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Numbers and units

The complete measurement is called a physical quantity. It is made up of two parts: a number and a unit.

For example distance is measured as 10 meters, speed as 10metre/seconds, and weight as 100 kg and so on.

A system of units

SI units

Most scientists use SI units (Le Systeme International d’Unites). The basic SI units for measuring mass, time and length are the kilogram, the second, and the meter respectively.

Mass

Mass is a measure of the amount of substance in an object. It has two effects

1. All objects are attracted to the Earth. The greater the mass of an object, the stronger is the Earth’s gravitational pull on it.
2. All objects resist attempts to make them go faster, slower or in a different direction.

Time

The SI base unit of time is the second.

1 millisecond (ms) = (1/1000) s

1 microsecond (µs) = (1/1000000) s

1 nanosecond (ns) = (1/1000000000) s

Length

The SI base unit of length is the meter.

Measuring length

Length from a few millimeters up to a metre can be measured using a rule. If this is not possible, calipers can be used.  Lengths of several meters can be measured using a tape with a scale on it.

Micrometer, Vernier calipers are some more measuring instruments of length.

Measuring time

Time interval of many seconds or minutes can be measured using a stop clock or a stop watch. Some instruments have an analogue and some have a digital display.

Volume and Density

Volume

The quantity of space an object takes up is called its volume. The SI unit of volume is the cubic meter (m³).

Measuring volume

A volume of about a litre or so can be measured using a measuring cylinder. When the liquid is poured into the cylinder, the level on the scale gives the volume.

Density

Density is defined as the ratio of mass and volume. Density is denoted by ρ and measured in kg/m³.

Measuring density

The density of a material can be found by calculation, after measuring the volume and mass.

Density = mass / volume

Relative density

The relative density of a substance tells you how the density compares with that of water. It is calculated by the following formula

            Relative density = density of substance / density of water

Relative density has no units.

Speed, velocity and acceleration

Speed

If a car travels between two points on a road, its average speed can be calculated like this:

            Average speed = distance moved / time taken

If distance is measured in metres (m) and time in seconds (s), speed is measured in metres per second (m/s).

Velocity

Velocity means the speed of something and its direction of travel. Quantities such as velocity which have a direction as well as magnitude (size) are called vectors.

Acceleration

If velocity is changing, then the object is accelerating. Acceleration is calculated by:

            Average acceleration = change in velocity / time taken

                        a= v - u /t

where u is the initial velocity and v is the final velocity.

Acceleration is measured in metres per second² (m/s²). Acceleration is a vector.

A negative acceleration is called a deceleration or retardation. A uniform acceleration means a constant acceleration.

Motion graphs

Distance-time graphs

Graphs can be useful when studying motion. The dependence of position of an object with time can be shown on the following distance-time graph which is shown as below. We can take a convenient scale of choice. Here in the graph, time is taken along x-axis and distance is taken along y-axis. Distance-time graphs can also be used to describe various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.

 

 

 

A graph of distance travelled against time is a straight line, as shown in the above figure

Velocity-Time graphs

The variation in the velocity with time for an object moving in a straight line can be shown by a velocity-time graph. In this graph, time is shown along the x-axis and the velocity is shown along the y-axis. If the object moves at uniform velocity, the height of its velocity-time graph will not change with time. It shall be a straight line parallel to the x-axis.

 

The velocity-time graph for the motion of the car is shown as in the figure below. The nature of the graph shows that the velocity changes by equal amounts in equal intervals of time. Thus, for all uniformly accelerated motion, the velocity-time graph is generally a straight line.

 

The above graphs represent a velocity-time graph. The first graph shows the motion of an object whose velocity is decreasing with time and the second graph represents the motion of object with time with a non-uniform variation.

The acceleration of free fall, g

If you drop a lead weight and a feather, both fall downwards because of gravity. However, the feather is slowed much more by the air. Assume if there was no air resistance. Both objects would fall with the same downward acceleration: 9.8m/s². This is called acceleration of free fall. It is the same for all objects falling near the Earth’s surface.

The acceleration of free fall is represented by the symbol g.

Force, mass and acceleration

A force is a push or a pull exerted by one object on another. It has direction as well as magnitude, so it is a vector. The SI unit of force is the Newton (N). 1 Newton is the force required to give a mass of 1 kilogram and acceleration of 1m/s².

Inertia and mass

If an object is at rest, it takes a force to make it move. If it is moving, it takes a force to make it go faster, slower, or in a different direction. So all objects resist a change in velocity. The resistance to change in velocity is called inertia.

