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# Physics

## Physical quantities and SI units

Physical quantities have a numerical value (a number) and a unit of measurement (e.g. two kilograms, one metre, ten newtons).

In "2 kilograms of bananas", "2" is the numerical value and "kilograms" is the unit.

A unit of measurement is a specific magnitude of a physical quantity that has been adopted by convention.

Kilogram, degree Celsius and centimetre are different units.

The International System of Units, abbreviated as SI (in French), defines the set of units of measurement and their symbols that are most widely used by scientists.

The metre is the SI unit for distance. The kelvin is the SI unit for temperature.

The mass of some strawberries is measured. They have a mass of $146 \text{ g}.$

## Definition of speed

Speed is the distance travelled per unit of time. It is a scalar quantity.

If you run at 12 km/h, you will cover 12 km in one hour, 6km in half an hour, 24 km in two hours, etc.

Speed is written $S$ or $v$. It is the ratio

$$\Tgreen{\text{speed}} =\frac{\Tred{\text{distance}}}{\Tblue{\text{time}}}.$$
• A car drove 20 km in 20 minutes (1/3 hour). Its speed was $$\frac{\Tred{20\ukm}}{\Tblue{20\umin}} =\frac{\Tred{20\ukm}}{\Tblue{1/3\uh}} = \Tgreen{60\ukmph}.$$
• A plane flew at 1000 km/h for 3 hours. It covered $$\Tgreen{1000\ukmph}\times \Tblue{3\uh} = \Tred{3000\ukm}.$$
• Paul ran 1 km at a speed of 10 km/h. The run took him $$\frac{\Tred{1\ukm}}{\Tgreen{10\ukmph}} = \frac{\Tred{1}}{\Tgreen{10}}\Tblue{\uh} = \frac{\Tred{1}}{\Tgreen{10}} \Tblue{60} \Tblue{\umin} = \Tblue{6\umin}.$$
The ThrustSSC holds the record for the fastest speed ever recorded by a car $(1228 \ukmph)$

## Free-body diagrams

A free-body diagram is a diagram showing all of the forces acting on a single object.

Free-body diagrams are useful in determining if the forces on an object are balanced.

The object is drawn as a rectangle and each force is represented by an arrow in the direction of the force.

Each arrow must be labelled with the symbol of the force (e.g. $F_{1}$, $N$, $W$).

The magnitude of each force can be indicated by the length of the arrow. However, this is only true if stated in the description of the diagram.

A free-body diagram of an object sliding down a slope.

## Measuring density

To find the density of an object you have to measure its mass and its volume .

The mass of an object can be found using a balance or a set of scales.

The volume of an object can be found in two ways:

• If the object is a regular shape like a cuboid then its volume can be calculated with a formula such as $\text{volume} = \text{height} \times \text{width} \times \text{length}$
• If an object is not a regular shape then its volume can be measured by placing it in a liquid. This method is called displacement.

Pour some water into a measuring container and record its volume. Place the object into the container with the water and record the new volume. The difference between these two values is the volume of the object.

The volume of a small irregular piece of plastic is measured. This allows the density to be calculated.

## Calculating moments

The moment of a force can be calculated using the formula $$\Tblue{\text{moment}} = \Tred{\text{force}} \times \Tgreen{\text{perpendicular distance to pivot}}$$

The perpendicular distance is the length of a line drawn between the vector representing a force and the pivot, at right angles to the force.

The perpendicular distance is greatest if the force is at right angles to the object.

The SI unit of a moment is the newton metre and has the symbol $\text{Nm}.$

If you apply a $\Tred{10\text{ N}}$ force on a door at a point $\Tgreen{0.5 \text{ m}}$ away from the pivot, the moment is equal to $\Tred{10\text{ N}} \times \Tgreen{0.5 \text{ m}} = \Tblue{5 \text{ Nm}}.$

The force in the picture is not at right angles to the object. The perpendicular distance of $0.2 \um$ must be used to calculate the moment. Do not use $0.3 \um.$

The force on the beam is on the left hand side of the pivot. It causes a moment of $3 \text{ Nm} \text{ anti-clockwise}.$

## Energy definition

Energy $(E)$ is a quantity that describes the ability of an object to do work on other objects.

The energy that an object has indicates how much work it could do.

A battery with $10 \text{ kJ}$ of energy can do $10 \text{ kJ}$ of work when connected to a motor.

Energy cannot be measured directly and must be determined using other properties of the system (e.g. velocity, position or temperature).

The SI unit of energy is the same as the SI unit for work, the joule $(\text{J})$.

Example Energy (estimation)
Camera flash $10\text{ J}$
Chocolate bar $1.2\text{ MJ}$
Lightning bolt $1\text{ GJ}$
Fuel carried by an aircraft $5\text{ TJ}$
Lightning transfers electrical energy from the clouds to the ground

## Particle movement and pressure

A gas in a closed container exerts a pressure on that container.

When a particle in a gas collides with one of the walls of its container it applies a force on the wall. Many particles collide with the walls every second, each applying a small force.

