Mass and weight Revision Notes

Mass is a measure of the amount of matter contained in an object. Matter is anything that has substance and occupies space, made up of atoms and molecules. The greater the amount of matter, the larger the mass of the object.

Mass is a scalar quantity, meaning it has magnitude but no direction. This distinguishes it from vector quantities like force or velocity.

Mass is measured using units such as kilograms (kg) or grams (g). For example, a textbook might have a mass of 1.2 kg, while a paperclip might have a mass of 5 g.

• Mass quantifies how much matter an object contains.
• It is a scalar quantity with no direction.
• Common units are kilograms (kg) and grams (g).

Unlike weight, which depends on gravitational pull, mass remains constant regardless of where the object is. Whether the object is on Earth, the Moon, or floating in space, its mass does not change.

For example, an astronaut's mass on the Moon is the same as on Earth, even though their weight is less due to the Moon's weaker gravity.

This constancy makes mass a fundamental property for scientific calculations and comparisons.

• Mass does not change with location.
• Weight varies with gravitational field strength, but mass does not.
• Example: Mass of 70 kg on Earth is still 70 kg on the Moon.

Mass is measured using instruments such as a balance or scale. A balance compares the mass of an object to known masses, while a digital scale measures the force exerted by gravity and converts it to mass assuming standard gravity.

In practical settings, a beam balance is often used because it directly compares masses and is unaffected by local gravity variations.

For example, to measure the mass of a rock, place it on one side of a balance and add standard masses to the other side until equilibrium is reached. The total of the standard masses equals the rock's mass.

• Balances compare unknown mass to known masses.
• Digital scales infer mass from weight assuming standard gravity.
• Balances provide accurate mass measurements independent of location.

Consider a metal cube with a mass of 2 kg. This means it contains twice as much matter as a 1 kg cube of the same material.

If you have 500 g of sugar, you have half the amount of matter compared to 1 kg of sugar.

Mass helps in calculating other properties such as density, where density = mass ÷ volume. For example, if the 2 kg metal cube has a volume of 0.0005 m³, its density is 2 kg ÷ 0.0005 m³ = 4000 kg/m³.

• Mass quantifies matter amount in objects.
• Used in calculations like density.
• Example: 2 kg metal cube has more matter than 1 kg cube.

Recognizing mass as the amount of matter is crucial for understanding physical phenomena such as inertia, where objects with greater mass resist changes in motion more strongly.

It also underpins the concept of weight, which is the gravitational force acting on a mass.

In scientific experiments, knowing the mass allows accurate calculation of other quantities and ensures consistency in measurements.

• Mass relates to inertia and resistance to motion changes.
• Mass is fundamental to calculating weight.
• Accurate mass measurement is essential in experiments.

Weight is the force that gravity exerts on an object because the object has mass. Unlike mass, which is the amount of matter in an object and remains constant, weight depends on the gravitational pull at the object's location.

Since weight is a force, it is measured in newtons (N). Mass is measured in kilograms (kg).

The greater the mass of an object, the greater its weight, assuming the gravitational field strength is constant.

• Weight is a force, measured in newtons (N).
• Mass is the amount of matter, measured in kilograms (kg).
• Weight depends on both mass and gravity.

Gravitational field strength (g) is the force of gravity per unit mass at a location, measured in newtons per kilogram (N/kg). Near Earth's surface, g is approximately 9.8 N/kg, but it varies slightly with altitude and location.

Because weight depends on gravity, an object’s weight changes if the gravitational field strength changes, such as on the Moon or other planets.

Mass remains the same regardless of location, but weight changes with gravitational field strength.

• Gravitational field strength (g) ≈ 9.8 N/kg on Earth.
• Weight changes if g changes; mass does not.
• Weight = mass × gravitational field strength.

The weight (W) of an object can be calculated by multiplying its mass (m) by the gravitational field strength (g): W = mg.

For example, a 5 kg object on Earth experiences a weight of W = 5 kg × 9.8 N/kg = 49 N.

Units must be consistent: mass in kilograms, g in newtons per kilogram, resulting in weight in newtons.

