They are electromagnetic waves that are transverse waves caused by oscillations in an electromagnetic field.
They transfer energy and are transverse waves with oscillations perpendicular to the direction of energy transfer.
They have very short wavelength ( about an atom diameter)
They cause ionisation by adding or removing electrons.
They affect photographic films
They are absorbed by metals and bones
They are transmitted by healthy body tissues
In old X ray machines you can put a white photographic film behind a patient and x ray will pass through it into the photographic film turning it black.
It will be absorbed by X ray so it stays white where the bones are and dark where there aren't bones.
CCDs
Charged Coupled devices are used to form the images electronically allowing them to be recorded and stored more easily
CT scans
Computerised tomography is where you use x-rays and a computer to create detailed images of the inside of the body and requires taking a range of x ray images from various angles.
A computer processes these images and builds a 3D image which can be manipulated to see different layers at different angles of the body. Allows doctors to get a greater insight.
Ionising effect of X rays
The ionising effect can damage the DNA of the nucleus of cells.
These can lead to cancer.
Low doses may cause cancer and high doses may kill cancerous cells
Treatment
Tumors formed by cells dividing uncontrollably because of the change in DNA.
Directing high energy x rays at these can cause so much damage they they die and this is called radiotherapy.
Precautions
Patients are limited to the number of x rays scans so they are not exposed to too much radiation.
Hospital staffs are shielded by walls containing lead in x ray rooms.
Radiographers routinely leave the room or stand behind a screen. they wear a lead apron which acts as a protective layer of clothing
Ultrasound
These are high frequency sound waves that is too high for humans to hear - over 20,000 Hz.
When ultrasound waves reach a boundary between 2 media with different densities, they are partially reflected back. The remainder continues to pass through.
A detector can be placed near the source of the ultrasound and can detect the reflected wave.
It can measure the time between an ultrasound wave leaving the source and reaching the detector.
s= v*t
When it is an echo- a reflection, divide the distance by 2 because it had traveled both ways.
Medical imaging
prenatal scanning to check a foetus is developing normally. Computers combine many ultrasound reflection to produce a detailed image.
They can also be used to scan organs to look for signs of disease
Kidney stones can be treated by focusing ultrasound at them causing them to vibrate and breaking into smaller pieces so they can be passed out in the urine.
Comparing Ultrasound and X ray
X rays have a much shorter wavelength so they can produce higher quality images than ultrasound scans they show grater detail and vital in detecting small bone fractures.
CT scans provide even more high quality images and can see different layers other other structures obscuring the area of interest.
However x rays are ionising and can damage living tissue and DNA within cells.
Rapid dividing of cells are particularly vulnerable.
This makes them damaging to a developing foetus. Ultrasound waves are not ionising so they are safe to use.
Lenses
Refraction
this is when light changes direction when it passes from one medium to another. The two media must have different densities.
When light passes into the denser medium. the light bends towards the normal ( 90 degree from the surface) which means the angle of incidence is greater than the angle of refraction.
When light passes into a less dense medium, it speeds up so it moves away from the normal which makes the angle of incidence smaller.
Refractive index
Depends on:
The angle the light hits the boundary between the substances.
The difference in relative densities between 2 media.
The degree to which a material slows the speed of light is its refractive index.
Calculation
refractive index = sin i / sin r
incidence and refraction angles are from the normal.
Lenses
A lens is a transparent block they causes light to refract to form an image.
They can be converging or diverging
These have different effects on light and form different types of images.
This depend on the refractive index and how curved the lenses are.
Converging lenses
They are curved outwards on both sides.
Rays from a single point on a distant object arrive at the lens parallel to one another
Converging lens refract these parallel rays so they come together at a point called the principal focus labelled F.
These lens focus the rays to produce a real image that can be projected on a screen. The focal length is the distance between the centre of the lens and the image.
Diverging lenses
They curve inwards on both sides
They refract parallel rays of light so they spread apart from one another. They form a virtual image that cannot be projected onto a screen.
The diverging rays can only be seen by the eye and appear as having come from a different point to where the object is.