Since pressure is equal to force over area, this results in pressure being applied to the wall.

The pressure on one wall of the container is equal to the $$\dfrac{\Tred{\text{sum of all the forces from collisions of particles with wall}}}{\Tblue{\text{area of wall}}}$$

Because the gas particles move about at random, the pressure exerted by the gas is the same everywhere.

The pressure is higher if:

• The particles collide with the walls of the container more frequently.

• The particles in the gas have more mass or more energy.

Particles in a gas are in constant motion.

## Convection mechanism

Convection happens naturally because of gravity:

Pockets of denser fluid tend to fall because they are heavier while pockets of less dense fluid tend to rise because they are lighter.

1. A pocket of fluid which is warmer than its surroundings expands and becomes less dense. The pocket begins to rise.
2. The pocket is replaced by colder, denser fluid. This pocket of fluid is then also heated and starts to rise.
3. As a pocket of fluid rises it begins to cool. It contracts and becomes denser again. The pocket starts to fall back down.

In this way, heat is transported throughout the fluid.

Remember that a fluid can be a liquid or a gas.

A radiator in a home heats the air around it. This hot air then rises and some colder air takes its place. The radiator then heats the new colder air and the cycle continues.

The radiator can heat all of the air in the room in this way.

A set of convection currents inside a beaker of water that is heated from below.

## Temperature scales

A temperature scale is a way of assigning a numerical value to a particular temperature.

This is similar to the length scale on a ruler (e.g. in inches or centimetres) in the measurement of length.

A temperature scale needs to be calibrated (marked so that it can be used in different situations) using at least two fixed points.

A fixed point is a standard known temperature like the boiling point of pure water.

Temperature scales can have different zero values and unit (interval) values.

The Celsius and Fahrenheit scales have different zero values $(0^{\circ}\text{C}=32^{\circ}\text{F})$ and different interval values. An interval of $1^{\circ}\text{F}$ is equal to an interval of $5/9^{\circ}\text{C}.$

Two thermometers calibrated according to the Celsius scale and the Fahrenheit scale.

## Specific latent heat

The specific latent heat ($\ell$) of a substance is the thermal energy absorbed or released when $1 \text{ kg}$ of a substance changes state at constant temperature.

The specific latent heat is given by:$$\Torange{\text{specific latent heat}}=\frac{\Tred{\text{thermal energy}}}{\Tblue{\text{mass}}} = \frac{\Tred{Q}}{\Tblue{m}}$$

The SI unit of specific latent heat is joules per kilogram ($\text{J} / \text{kg}$).

$\Tblue{0.2 \text{kg}}$ of ice absorbs $\Tred{60\,000 \text{J}}$ as it melts into water.

The specific latent heat is $\dfrac{\Tred{60\,000 \text{J}}}{\Tblue{0.2 \text{ kg}}} = \Torange{300\, 000} \text{ J}/\text{kg}.$

Latent heat is absorbed by ice when it melts into water

## Waves on a slinky spring

To show examples of different waves, a "slinky" spring can be fixed at one end of a horizontal table.

A slinky spring (a type of spring which is long and easily stretched).

Moving the free end of the spring back-and-forth in a direction perpendicular to its length produces transverse waves along the spring.

Moving the free end of the spring back-and-forth in a direction parallel to its length produces longitudinal waves along the spring.

View looking down on the table. Top: a slinky being used to make a transverse wave. Bottom: a slinky being used to make a longitudinal wave.

## Ray diagrams

Ray diagrams can be used to work out the appearance of images created by lenses and whether they are real or virtual.

1) Draw the lens and the $\Tgreen{\text{principal foci}}$ on both sides of the lens, and mark the position of the $\Tviolet{\text{object}}$.

2) Draw $\Tred{\text{one ray}}$ from the object straight through the centre of the lens without it changing direction.

3) Draw a $\Tblue{\text{second ray}}$ parallel to the axis heading towards the lens. At the centre of the lens, it is refracted so that it passes through the principal focus.

How to construct a ray diagram

A real $\Torange{\text{image}}$ is formed where the two lines meet. If the image is on the same side of the axis as the object it is upright. If the image is further from the axis than the object it is magnified.

If the two lines do not meet, a virtual image is formed. To draw it, extend the rays coming from the lens to the side of the lens where the object is found. This is how a magnifying glass works.

## The electromagnetic spectrum

The electromagnetic spectrum is a continuous range of related waves. The waves in this spectrum are called electromagnetic waves or electromagnetic radiation.

Different types of electromagnetic waves are characterised by their frequencies and wavelengths. Waves which have a higher frequency have more energy.

All of the waves in the spectrum share the following properties:

• They are transverse waves.
• They can travel through a vacuum
• They travel at the same speed in a vacuum $(3 \times 10^{8} \text{ m/s})$.
• They transmit energy.

## Echo

An echo is a reflection of sound. A sound hits an object and is reflected back to its source.

If you stand inside a large empty room with smooth walls and begin talking you can produce an echo with your voice.

Echoes are used for measuring distances.