• Formula: W = mg
• Example: 5 kg × 9.8 N/kg = 49 N
• Weight units: newtons (N)

If you take a 10 kg object to the Moon, where g ≈ 1.6 N/kg, its weight becomes W = 10 kg × 1.6 N/kg = 16 N, much less than on Earth.

This explains why astronauts feel lighter on the Moon despite having the same mass.

Scales measure weight (force), not mass directly, so readings vary with location unless adjusted.

• Weight varies with location due to g changes.
• Mass remains constant everywhere.
• Scales measure weight, not mass.

Mass is a scalar quantity representing the amount of matter and does not change with location.

Weight is a vector force directed towards the centre of the gravitational field.

Confusing mass and weight can lead to errors in calculations and understanding forces acting on objects.

• Mass is constant; weight varies.
• Weight is a force; mass is not.
• Weight acts downwards due to gravity.

Gravitational field strength, symbolised as g, quantifies the force of gravity acting on each kilogram of mass at a specific location. It is defined as the gravitational force experienced per unit mass. This means if you place a 1 kg mass in a gravitational field, the force it experiences due to gravity is equal to the gravitational field strength at that point.

Gravitational field strength is a vector quantity, pointing towards the centre of the mass creating the field, such as the Earth. Its magnitude tells us how strong the gravitational pull is at that location.

• Gravitational field strength (g) = gravitational force (N) / mass (kg)
• Units of g are newtons per kilogram (N/kg)

Near the surface of the Earth, the gravitational field strength is approximately constant and has a value of about 9.8 N/kg. This means that every kilogram of mass experiences a gravitational force of roughly 9.8 newtons directed downwards towards the Earth's centre.

This value can vary slightly depending on altitude and geographical location, but for most calculations in physics at or near the Earth's surface, 9.8 N/kg is used as a standard approximation.

• Standard value of g near Earth's surface ≈ 9.8 N/kg
• Direction of g is towards Earth's centre

Weight is the force exerted on an object due to gravity. It depends on both the mass of the object and the gravitational field strength at its location.

The relationship between weight (W), mass (m), and gravitational field strength (g) is given by the equation:

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). This formula allows calculation of the weight of any object if its mass and the local gravitational field strength are known.

• Weight (W) = mass (m) × gravitational field strength (g)
• Units: W in newtons (N), m in kilograms (kg), g in newtons per kilogram (N/kg)

Suppose a student has a mass of 50 kg. To find their weight near the Earth's surface, use the formula W = mg.

Substitute the values: m = 50 kg, g = 9.8 N/kg, so:

W = 50 kg × 9.8 N/kg = 490 N. Therefore, the student's weight is 490 newtons, directed downwards towards the Earth’s centre.

• Calculate weight using W = mg
• Example: 50 kg × 9.8 N/kg = 490 N

Understanding gravitational field strength is essential for solving problems involving forces due to gravity. It helps distinguish between mass, an intrinsic property of matter, and weight, a force that depends on gravitational field strength.

This concept is also important when comparing weights on different planets, where gravitational field strength differs. For example, on the Moon, g is about 1.6 N/kg, so an object’s weight there is less than on Earth, even though its mass remains the same.

• Mass is constant; weight varies with g
• Weight changes on different celestial bodies due to different g values

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

Weight, however, is a force resulting from the gravitational attraction acting on that mass. It is a vector quantity measured in newtons (N).

Because weight depends on gravity, it can vary depending on where the object is, while mass remains constant. For example, an object’s mass is the same on Earth and the Moon, but its weight is less on the Moon due to weaker gravity.

• Mass is constant and measured in kilograms (kg).
• Weight is a force measured in newtons (N).
• Weight depends on gravitational field strength; mass does not.

A gravitational field exists around any mass, such as a planet, and exerts a force on other masses within that 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.

Near Earth's surface, g is approximately 9.8 newtons per kilogram (N/kg), meaning each kilogram of mass experiences about 9.8 N of gravitational force downward.

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

Weight (W) can be calculated by multiplying the mass (m) of an object by the gravitational field strength (g) at its location.

The formula is: W = m × g, where W is in newtons (N), m in kilograms (kg), and g in newtons per kilogram (N/kg).