The point at which the rays appear to have come from is the principal focus. The focal lenth is the distance between the centre of the lens and the virtual image.
Ray diagrams
Show action of converging lenses
Ray diagrams allow us to work out the nature of the image
They can be
Magnified or diminished
Upright or inverted
Real or virtual
Nature if images from convex lenses
Where object is compared to the principal focus determines the image nature.
Closer than F Magnified upright and virtual with the position same as the object
F no image because the emerging rays tare parallel to the axis.
2F and F Magnified inverted real and position is further than 2F.
2F Same size inverted real and position is at 2F
Further than 2F is diminished inverted real and between 2F and F
The image is inverted and real unless object is at F or closer
Gets larger as object gets closer
Gets further away as the object gets closer unless the object is at F or closer.
Magnifying glasses
If the object is placed between the principal focus F and the lens, a converging lens will produce a magnified upright, virtual image which can only be seen by looking through the lens. It will appear on the same side of the lens as the object.
The magnification can be worked out by
Magnification = image height / object height
We can state that
A magnification above 1 = larger
below 1 = smaller
1 = same size
Nature of images form diverging lenses
They always produce images that are virtual, upright and diminished in size compared to the object.
The image always appears to come from the same side of the lens as the object.
Ray diagrams
As the image is virtual the rays leaving the lens must be traced backwards in straight lines until they reach a point where they cross. This is where the virtual image appears to come from.
The eye
Cornea- Convex lens outside that reflects light as it enters the eye by a fixed amount
Iris- Muscles that contract and relax to adjust the size of the pupil and controls how much light enters the pupil
Pupil- a hole that allows light to pass through
Lens Transparent bi convex flexible disk that is attached to the ciliary muscles by the suspensory ligament. They refract light to focus onto the retina the amount can be adjusted by altering the thickness and curvature of the lens.
Ciliary muscles- Muscles that is connected to the lens and adjusts the shape of the lens to make it more or less curved.
Suspensory ligaments Holds the lens in place. Slacken or stretch as the ciliary muscles contract or relax
Retina- lining at the back of the eye where rods and cones are. Contains light receptors that trigger electrical impulses toe the brain when light is detected.
Accommodation
The eye changes the shape of the lens to adjust the degree of refraction.
The ciliary muscles contract for near objects which makes the suspensory ligaments slacken and make the muscle tension on the lens low so it is fat and more curved.
The ciliary muscles relax for distant objects which stretch the suspensory ligaments and make the muscle tension on the lens high that makes it thin and less curved.
The near point is the closest and object can be seen from the eye without it blurring our lens cannot sufficiently curve to refract the diverging rays to focus them on the retina This is normally 25 cm.
Long sighted people has this further than 25cm.
The far point is the furthest and object can be from the eye without it blurring.
The eye of someone without vision defects has this at infinity as light rays arrive parallel to each other.
Some one with short sightedness has this closer than infinity which means they cannot focus on distant objects.
The near point and the far point difference is the range of vision.
Camera
Cameras are devices that focus light onto a photosensitive surface using a convex lens.
The image is diminished inverted and real.
Lens = Lens
Focusing screw = ciliary muscles
Aperture= Iris
Shutter= eyelids
Photo sensitive surface= retina
It does not change shape of the lens but move it forward + backwards.
Correcting vision defects
Short sight
Someone with short sight can see near objects clearly, but their far point [far point: The farthest point from the eye at which images are clear.] is closer than infinity. This means they cannot focus properly on distant objects.
Short sight is caused by one of the following:
The eyeball being elongated - so that the distance between the lens and the retina is too great.
The lens being too thick and curved - so that light is focused in front of the retina.
Short-sightedness can be corrected by placing a diverging lens [diverging lenses: A lens that causes a parallel beam of light passing through it to diverge (spread out).] in front of the eye, as shown in the diagrams below.
Myopia - short-sightedness
Concave lens cures short-sightedness
Long sight
Someone with long sight can see distant objects clearly, but their near point is further away than 25 cm. This means they cannot focus properly on near objects.