Ships use echoes to measure the depth of the ocean. The ship sends a sound wave down towards the sea bed. It is reflected back towards the ship and detected.

The time difference between sending the sound and receiving the echo is recorded.

The speed of sound in water is already known so the depth of the ocean is calculated using $$\text{depth of ocean} = \frac{1}{2} \times \text{time difference} \times \text{speed of sound}$$

A ship uses echo to calculate the depth of the ocean.

## Definition of electric charge

An object carries an electric charge if it can exert a force on other charged objects.

Protons carry a positive ($\Tred{+}$) charge while electrons carry an equal negative ($\Tblue{-}$) charge. Neutrons have no charge.

The total or net charge of an object is equal to the sum of all the positive charges from protons and the negative charges from electrons.

The electric shock you sometimes get when you touch an object is caused by the transfer of charges from the object to your hand.

Any charged object (with a net positive or negative charge) carries an unequal number of protons and electrons. If an object has an imbalance of protons and electrons, it is said to be charged. The imbalance of charges is called static electricity.

If an object carries more electrons than protons, it is negatively charged.

A lithium ion with 3 protons, 4 neutrons and 2 electrons will have the same positive net charge as a single proton.

(Left to right) A positive proton, a neutral neutron and a negative electron (not to scale).

## Definition of resistance

Resistance can be thought of as a quantity that prevents or slows down the flow of charge.

The higher the resistance of a wire, the more energy is lost as a charge flows through it.

Objects lodged in water pipes prevent the flow of water. Similarly, metal atoms in wires prevent the flow of electrons.

The resistance ($R$) of a conductor is the ratio of the potential difference ($\Tblue{V}$) across the conductor to the current ($\Tred{I}$) flowing through it.

$$\text{resistance} = R =\frac{\Tblue{\text{potential difference}}}{\Tred{\text{current}}} = \frac{\Tblue{V}}{\Tred{I}}$$

The SI unit for resistance is the ohm $(\Omega)$. One ohm is equivalent to one volt per ampere (i.e. $1\text{ }\Omega=1\text{ V } / \text{ A}$).

Metals like copper or gold have low resistance while non-metals like plastic and rubber have high resistance.

A common resistor. The coloured bands on the resistor indicate its resistance (given by a colour code chart).

## Series circuits

In a series circuit, the flow of charge only has one path to follow.

An example of a series circuit
• The current $I$ in a series circuit is equal at every point in the circuit ($I=I_{1}=I_{2}=I_{3}=...$).

In a single water pipe, the amount of water passing though the pipe is the same at every point.

• The total potential difference $V$ across all of the components is the sum of the potential difference across each individual component (i.e. $V=V_{1}+V_{2}+V_{3}+...$).

• The total (effective) resistance $R$ is the sum of the resistances of each individual component (i.e. $R=R_{1}+R_{2}+R_{3}+...$).

## Mains power supply

The electrical circuit that supplies electric power to homes is the mains power supply.

In the UK, Europe and Singapore, the mains supply is $230\text{ V}$ A.C. current with a frequency of $50\text{ Hz}$.

Electrical appliances are connected to the mains power supply in parallel. This means that the same voltage is supplied to each appliance.

The mains power supply is made up of two wires that connect the home and the substation:

• The high-voltage ($230\text{ V}$) live wire carries current into the home.
• The zero-voltage ($0\text{ V}$) neutral wire carries current out of the home.

When electrical appliances are plugged in, they are connected to a live wire and a neutral wire, creating a complete circuit. This allows current to flow through the appliance from the live wire to the neutral wire.

The mains power supply is made up of the live wire (brown) and the neutral wire (blue).

## Field lines between two magnets

The field lines around two magnets form distinctive patterns depending on whether the magnets attract or repel.

If two like poles are placed next to each other, the field lines will be drawn from the north pole to the adjacent south pole. The magnets attract.

If two unlike poles are placed next to each other, the field lines will be pushed away from the other magnet. The magnets repel.

Magnetic field pattern between two unlike poles (left) and two like poles (right)

## Currents and magnetic fields

Moving charged particles produce magnetic fields .

A current in a wire produces a magnetic field around the wire.

A moving electron also produces a magnetic field.

Similarly, magnetic fields interact with charged particles . A charged particle that moves through a magnetic field will experience a force.

An electron in a magnetic field will follow a curved path!

Electricity and magnetism are fundamentally connected to each other. The relationship between electricity and magnetism is called electromagnetism.

This is a Tesla coil. It uses alternating currents and magnetic fields to produce impressive lightning-like effects.

## Changing magnetic field causes current

A solenoid is connected in series to a galvanometer as shown below.

A galvanometer measures both the magnitude and the direction of a current.

A bar magnet is moved in and out of the solenoid.

This is the set-up of Faraday's experiment on electromagnetic induction.

Observations:

• Current flows when the bar magnet is moving into the solenoid or out of the solenoid.
• Current is zero when the magnet is stationary.

Conclusion:

• A potential difference (electromotive force) is induced whenever the magnetic field passing through the solenoid changes. This causes a current to flow, which is detected by the galvanometer.