For example, a 5 kg object on Earth experiences a weight of W = 5 kg × 9.8 N/kg = 49 N downward.

• Formula: W = m × g
• Units: W in newtons (N), m in kilograms (kg), g in newtons per kilogram (N/kg)
• Example: 5 kg mass → weight = 5 × 9.8 = 49 N

Because gravitational field strength varies depending on the celestial body or altitude, weight changes accordingly.

An object weighs less on the Moon because the Moon’s gravitational field strength is about 1.6 N/kg, much less than Earth's 9.8 N/kg.

For example, the same 5 kg object weighs W = 5 × 1.6 = 8 N on the Moon, significantly less than on Earth.

• Weight depends on local gravitational field strength.
• Weight on Moon is about one-sixth of weight on Earth.
• Mass remains constant regardless of location.

Measuring weight can be done using a spring balance, which measures the force exerted by gravity on the object.

Mass can be measured using a balance that compares masses, unaffected by gravity variations.

Understanding weight as a force helps explain phenomena such as why astronauts feel weightless in orbit (free fall) despite having mass.

• Spring balance measures weight (force).
• Mass balances measure mass independent of gravity.
• Weightlessness occurs when gravitational force is not felt as a support force.

Gravitational field strength (symbol: g) is a measure of the gravitational force exerted on each kilogram of mass at a specific location. It is defined as the gravitational force per unit mass, with units of newtons per kilogram (N/kg). This means that if an object has a mass of 1 kg, the gravitational force acting on it equals the gravitational field strength at that point.

For example, near the Earth's surface, the gravitational field strength is about 9.81 N/kg. This means every kilogram of mass experiences a downward force of approximately 9.81 newtons due to gravity. Gravitational field strength varies slightly with altitude and location but is generally taken as 9.8 N/kg for most calculations.

• Gravitational field strength = gravitational force ÷ mass
• Units: newtons per kilogram (N/kg)
• Near Earth’s surface, g ≈ 9.81 N/kg

When an object is dropped and allowed to fall freely under gravity alone (ignoring air resistance), it accelerates downwards. This acceleration is caused by the gravitational force acting on the object's mass.

The acceleration of free fall is numerically equal to the gravitational field strength at that location. On Earth, this acceleration is approximately 9.81 metres per second squared (m/s²). This means the object's velocity increases by about 9.81 m/s every second it falls.

For example, if a ball is dropped from rest, after 1 second its speed will be about 9.81 m/s, after 2 seconds about 19.62 m/s, and so on, assuming no air resistance.

• Free fall acceleration = gravitational field strength
• Units: metres per second squared (m/s²)
• On Earth, free fall acceleration ≈ 9.81 m/s²

Gravitational field strength and free fall acceleration are two ways of describing the same physical quantity. Gravitational field strength tells us the force per unit mass, while free fall acceleration tells us how quickly an object speeds up when falling under gravity.

Mathematically, the weight (W) of an object is given by the equation:

W = m × g, where W is weight in newtons (N), m is mass in kilograms (kg), and g is gravitational field strength in N/kg (or equivalently acceleration in m/s²). Since weight is a force, and force causes acceleration, the acceleration of the object in free fall equals g.

• Weight W = mass m × gravitational field strength g
• g represents both force per unit mass and acceleration
• This equality links force and motion under gravity

Consider a 2 kg object near the Earth's surface. Using g = 9.81 N/kg:

Weight W = m × g = 2 kg × 9.81 N/kg = 19.62 N. This means the Earth pulls the object downward with a force of 19.62 newtons.

If this object is dropped, it will accelerate downwards at 9.81 m/s², increasing its velocity by this amount every second, assuming no air resistance.

• Mass = 2 kg, g = 9.81 N/kg
• Weight = 2 × 9.81 = 19.62 N
• Free fall acceleration = 9.81 m/s²

Gravitational field strength is a property of the gravitational field at a location, indicating how strong gravity is there.

It is numerically equal to the acceleration of any object in free fall at that location.

Weight depends on both mass and gravitational field strength; mass is constant, weight varies with g (e.g., on other planets).

• g links gravitational force and acceleration
• Weight changes if g changes, mass does not
• Free fall acceleration is independent of the object's mass