Friction and braking

Friction is the force that tries to stop materials sliding across each other. There is friction between your hands when you rub them together. Friction prevents machinery from moving freely and heats up its moving parts.

Static and dynamic friction

When a block is pulled gently the friction stops it moving. As the force is increased, the friction rises until the block is about to slip. This is the starting or static friction.

With a greater downward force on the block, the static friction is higher. Once the block starts to slide, the friction drops: moving or dynamic friction is less than static friction.

Stopping distance

The car’s stopping distance is the sum of the following:

1. The thinking distance

This is how far the car travels before the brakes are applied, while the driver is still reacting.

2. The braking distance

This is how far the car travels after the brakes have been applied.

It takes an average driver about half a second to react and press the brake pedal. This is the driver’s reaction time.

Gravitational force

If you hang an object from a spring balance, you measure a downward pull from the Earth. This pull is called a gravitational force.

Weight

Weight is another name for the Earth’s gravitational force on an object. It is also measured in newtons (N).

Gravitational field strength, g

A gravitational field is a region in which a mass experience a force due to gravitational attraction. The Earth has a gravitational field around it.

Gravitational field strength is represented by the symbol g. so

    Weight = mass x g,    g = 10 N/kg

           W = mg

On the Moon, your weight would be less than on Earth, because the Moon’s gravitational field is weaker. Moving away from the Earth, your weight decreases.

Action and reaction pairs

Action and reaction are paired forces acting on anybody. One cannot exist without the other.

If object A exerts a force on object B, then object B will exert an equal but opposite force on object A.

To every action there is an equal but opposite reaction.

Vectors and scalars

Quantities such as force, which have direction as well as a magnitude, are called vectors.

Quantities such as mass and volume which have magnitude but no direction are called scalars.

Centripetal force

The inward force needed to make an object to move in a circle is called the centripetal force. More centripetal force is needed if:

1. The mass of the object is increased
2. The speed of the object is increased
3. The radius of the circle is reduced.

Changing velocity

Velocity is speed in a particular direction. So a change in velocity means either a change in speed or a change in direction. If something has a changing velocity, then it has acceleration in the same direction as the force. So with circular motion, the acceleration is towards the centre of the circle.

Orbits

Satellites around the Earth

A satellite travels round the Earth in a curved path called an orbit. Gravitational pull provides the centripetal force needed. When a satellite is put into orbit, its speed is carefully chosen so that its path does not take it further out into space or back to Earth.

Planets around the Sun

The Earth and other planets move in approximately circular paths around the Sun. the centripetal force needed is supplied by the Sun’s gravitational pull.

Electrons around the nucleus

In atoms, negatively charged particles called electrons are in orbit around a positively charged nucleus. The attraction between opposite charges provides the centripetal force needed.

Forces and turning effects

Moment of a force

The turning effect of a force is called a moment. It is calculated like this:

Moment of a force about a point = force x perpendicular distance from the point.

Moments are described as clockwise or anticlockwise depending on their direction. The moment of a force is also called a torque.

The principle of moments

If an object is in equilibrium: the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about this point.

Conditions for equilibrium

If an object is in equilibrium, the forces on it must balance as well as their turning effects. So:

1. The sum of the forces in one direction must be equal to the sum of forces in the opposite direction.
2. The principle of moments must apply.

Types of equilibrium

There are three types of equilibrium:

1. Stable equilibrium
2. Unstable equilibrium
3. Neutral equilibrium

Centre of mass

Consider a beam. It is made up of lots of tiny particles each with a small gravitational force on it. The beam balances when suspended at one particular point, G, because the gravitational forces have turning effects about G which cancel out. G is the centre of mass or centre of gravity.

Principle of moments

If a system is in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that point.

Stretching and compressing

Elastic and plastic

If we bend a ruler slightly and release it, it springs back to its original shape. Materials that behave like this are called elastic. They stop being elastic if bent or stretched too far. They either break or become permanently deformed.

If you stretch or bend plasticine, it keeps its new shape. Materials that behave like this are called plastic.

Consider a spring. A load is applied on the spring and it starts stretching. As the load is increased, the spring stretches more and more. Its extension is the difference between its stretched and unstretched lengths. Till a point, the extension is proportional to the load. This point is called limit of proportionality. Till Elastic limit, the spring behaves elastically and returns to its original length when the load is removed. Beyond the Elastic limit, the spring is left permanently stretched.

