Understanding Density and Volume

Density

• Density is defined as mass divided by volume.
• The equation for density is p = m / v, where p is density (rho), m is mass, and v is volume.

Measuring Volume

• For regular objects, volume is calculated by multiplying base x width x height (bwh).
• Mass is measured using a scale.

Measuring Volume of Irregular Objects

• To measure the volume of an irregular object, use a displacement can (Eureka Can) and a measuring cylinder.
• Submerge the object in the Eureka can filled to the spout, and measure the displaced water in the measuring cylinder.

Determining if an Object Will Float

• Objects float if less dense than the liquid they are placed in, and sink if denser.
• The density of water is 1g/cm³ or 1000kg/m³.

Measuring Liquid Volume and Density

• Liquid volume is measured with a beaker or measuring cylinder.
• To find the mass of the liquid, place a beaker on a scale, reset the weight, and add the liquid. The new weight is the mass of the liquid.
• For more precise results, plot a graph with volume on the x-axis and mass on the y-axis, draw a line of best fit, and pick a point on the line to calculate density.

Pressure in Solids

• Pressure increases with smaller area, showing an inversely proportional relationship.
• Force and pressure are proportional.
• Pressure is calculated as force / area (p = f/a).
• The unit for pressure is Pascal (Pa), equivalent to n/m².

Pressure in Fluids

• Density increases deeper in a fluid due to the weight of the liquid and atmosphere above.
• Change in Pressure = gravitational field strength x density x height or depth.
• This is expressed as ΔP = g x p x h.
• Total Pressure at a deeper level = atmospheric pressure + pressure difference
• Total Pressure at a higher level = atmospheric pressure – pressure difference
• Earth's gravitational field strength is 10 n/kg.

Hydraulics

• Hydraulics relies on the principle that pressure is equal throughout the fluid.
• A small force on a small surface area produces a large force on a large surface area.
• P₁ = P₂, and F₁ / A₁ = F₂ / A₂.

Communicating Vessels

• If several open tubes are connected at the bottom and filled with water, the water level will be the same in all tubes, due to equal atmospheric pressure.

Pressure in Gases

• Gas molecules move randomly and equally in all directions, exerting pressure when colliding with something.
• More frequent and powerful collisions increase pressure.
• Pressure increases with temperature because the molecules have more kinetic energy.

Boyle's Law

• For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.
• This is expressed as P1V1 = P2V2.
• P1 + p2 = The initial and final pressures and V1 + V2 = The initial and final volumes.

Charles's Law

• For the same pressure, the volume and temperature of a gas are proportional.
• Temperature is measured in Kelvin.
• V1/T1 = V2/T2.

Measuring Gas Pressure

• A manometer, a partially mercury-filled U-tube, measures gas pressure by comparing it to atmospheric pressure.
• Equal mercury levels indicate equal pressure.
• Higher mercury on the gas's side means the gas pressure is lower than atmospheric pressure (atmospheric pressure + phg or ΔP).
• Lower mercury on the gas's side means the gas pressure is higher than atmospheric pressure (atmospheric pressure - phg or ΔP).

Measuring Atmospheric Pressure

• A barometer, a closed glass tube filled with mercury, measures atmospheric pressure.
• Atmospheric pressure pushes down on the exposed liquid, raising the liquid in the tube against its weight, creating a vacuum.
• Higher liquid level indicates higher atmospheric pressure.
• Atmospheric pressure is calculated by h x g x p.

Kinetic Theory and States of Matter

• Solids have particles closely arranged in a regular pattern, vibrating back and forth with a fixed shape.
• Liquids have particles close together but in a random arrangement, moving around each other, and taking the shape of a container.
• Gases have particles far apart in a random arrangement, moving quickly in all directions, and filling a container.

Waves

• A wave is a vibration or oscillation that transfers energy without transferring any matter.
• Transverse and longitudinal waves are two types of wave.

Wave Definitions

• Equilibrium position is the undisturbed position of a particle, halfway between the peak and trough of a wave.
• Displacement is the distance a particle is from its equilibrium position, which can be positive or negative.
• Amplitude is the maximum displacement of a particle from its equilibrium position.
• Wavelength is the distance between two consecutive corresponding points on a wave, such as peak to peak or trough to trough.
• Wavefronts are imaginary lines connecting points on adjacent waves that vibrate together.
• The distance between two wavefronts is the wavelength.
• Period of a wave is the time it takes for a wave to complete a wavelength.
• Time period is the time taken for one complete oscillation.
• Frequency is the number of oscillations a particle makes in a second, measured in Hertz (Hz), where one Hertz is a cycle per second.