Long sight is caused by one of the following:
The eyeball being too short - so the distance between the lens and retina is too small.
A loss of elasticity in the lens - meaning it cannot become fat enough to focus (which is often age-related).
As a result, the lens focuses light behind the retina instead of onto it. Long-sightedness is corrected by putting a converging lens in front of the eye, as shown in the diagrams below.
An image passing through an eye lens and focusing behind the retina equates to long-sightedness (Hypermetropia)
A convex lens corrects long-sightedness, allowing an image to focus on the retina
Power of lenses
When correcting long or short sightedness, an optometrist [optometrist: A specialist in eye examination.] must choose a lens that refracts the light sufficiently for light to be focused onto the retina. The degree to which a lensrefracts [refraction: There is refraction when waves or light change direction as they move from one substance to another.] the light is the power of the lens, measured in dioptres, D.
Lens power can be calculated using the following equation
P = 1/f
where: P = lens power in dioptres, D
f = focal length in metres, m
The focal length [focal length: The distance between the optical centre and the focal point.] , f, of a lens is determined by two factors:
the refractive index [refractive index: A measurement of the speed at which light passes through a substance, relative to the speed of light in a vacuum. It also indicates how much light will be bent when it passes from one substance into another.] of the material that the lens is made from the curvature of the two surfaces of the lens (how thick or fat the lens is)
Note that the power of a diverging lens (used to correct short-sight) isnegative, while the power of a converging lens (used to correct long-sight) is positive.
Worked example 1
Two diverging lenses with near and far objects
In this case, the lens on the left is more powerful as it has a shorter focal length, f. Diverging lenses always give a negative lens power value.
Worked example 2
Two converging lenses with near and far objects. One has a focal length of 10cm the other 40cm.
In this case, the lens on the left is more powerful as it has a shorter focal length, f. Converging lenses always give a positive lens power value.
Read on if you're taking the higher paper.
Power of lenses - Higher tier
People who have short or long sightedness require a certain lens power, with a certain focal length [focal length: The distance between the optical centre and the focal point.] , to correct their vision.
For a given focal length, the greater the refractive index [refractive index: A measurement of the speed at which light passes through a substance, relative to the speed of light in a vacuum. It also indicates how much light will be bent when it passes from one substance into another.] , the flatter the lens can be. This means that modern lenses made from materials with a high refractive index are thinner, making them lighter for people to wear.
The properties of light mean that it has been used in many modern-day applications at home, in industry, and in the field of medicine. Lasers are used in applications ranging from cutting materials to laser eye surgery. Optical fibres can carry large amounts of information for use in telecommunications, and they allow detailed images from endoscopes.
Lasers
A laser [laser: An intense beam of light that is monochromatic and coherent (in phase).] produces an intense narrow beam of light. Laser light has a low divergence - which means that it spreads out very little.
Lasers can be used as an energy source for many applications:
cutting through materials (such as metal)
burning (eg laser engraving)
cauterising
Cauterising
In medicine, lasers are used to destroy damaged tissue or to stop bleeding, eg after surgery. This is known as cauterising.
Lasers are used in eye surgery to repair damaged retinas [retina: The inside layer in the eye that is responsive to light.] and to correct vision defects. A laser can be used to precisely cut the cornea [cornea: The transparent front part of the eye.] , altering its shape to correct a person’s vision.
Laser eye surgery
Total internal reflection
Light going from a dense medium, such as glass, into a less dense medium, such as air, speeds up at the boundary. This causes light rays to bend when they pass from glass to air at an angle other than 90º. This is refraction [refraction:There is refraction when waves or light change direction as they move from one substance to another.] . However, not all of the light refracts - and a small amount reflects back into the glass.
As the angle of incidence [angle of incidence: Angle between the normal and a light ray travelling towards a mirror or into another substance.] increases, so does the angle of refraction [angle of refraction: Angle between the normal and a refracted light ray.] . Beyond a certain angle, called the critical angle, all the waves reflect back into the glass and no refraction occurs. This is known as total internal reflection.