Hooke’s law

In 1660, Robert Hooke investigated how springs and wires stretched when loads are applied. He found that for many materials the extension and load were in proportion, provided the elastic limit was not exceeded:

A material obeys Hooke’s law if the extension is proportional to the load beneath its elastic limit.

Spring constant

Load = spring constant x extension

In symbols, F= k X x

Compressing and bending

Materials can be compressed as well as stretched. If the compression is elastic, the material will return to its original shape when the forces are removed. When a material is bent, the applied forces produce compression on one side and stretching on the other. If the elastic limit is exceeded, the bending is permanent.

Pressure

Pressure is defined as the force per unit area. In symbols,

P = F/A

Units of pressure are N/m². 1 N/m² is called 1 Pascal (Pa). Pascal is a very small unit. In practical situations, it is often more convenient to use the kilopascal (kPa)

1kPa = 1000 Pa

Pressure in liquids

A liquid is held in its container by its weight. This causes pressure on the container. The following properties apply to any stationary liquid in an open container.

Pressure acts in all directions

The liquid pushes on every surface in contact with it, no matter which way the surface is facing.

Pressure increases with depth

The deeper into a liquid you go, the greater the weight of liquid above and the higher the pressure.

Pressure depends on the density of the liquid

The more dense the liquid, the higher the pressure at any particular depth.

Pressure doesn’t depend on the shape of the container

Whatever the shape or width, the pressure at any particular depth is the same.

Calculating the pressure in a liquid

The pressure in a liquid is calculated by the formula,

                        Pressure = ρgh

Hydraulic systems

The machines in which the forces are transmitted by liquids under pressure rather than by levers are called hydraulic machines. They make use of the following properties of liquids:

1. Liquids are virtually incompressible. They cannot be squashed.
2. If a trapped liquid is put under pressure, the pressure is transmitted to all the parts of the liquid.

Hydraulic brakes, hydraulic jack are some hydraulic systems that work with the above principle. Car brakes work hydraulically and a hydraulic jack is used to lift loads easily.

A hydraulic press is used for compressing things.

Atmospheric pressure

At sea level, atmospheric pressure is about 100kPa. It is equivalent to the weight of ten cars pressing on every square metre.

Instruments that measure atmospheric pressure are called barometers.

Standard atmospheric pressure

The pressure that will support a column of mercury 760.0 mm high is known as standard atmospheric pressure or 1 atmosphere.

A manometer measures pressure difference. The height difference in the tube for which the pressure is to be measured, show the extra pressure that the gas supply has in addition to atmospheric pressure. This extra pressure is called excess pressure. To find the actual pressure of the gas supply, you add atmospheric pressure to this excess pressure.

Gas pressure and volume

When dealing with a fixed mass of gas, there are always three factors to consider: pressure, volume and temperature. A change in one of these factors always produces a change in at least one of the others.

Boyle’s law

For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.

P₁ x   V₁   =   P₂ x V₂

A gas that obeys Boyle’s law is called an ideal gas. Real gases come close to this provided they have a low density, a temperature well above their liquefying point. An idea gas has no attractions between its molecules.

Work and energy

Work

Work is done whenever a force makes something move. The greater the force and the greater the distance moved, the more work is done.

The SI unit of work is the joule (J).

1 joule of work is done when a force of 1 Newton moves an object 1 metre in the direction of the force.

Work done = force x distance moved in the direction of the force

W= F x d

Energy

Things have energy if they can be used to do work.  Energy is also measured in joules like work.

Forms of energy

The various forms of energy are:

Kinetic energy

This is energy due to motion. All moving objects have kinetic energy.

Potential energy

Potential Energy is defined as the work done against a given force in changing the position of an object with respect to a reference position.

There are several different types of potential energy

Gravitational potential energy

A stone held up in the air can do work when dropped because gravity will pull it downwards. The stone has Gravitational potential energy

Elastic potential energy

A stretched rubber band can do work when released as it has elastic potential energy.

Chemical potential energy

When a fuel burns, its energy is released by chemical reactions. The energy stored in the fuel is called chemical potential energy (chemical energy).

Electrical potential energy

In circuits, the current is a flow of tiny charged particles called electrons. Electrons can transfer energy. They have electrical potential energy (electrical energy).

Nuclear potential energy

An atom has nucleus at its centre. This is made up of particles held there by strong forces. The nucleus splits and energy is released. This is called nuclear potential energy (nuclear energy).