Wave Equations

• Wave speed = distance travelled / time taken (v = d/t).
• Wave speed = frequency x wavelength (v = fλ).
• Frequency = 1 / time period.
• "f=1/T” = “T=1/f”.
• T is time period, the time taken for a particle to complete an oscillation
• t = (time taken for a wave to travel) = time takes for a wave to travel from A to B

Transverse Waves

• Particles vibrate perpendicular to the direction of energy transfer.
• They travel in solids, while electromagnetic waves are exceptions.
• Examples include ripples in water, electromagnetic waves, and strings.

Longitudinal Waves

• Particles vibrate parallel to the direction of energy transfer.
• They can travel in solids, liquids, and gases.
• Examples include sounds, springs, and seismic p waves in earthquakes.
• They have compressions (high pressure regions) and rarefactions (low pressure regions).
• Wavelength is the distance between the centers of consecutive compressions or rarefactions.
• Amplitude is the maximum displacement from the equilibrium position.

Electromagnetic Spectrum

• EM waves can be harmless or dangerous.
• Higher frequency waves are more dangerous due to higher energy.
• Microwaves heat body tissue.
• Infrared radiation causes burns.
• UV radiation damages cells and causes blindness.
• Gamma rays are concentrated on a point in the body with cancer from lots of different angles and can kill the cancer
• UV and gamma rays are ionizing and can cause cell mutation, destruction, and cancer.

Types of EM Waves

• Electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet light, x-rays, and gamma rays.
• They are transverse and travel at the speed of light in a vacuum.

Radio Waves

• Radio waves have the largest wavelengths (over 10cm to 10 km).
• They are used for communication.
• Long-wave radio (1-10 km) bends around the Earth.
• Short-wave radio (10-100 m) reflects off the ionosphere.
• Radio and TV waves have small wavelengths (around 10cm-10m), requiring direct line of sight.

Microwaves

• Second biggest wave ranging from 10cm to 1mm and used for communication.
• Uses include satellite TV, phone calls, and microwave ovens.
• Microwaves in ovens are absorbed by water molecules in food.

Infrared Radiation (IR)

• Wavelength between 1mm and 1µm.
• Used for heating and cooking.
• Can also be detected by night-vision cameras.

Visible Light

• Wavelength between 400 to 700 nm.
• Used in optical fibers for communication.
• Also used in cameras.
• Order of light waves: red, orange, yellow, green, blue, indigo and violet.

Ultraviolet (UV) Light

• Wavelength goes from 100 to 400 nm.
• UV light is absorbed and visible light is emitted in florecent materials

X-Rays

• Second smallest wavelength in the EM spectrum (0.01 to 10nm).
• Used to view internal structures.
• Radiographers use it to diagnose broken bones.
• Excessive exposure can cause cancer and mutations.

Gamma Rays

• Smallest EM wave with wavelength less than 10 picometers.
• Used for sterilizing medical equipment and food.
• Used in cancer treatment to kill cancer cells.

Reflection and Refraction

• All waves can be refracted and reflected.
• The normal in a ray diagram is perpendicular to the material or boundary involved.

Reflection

• Angle of incidence = angle of reflection.

Refraction

• Refraction is the change in direction of a wave as it passes through something on an angle.
• It occurs due to changes in density.
• Waves bend towards the normal when entering a denser medium and away from the normal when exiting.
• In a triangular prism, white light is dispersed.
• Different wavelengths are refracted by different amounts and white light disperses into different colors as it enters a prism

Energy Transfer

• Energy stores are kinetic, gravitational potential, chemical, electrostatic, magnetic, elastic potential, nuclear, and thermal.

Energy Transfers

• Energy transfers include heating, electrical, radiation, and mechanical.

Describing Energy Transfers

• To describe the energy transfer from one store to another, use this model paragraph:"The ____ energy store in the _____ is transferred ______ to the ______ energy store in the ______."

Efficiency

• A closed system can be treated completedely on its own without any matter being exchanged with the surroundings
• The principle of conservation of energy: energy can be changed from one form to another, but it cannot be created or destroyed.
• Useful energy is the energy transferred to where it is required, always less than total energy.
• Energy input = useful energy output + wasted energy.
• Efficiency = (useful energy output/total energy output) * 100.

Sankey Diagrams

• Sankey diagrams illustrate energy use and waste.
• Arrow thickness indicates the amount of energy.
• The energy going down is the wated energy and the energy going forward is the useful energy.
• The diagram must be drawn to scale, efficiency was 90% and the width was 10cm, then the line going forward would have to be 9cm.