Optical fibres
An optical fibre is a thin rod of high-quality glass. Light getting in at one end undergoes repeated total internal reflection [total internal reflection:Complete reflection of a light ray reaching a boundary at greater than the critical angle.] - even when the fibre is bent - and emerges at the other end.
Total internal reflection in optical fibres
Optical fibres have become very important in high-speed communications, such as cable TV and high-speed broadband [broadband: high speed Internet access] services.
Information, in the form of pulses of light, is sent down bundles of optical fibres. Fibre optic cables are able to carry more signals than traditional copper cable telephone lines.
Bundles of optical fibres
Endoscopes
Endoscopes [endoscope: An instrument used in medicine to help examine the inside of the body, which uses a bundle of optical fibres to transmit the image around corners.] also use optical fibres. A doctor can insert a bundle of optical fibres into the body. Some carry light into the body, and some carry light reflected off internal body surfaces back out. This allows the doctor to see the inside of the body clearly – and help them diagnose diseases like cancer, or see what they are doing during keyhole surgery.
Endoscope examination and biopsy of the stomach
Read on if you're taking the higher paper.
Total internal reflection and the critical angle – Higher tier
The critical angle is the angle above which total internal reflection [total internal reflection: Complete reflection of a light ray reaching a boundary at greater than the critical angle.] occurs. It varies depending on the refractive index [refractive index: A measurement of the speed at which light passes through a substance, relative to the speed of light in a vacuum. It also indicates how much light will be bent when it passes from one substance into another.] of the material - the lower the refractive index, the higher the critical angle
The critical angle of a material can be calculated using this equation:
refractive index = 1/sin c
where c is the critical angle in degrees, °
Worked example 1
Calculate the refractive index for water, which has a critical angle of 49°.
Step 1: Calculate sin c
sin 49° = 0.75
Step 2: Substitute the value of sin c into the equation
refractive index = 1 ÷ sin c
refractive index = 1 ÷ 0.75 = 1.33
Worked example 2
Calculate the critical angle for glass (refractive index 1.5).
Step 1: Change the subject of the equation to find c
sin c = 1 ÷ refractive index
Step 2: Put in the number from the question
sin c = 1 ÷ 1.5 = 0.67
Step 3: Work out the inverse sine (sin -1)
c = 42°
In many applications it is important that objects are designed with stability in mind. This requires an understanding of the centre of mass, as well as an ability to find out where it is. By incorporating a low centre of mass and wide base into an object, we can reduce the chance of it toppling over.
The centre of mass
Mass is the amount of matter an object has. Every part of an object forms part of its overall mass. But when we try to balance an object on a point, there will only be one place where it will balance. You can therefore think of the mass of an object being concentrated at this point, known as the centre of mass.
Finding the centre of mass for symmetrical objects
The centre of mass for a symmetrical object can be found easily. The axes of symmetry [axis of symmetry: An imaginary line through a figure that divides the figure into two symmetrical parts which are mirror images of each other. A figure may have more than one axis of symmetry.] are marked on the object. The centre of mass is where the axes of symmetry cross.
The centre of mass
Finding the centre of mass by suspending objects
The centre of mass for an irregular shaped, non-symmetrical object is found in a different way.
Drill a small hole in the object and hang it up so that it is free to swing without obstruction.
Hang a plumb line (a piece of string with a weight hanging from it) from the same suspension point. This lets you mark the vertical line directly below the suspension point.
Drill another hole at a different location within the object.
Again hang a plumb line to determine the vertical and mark it on.
The point at which the two marked lines cross is the centre of mass.
Note - you should be able to describe how to do this for your exam.
How to find the centre of gravity on one shape
Simple Pendulums
A plumb line is an example of a simple pendulum. This is a simple machine consisting of a weight (called a bob) suspended from a suspension point by a thin piece of material such as string or a chain. The bob should be free to swing.