Thermal energy

When hot objects cool down, their atoms and molecules slow down and lose energy. This is called thermal energy or heat.

Radiated energy

The Sun radiates light. Loud speakers radiate sound. Light and sound both travel in the form of waves. These carry energy.

Conservation of energy

Energy cannot be made or destroyed, but it can change from one form to another. This is called the law of conservation of energy.

Work done = energy transformed

Calculating Potential energy (P.E.)

The potential energy is due to the Earth’s gravitational pull. The potential energy is calculated by the following formula:

Gravitational potential energy = mgh

Calculating Kinetic energy (K.E.)

The kinetic energy of any object is equal to the work which the object could do by losing all of its speed.  It is calculated by the following formula:

Kinetic energy = force x distance moved

Substituting all the parameters we get KE = ½ mv²

Energy is a scalar quantity as it has magnitude but no direction.

Efficiency

Efficiency is defined as the ratio of useful work done to the total energy output. It can be also defined as the useful energy output to the total energy input.

Power

Power is defined as the rate at which the work is done. The SI unit of power is watt (W). A power of 1Watt means that work is being done at the rate of 1 joule per second.

Power = work done / time taken

Thus efficiency can be defined as

Efficiency = useful power output/ total power input

Energy for electricity

Industrial societies spend huge amount of energy. Much of it is supplied by electricity which comes from generators in power stations

Thermal power stations

In most power stations, the generators are turned by turbines, blown round by high pressure steam. To produce steam, water is heated in a boiler. The thermal energy comes from burning fuel or from a nuclear reactor. Nuclear fuel does not burn. Its energy is released by nuclear reactions which split uranium atoms. The process is called nuclear fission.

Energy spreading

Thermal power stations waste more energy than they deliver. Most is lost as thermal energy in the cooling water and waste gases. Engineers try to make power stations as efficient as possible. But once energy is in thermal form, it cannot all be used to drive generators. Thermal energy is the energy of randomly moving particles. It has a natural tendency to spread out. As it spreads, it becomes less and less useful.

District heating

The unused thermal energy from a power station does not have to be wasted. It can heat homes, offices using long water pipes.

Reactions for energy

When fuels burn, they combine with oxygen in the air. With most fuels, the energy is released by this chemical reaction:

Fuel + oxygen            →          carbon dioxide + water + thermal energy

Pollution problems

Thermal power station can cause pollution in a variety of ways:

1. Carbon dioxide is released into the atmosphere. It traps sun’s energy and adds to global warming.
2. Sulphur dioxide can damage stone work and harm wild life
3. Transportation of fuels can cause pollution.
4. The radioactive waste from nuclear power plant is highly dangerous. 

Energy resources

The energy resources on earth can be renewable or non-renewable.

Renewable energy resources

Hydroelectric energy

A river fills a lake behind a dam. Water flowing down from the lake turns generators.

Problems

It is expensive to build and only few areas of the world are suitable. Flooding land and building a dam causes environmental damage.

Tidal energy

Tide is the rise or fall of water due to the attraction of moon. The rise of water is called high tide and the fall is called low tide. This movement of water produces a large amount of energy which is called tidal energy. This tidal energy can be used by constructing a dam.

Wind energy

When large volumes of air move from one place to another it is referred to as wind. In this process kinetic energy gets associated with it which is referred to as wind energy.

Problems

Large, remote, windy sites are needed. Winds are variable. The wind turbines are noisy and can spoil the landscape.

Wave energy

Wave energy is the energy obtained from high speed of waves in sea. These waves have a lot of kinetic energy which can be converted into electrical energy using dynamos.

Problems

Difficult to build.

Geothermal energy

Geothermal energy is the heat of the earth and is the naturally occurring thermal energy found within rock formations and the fluids held within those formations. Geothermal energy does not come directly or indirectly from the solar energy.

Problems

Deep drilling is difficult and expensive.

Solar energy

The energy produced by the sun in the form of heat and light is called solar energy. Solar panels absorb this energy and use it to heat water. Solar cells are made from materials that can deliver an electric current when they absorb the energy in light.

Problems

Variable amounts of sunshine in some countries. Solar cells are expensive.

Biofuels

These are fuels made from plant or animal latter sometimes called biomass. They include alcohol, wood, and methane gas from rotting waste.

Problems

Huge areas of land are needed to grow plants.

Saving energy

Burning fossil fuels causes pollution. But the alternatives have their own environmental problems. We should be less wasteful with energy. Methods could include using public transport and bicycles instead of cars and recycling more waste materials.