3.1: Density

• The density of an object is the mass per unit volume.
• Density refers to the measure of mass per unit volume of a substance. It is typically expressed in units such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).
• Hollow: Hollow describes an object or structure that has empty space or voids inside, rather than being solid throughout.
• Irregular: Irregular refers to something that lacks uniformity in shape, size, or arrangement. Irregular objects do not conform to a specific pattern or structure.
• Regular: Regular indicates something that has a uniform shape, size, or arrangement, adhering to a consistent pattern or structure.
• Solid: Solid refers to a state of matter characterized by particles that are closely packed together in a fixed arrangement. Solids have a definite shape and volume, and their particles vibrate but do not move freely like those of liquids or gases.
• Volume: Volume refers to the amount of three-dimensional space occupied by an object. The volume of an object is calculated by multiplying its length, width, and height.
• Weight: Weight is the force exerted on an object due to gravity. An object's weight depends on both its mass and the strength of gravity acting upon it.
• Mass: Mass refers to the quantity of matter contained within an object. It is measured using a balance scale and is independent of gravitational forces.
• Density is a measure of how much mass a substance has per unit of its volume
• To find density, divide the substance's mass by its volume
• Density is measured in kilos per meter cubed in physics
• Common units for density include kilos per meter cubed and grams per centimeter cubed
• 1 gram per centimeter cubed is equivalent to 1,000 kilos per meter cubed
• To calculate volume, divide the mass by the density
• Example: Calculate the volume of 420 kilos of aluminium with a density of 2,710 kilos per meter cubed

  • Volume = 420 kilos / 2,710 kilos per meter cubed = 0.155 meters cubed
• To calculate the density of a solid experimentally:

  • Find the mass by placing the solid on a balance and measuring it
  • Find the volume by measuring the dimensions (length, width, height) and multiplying them for regular shapes like cubes or cuboids
  • For irregular shapes, use a eureka can filled with water and a measuring cylinder to measure the volume
• To calculate the density of a liquid experimentally:

  • Place an empty measuring cylinder on a balance and zero it
  • Pour the liquid into the cylinder and record the mass
  • Divide the mass by the volume (in milliliters, which is equivalent to centimeters cubed) to find the density
• For more accurate density measurements:

  • Measure larger volumes to minimize measurement uncertainties
  • Take multiple measurements to identify anomalies and calculate a mean
• Gravity: Gravity refers to the attractive force between two masses, causing them to pull towards one another. This force varies depending on the distance between the masses and can be described mathematically through Newton's law of universal gravitation.
• Liquid: Liquid is one of the three states of matter (solid, liquid, gas) and is characterized by having no fixed shape or volume. Its particles flow around each other and take up the shape of any container they occupy.
• Gas: Gas is another state of matter, where particles are far apart from each other and move rapidly in random directions. Gases have no definite shape or volume and expand to fill any available space.
• Objects vary in mass depending on both volume and density, challenging the assumption that rocks or metals are always heavier than feathers or polystyrene.
• Large blocks of polystyrene may have greater mass than small metal pieces due to their larger volume, despite being lightweight.
• Different objects with different densities will sink or float based on their relative densities compared to water.
• Large blocks of polystyrene may have greater mass than small metal pieces due to their larger volume, despite being lightweight.
• Hollow objects, like polystyrene food containers, feel light as they have large volumes, small masses, and contain air spaces.
• In contrast, solid objects such as iron nails feel heavier because they have smaller volumes and lack air spaces.
• Density, representing mass per unit volume, clarifies these differences, with regular-shaped objects' volumes calculated by multiplying side lengths and irregular-shaped objects' volumes determined using the displacement method.
• An object's weight changes when placed at different locations on Earth due to variations in gravitational field strength.
• To determine if an object floats, it must be placed into water and observed whether it remains above or below the surface.
• Objects that are denser than water will sink, while those less dense than water will float.
• Materials and Density: When comparing the densities of materials like wood with that of water, it becomes evident that materials with lower densities than water, such as wood, will float. The density of wood is typically around 0.5 g/cm³, whereas water has a density of 1.0 g/cm³.
• Determining Floatation: The principle behind whether an object will float or sink in water relies on its density relative to water. If the object is denser than water, it will sink; if it is less dense, it will float. This fundamental concept is crucial in understanding buoyancy.
• Buoyant Force: Buoyancy refers to the upward force exerted by fluids (such as air or water) on an object submerged within them. It can also refer to the ability of a fluid to support an object without sinking.
• Low-Density Design: Objects designed to float, like swimming pool floats, are intentionally crafted with low densities. This is achieved by using lightweight materials such as polystyrene or creating hollow structures filled with air. These design choices ensure that the overall density remains lower than that of water.
• Ships and Buoyancy: While steel, a common material in ship construction, has a density much greater than that of water (8–9 g/cm³), ships can still float. This is due to the fact that ships are not solid masses of steel; rather, they consist of large, air-filled spaces. These voids significantly increase the ship's volume, resulting in an average density less than that of water.
• Average Density Dynamics: The average density of a ship is a crucial factor in determining its buoyancy. It is calculated by considering the mass of all materials within the ship, including air-filled spaces, and dividing this by the total volume of the ship. As ships take on cargo, passengers, or fuel, their mass increases, altering the average density. This dynamic relationship between mass, volume, and density influences a ship's ability to float or sink.
• If the weight of the object is more significant than the buoyant force, then the object will sink.
• The buoyant force acting upwards on an object equals the weight of the displaced fluid.