Kinetic energy in a swinging ball
Common examples of pendulums include:
swings at playgrounds
some fairground rides - eg pirate ship rides
the inside mechanisms of some clocks - eg grandfather clocks
A woman pushing a boy on a swing set
Calculating time period for a pendulum
The time period for a pendulum, T, is the time taken for a pendulum to swing from one side to the other, and then back again to its original position.
The number of complete swings (from one side to the other and back again) made by a pendulum per second is its frequency, f.
Time period and frequency are related by the equation:
T = 1/f
where:
T = time period in seconds, s
f = frequency in Hertz, Hz
The time period of one swing of a pendulum is dependent only upon the length of the pendulum and not upon the mass of the bob, or how high it swings. Longer pendulums have greater time periods than shorter pendulums.
Worked example
A pendulum has a frequency of 2.0 Hz. Calculate the time period for one swing of the pendulum.
Time period
= 1 ÷ frequency
= 1 ÷ 2.0
= 0.5 s
Stability of objects
Stability is a measure of how likely it is for an object to topple over when pushed or moved. Stable objects are very difficult to topple over, while unstable objects topple over very easily.
The stability of an object is affected by two factors:
the width of the base of the object
the height of its centre of mass [centre of mass: The point representing the mean position of the matter in a body.]
Objects with a wide base, and a low centre of mass, are more stable than those with a narrow based and a high centre of mass.
The wider car will not topple over because it has a lower centre of gravity, but the narrow car will
If you are standing in a bus that is accelerating or braking, you usually spread your feet apart to increase the width of your base to make you more stable.
Everyday objects are also designed with this in mind. For example, a traffic cone has a wide base and is weighted at the bottom to give it a low centre of mass.
Motorway traffic cones
Buses have a wide base between the tyres and a low centre of mass (because the heavy engine is mounted low down).
A bus has a low centre of gravity because of its low heavy engine and will only topple if it is at an extreme angle
We utilise the turning effect of forces (moments) on a daily basis, for example when we use devices such as levers. However, in some circumstances we need to prevent the turning effect of forces by balancing them with an opposing moment. Understanding the principles involved allows us to both utilise and prevent the turning effect of forces.
Moments
A moment is the turning effect of a force around a fixed point called a [pivot:A point around which rotation occurs.] pivot. For example, this could be a door opening around a fixed hinge or a spanner turning around a fixed nut.
The size of a moment depends on two factors:
the size of the force applied
the perpendicular [perpendicular: At right angles to.] distance from the pivot to the line of action of the force
This explains why less force is needed to open a door by pushing at the side furthest from the hinge than at the side closest to the hinge. To push at the hinge side of the door requires more force to be exerted because the distance is smaller.
A moment can be calculated using this equation:
M = F × d
where:
M = the moment of the force in newton-metres, Nm
F = the force in newtons, N
d = the perpendicular distance from the line of action of the force to the pivot in metres, m
Worked example
A spanner is used to undo a nut. A force of 25 N is applied to the end of the spanner, which is 10 cm away from the centre of the nut. Calculate the moment when the spanner is horizontal.
10 cm
= 10 ÷100
= 0.10 m
moment
= force × perpendicular distance
moment
= 25 × 0.10
= 2.5 Nm
Balancing moments
Where an object is not turning around a pivot, the total clockwisemoment [moment: The turning effect of a force.] must be exactly balanced by the total anti-clockwise moment. We say that the opposing moments are balanced:
sum of the clockwise moments = sum of the anti-clockwise moments
See-saws
the person on the right exerts a force downward - which causes a clockwise moment
the person of the left exerts a force downward - which causes an anti-clockwise moment
If the people are identical weights and sit identical distances from the pivot, the see-saw will balance. This is because the total clockwise moment is balanced by the total anti-clockwise moment.
The see-saw can still be made to balance even if the people are different weights. To do this, the person with the bigger weight must sit closer to the pivot. This reduces the size of the moment so the opposing moments are once again balanced.
Cranes
Construction cranes lift heavy building materials using a horizontal arm called a jib. To prevent the crane toppling over, concrete blocks are suspended at the other end of the jib. They act as a counter-weight to create a moment that opposes the moment due to the load.
