Mass Weight And Density

Typed version of the handwritten O Level Physics class notes. The original handwritten pages are on the same page of megalecture.com.

Mass and weight

For an object falling freely towards the Earth: force = weight, so ma = mg and a = g.

• g = gravitational field strength, in m/s² or N/kg.
• a = acceleration due to gravity, 10 m/s².

Density

• The mass packed per unit volume; the ratio of the mass packed and the volume occupied.
• Density = mass / volume: ρ = m / V, in kg/m³ or g/cm³.
• It is a scalar quantity.
• It is the compactness of matter and is not related to heaviness or weight.
• If the mass is the same, then ρ ∝ 1/V (a curve falling as V increases): larger volume means lower density, smaller volume means higher density.
• If the volume is the same, then ρ ∝ m (a straight line through the origin).

Newtons = kg m/s².

Heating and density

When an object is heated → its molecules gain energy (kinetic energy) → these molecules start to move faster → they make more forceful and frequent collisions → they push each other apart → the intermolecular spaces increase → the volume increases but the mass stays the same → hence, density decreases on heating.

• This is thermal expansion.
• Molecules never break; the space between them increases.
• Less dense things always float and more dense things sink.
• The density of a pure material at a given temperature is always the same.
• For ρ = m/V, an electronic mass balance is easier to read.

To determine the density of a liquid

• Apparatus: beam balance, burette, beaker and stand.
• Find the mass of an empty beaker with a beam balance (m₁).
• Shift a known volume of the liquid from the burette to the beaker.
• Find the mass of the beaker and the liquid with the beam balance (m₂).
• Mass of liquid = m₂ − m₁; density = mass / volume.

To determine the density of a regular object

• Apparatus: beam balance, ruler, regular-shaped object.
• Determine the mass of the object with a beam balance.
• Measure the length, breadth and height using the metre rule.

To determine the density of an irregular object

• Find the mass of the irregular object using a beam balance.
• Fill a measuring cylinder with water up to a volume V₁.
• Completely immerse the object in the water. Find the new volume.

Precautions:

• Avoid parallax error.
• Place the measuring cylinder on a flat surface.
• Read the volume from the bottom of the meniscus.
• Measure the mass before the volume.
• If the object floats in water, tie a sinker to the object and subtract the sinker's volume.
• If the object is too big to be lowered into the measuring cylinder, use a displacement can: the object is lowered into the full can and the displaced water runs from the spout into a measuring cylinder.

Definitions

• Parallax error: an error in reading an instrument due to the eye of the observer and the pointer not being in a line perpendicular to the plane of the scale.
• Meniscus: the curved surface at the top of a column of a liquid.
• Gravitational field: a region in which a mass experiences a force due to gravitational attraction.
• Gravitational field strength: the gravitational force acting per unit mass, 10 N/kg (meaning the force of gravity acting on an object of mass 1 kg is about 10 N on the Earth's surface).
• Inertia: the ability of a body to resist when its state of rest or uniform motion tends to be changed. It depends on the mass of the body: massive bodies have more resistance when their state of rest or motion is changed, i.e. they have higher inertia than lighter bodies.