in kilograms, and g is gravitational field strength in newtons per kilogram.

This formula can be rearranged to find mass or gravitational field strength if the other quantities are known: m = W/g or g = W/m.

• W = mg (weight equals mass times gravitational field strength).
• Weight changes if gravitational field strength changes (e.g., on Moon vs Earth).
• Mass remains constant regardless of location.

Example: Calculate the weight of a 5.0 kg object on Earth where g = 9.8 N/kg.

Step 1: Write down the formula: W = mg. Step 2: Substitute values: W = 5.0 kg × 9.8 N/kg. Step 3: Calculate: W = 49 N. Step 4: State the answer with units: The weight is 49 newtons.

Common error: Using mass units (kg) as weight or forgetting to multiply by g.

• Formula: W = mg.
• Substitution: W = 5.0 × 9.8.
• Answer: W = 49 N.
• Weight is a force, so units must be newtons (N).

Weight depends on the gravitational field strength, which varies with location. For example, the Moon's gravitational field strength is about 1.6 N/kg, much less than Earth's 9.8 N/kg.

An object’s mass remains the same on Earth, Moon or in space, but its weight changes according to the local gravitational field strength.

This explains why astronauts feel weightless in orbit: the gravitational field strength is much weaker or the object is in free fall.

• Weight changes with gravitational field strength.
• Mass is constant everywhere.
• W = mg applies universally, but g varies.