Crane lifting block of limestone
Levers
A lever is a simple machine that makes work easier to do. Examples of simple levers include cutting with scissors, or lifting the lid on a tin of paint with a screwdriver. Levers reduce the force needed to perform these tasks.
When someone uses a lever, they exert a force (the effort) around apivot [pivot: A point around which rotation occurs.] to move an object (the load).
A see-saw style lever
Levers rely on the principle of moments [moment: The turning effect of a force.] to act as ‘force multipliers’ - they reduce the effort needed to move the load by increasing the distance over which it is acting. This means a relatively small effort force has a much greater effect.
The hammer
A hammer can be used to pull out a nail from a piece of wood.
A hammer pulls a nail out of wood
The load force [load force: A force that opposes or resists an effort force.] is 50 N and it acts at a perpendicular [perpendicular: At right angles to.] distance of 0.07 m. Its moment is 3.5 Nm (50 × 0.07).
The effort force [effort force: The force used to move an object over a distance.] acts at a longer perpendicular distance. This is 0.28 m or four times the distance of the load force. As a result, the effort needed is four times less than the load force, or 50 ÷ 4 = 12.5 N.
Note that the moment of the effort is 3.5 (12.5 × 0.28) – the same as the moment of the load.
In this case an effort force of 12.5 N is sufficient to pull against the load force of 50 N, making it relatively easy to pull the nail out.
Other examples
Levers also act as force multipliers in the following examples. Note that the load and effort can both be on the same side of the pivot, as shown in the wheelbarrow example.
Examples of levers
Read on if you're taking the higher paper.
Calculating how to balance moments – Higher tier
In your exam, you will be expected to calculate the force or distance that must be exerted on one side of a pivot [pivot: A point around which rotation occurs.] in order to balance out the moments [moment: The turning effect of a force.] .
Balanced moments
Step 1: Work out the moment for which you have been given all of the information
In this case it is the anti-clockwise moment.
moment
= force × perpendicular distance
moment
= 500 × 2
= 1000 Nm
Step 2: Change the subject of the equation to calculate the force
Remember that for the see-saw to be balanced, the total anti-clockwise moment must be equal to the total clockwise moment. Therefore the clockwise moment must be 1000 Nm.
moment
= force × perpendicular distance
force
= moment ÷ perpendicular distance
force
= 1000 ÷ 1.5
= 666.7 N
Stability – Higher tier
Weight pulls from an object’s centre of mass [mass: The amount of matter an object contains. Mass is measured in 'kg'.] in a vertical direction toward the Earth. This is known as the line of action of the object’s weight [weight: The force on an object caused by the pull of the Earth's gravity.] .
As an object is tilted, the line of action will continue to pull down in a vertical direction. If the line of action moves outside the base of the object, there will be a resultant moment [resultant moment: The difference between two opposing turning forces (moments).] and the object will topple over. For example, consider a lab stool.
A stool in three stages of toppling
In the left-hand scenario, the line of action of the stool’s weight is acting downwards from the centre of mass in the centre of the stool’s base. Note that the centre of mass is not within a solid part of the chair.
In the middle scenario, the stool has been tipped slightly. However, the line of action of the stool’s weight is still within the base of the stool. Therefore the clockwise moment is greater than the anticlockwise moment and the stool falls back to its upright position.
In the right-hand scenario, the stool has been tipped even further. Now the line of action of the stool’s weight falls outside the base of the stool. Therefore the anti-clockwise moment is greater than the clockwise moment and the stool topples over.
Pressure can be transmitted through liquids. In hydraulic machines, exerting a small force over a small cross-sectional area can lead to pressure being transmitted, creating a large force over a large cross-sectional area. This ability to multiply the size of forces allows hydraulics to be used in many applications such as car-braking systems.
Pressure in liquids
Particles in liquids are close together, making liquids virtuallyincompressible [incompressible: Cannot be compressed.] . As the particles move around, they collide with other particles and with the walls of the container. The pressure in a liquid is transmitted equally in all directions, so a force exerted at one point on a liquid will be transmitted to other points in the liquid.
