Matter Revision Notes

Upthrust and Archimedes' Principle

Upthrust is the upward force exerted by a fluid on an object submerged or floating in it. Archimedes' principle states that the upthrust acting on an object is equal to the weight of the fluid displaced by that object. This means the greater the volume of fluid an object displaces, the greater the upthrust. The weight of the displaced fluid depends on its density and the volume displaced. For instance, an object displacing 1 kg of water will experience an upthrust equivalent to the weight of 1 kg (approx. 9.8 N).

Density as a Key Factor (Higher Tier)

The primary factor determining whether an object floats or sinks is its average density compared to the density of the fluid. Density (ρ) is defined as mass (m) per unit volume (V), i.e., ρ = m/V.

• If an object's average density is less than the fluid's density, it floats. The upthrust will be greater than or equal to its weight, causing it to rise until the upthrust balances its weight.
• If an object's average density is greater than the fluid's density, it sinks. The upthrust on the fully submerged object is less than its weight, and it will descend.
• If an object's average density is equal to the fluid's density, it becomes neutrally buoyant, remaining suspended within the fluid.

Variables Influencing Floating/Sinking (Higher Tier)

Beyond the intrinsic average density of the object and the fluid, other factors indirectly influence floating and sinking by affecting these densities or the volume of fluid displaced:

1. Mass of the object: For a given volume, increasing mass increases the object's density, making it more likely to sink.
2. Volume of the object: For a given mass, increasing the volume (e.g., by making an object hollow) decreases its average density, making it more likely to float. This is crucial for ships.
3. Density of the fluid: A denser fluid (e.g., seawater vs. fresh water) provides greater upthrust for the same volume displaced, making it easier for objects to float. This is why boats float higher in salt water.
4. Temperature of the fluid: Changes in temperature can subtly alter fluid density (warmer water is generally less dense than colder water), which can affect buoyancy, though typically to a lesser extent than major density differences.

What is Density?

Density is a measure of how much mass is contained in a given volume. It is a characteristic property of a substance, meaning that a particular substance will always have the same density under the same conditions, regardless of the size or shape of the sample. For example, a small piece of iron has the same density as a large block of iron. This concept helps us understand why different materials behave differently when submerged in fluids, such as water or air. Materials with higher density have their particles packed more closely together, while less dense materials have particles that are more spread out.

Calculating Density

The formula for calculating density is: Density = Mass / Volume. This can be written symbolically as ρ = m/V, where 'ρ' (rho) is the symbol for density, 'm' is the mass, and 'V' is the volume. It is crucial to use consistent units for mass and volume to get the correct units for density. Common units include grams per cubic centimetre (g/cm³) or kilograms per cubic metre (kg/m³). For example, if you measure the mass of an object in grams and its volume in cubic centimetres, the density will be in g/cm³. If you measure mass in kilograms and volume in cubic metres, density will be in kg/m³.

Measuring Mass and Volume

To determine the density of an object, you need to measure its mass and its volume. Mass can be measured using a digital balance. For regular solid objects, volume can be calculated by measuring its dimensions (e.g., length x width x height for a cuboid) using a ruler or calipers. For irregular solid objects, the displacement method is used. This involves submerging the object in a known volume of liquid (usually water) in a measuring cylinder and observing the rise in the liquid level. The difference in the liquid levels before and after submersion gives the volume of the object. For liquids, mass can be found by weighing an empty measuring cylinder, then weighing it again with the liquid inside, and subtracting the 'empty' mass. The volume is read directly from the measuring cylinder.

P1: Determining Density of Regular and Irregular Solids

This PAG involves practical work to determine the density of different materials. For a regular solid (e.g., a metal cube): 1. Measure the mass using a digital balance. 2. Measure its length, width, and height using a ruler. 3. Calculate its volume (length × width × height). 4. Calculate density (mass / volume). For an irregular solid (e.g., a stone): 1. Measure the mass using a digital balance. 2. Fill a measuring cylinder with a known volume of water. 3. Carefully submerge the irregular object in the water, ensuring no splashes. 4. Read the new volume of water. 5. The difference between the initial and final volumes is the volume of the object. 6. Calculate density (mass / volume). It's important to take repeat readings and calculate averages for more accurate results. Safety precautions include handling glassware carefully and ensuring the balance is on a stable surface.

What The Diagram Shows

Gas Pressure on Wall is a physics diagram for Matter. Use it beside the written explanation so the visual supports the exact idea being revised.

What To Explain

The answer should use the diagram to identify the physical relationship, then explain it using the relevant quantity, force, field, wave or energy idea.

Syllabus Link

Private mapping: OCR GCSE physics-a-gateway J249, Matter.

Common Trap

Do not describe the diagram only as a picture. State the concept, then explain what the pattern, relationship, structure, or graph means.