Pressure is calculated using the equation:
where:
P = pressure in pascals, Pa
F = force in newtons, N
A = cross-sectional area in metres squared, m2
Worked example
A force of 250 N is exerted over an area of 10 m2. What is the pressure?
pressure
= force ÷ cross-sectional area
pressure
= 250 ÷ 10
= 25 Pa
Hydraulics
The pressure in a liquid is equally transmitted in all directions. This means that when a force is applied to one point of the liquid, it will be transmitted to other points within the liquid.
A bucket, filled with water, has holes in it. The water coming from each hole gives out equal pressure.
This principle can be exploited in hydraulic machines. Imagine that two syringes of different sizes were connected by tubing and filled with water.
Two syringes showing force in and force out
An effort force [effort force: The force used to move an object over a distance.] exerted on the plunger for syringe A puts greater pressure on the water in tube A. As water is virtually incompressible [incompressible: Cannot be compressed.] , the pressure is transmitted through the water into syringe B. The water pushes against the plunger in syringe B with equal pressure, exerting a load force [load force: A force that opposes or resists an effort force.] on it.
However, tube B has a plunger with a bigger cross-sectional area than tube A. This means that the load force exerted is larger than the effort force exerted. This is known as a force multiplier [force multiplier: Something that increases the effect of a force.]
Hydraulic systems therefore allow smaller forces to be multiplied into bigger forces. Note, however, that the bigger syringe moves a shorter distance than the smaller syringe.
Worked example
Study the diagram of the hydraulic jack [jack: Mechanical device used to lift heavy loads or apply great forces.] . Calculate the force on piston B.
Hydraulic jack
Step 1: Calculate the pressure of the liquid inside piston A
Force in piston A
= 30 N
Cross-sectional area in piston A
= 0.2 m2
pressure
= force ÷ cross-sectional area
pressure
= 30 ÷ 2
= 150 Pa
Step 2: Change the subject of the equation to find the force in piston B
Remember that the pressure within this closed system [closed system: A system in which inputs loop around continuously, for example, the water cycle. No reactants or products enter or leave the system.] is transmitted equally in all directions. Therefore the pressure in piston B is also 150 Pa.
Cross-sectional area in piston B = 1.0 m2
force
= pressure × cross-sectional area
force
= 150 × 1.0
= 150 N
In this example, the hydraulic jack can lift load forces five times greater than the effort force put in.
Applications of hydraulics
It takes a large force to slow down or to stop a car that is travelling at speed.Hydraulics are used in the braking system of a car. They cause a relatively small force from the driver’s foot to be multiplied to produce a greater force, which acts equally on all four brake pads.
How car brakes work
The force from the driver’s foot (the effort force [effort force: The force used to move an object over a distance.] ) exerts pressure on the brake fluid in a small piston [piston: A moving component of a machine that is contained by a cylinder and is made gas-tight by piston rings.] . The pressure is transmitted throughout the brake fluid in all directions.
Next to each brake disc, there is a much larger piston with a greater cross-sectional area. The transmitted pressure acts on this larger area to produce a larger load force [load force: A force that opposes or resists an effort force.] on the brake pads. The pads then rub against the brake discs and cause the car to slow down.
Hydraulic systems are also found in:
lifting equipment - eg hydraulic jacks and wheelchair lifts
lifting and excavating arms on machinery such as diggers
hydraulic presses - which are used during the forging of metal parts
wing flaps and some rudders on aircraft and boats
Hydraulic grapple lifting scrap steel
Objects travelling in a circular motion are prevented from moving off in a straight line by centripetal force. This resultant force pulls objects toward the centre of the circle, continually changing the direction that an object is travelling in to keep it in circular motion.
Centripetal force
There are many examples of objects travelling in a circular motion. For example:
fairground rides
a hammer-thrower spinning a hammer
the Earth orbiting the Sun
These objects continuously change direction as they move in a circle. This needs a resultant force [resultant force: The overall force acting on an object, taking into account the sizes and directions of all other forces.] to act on the object. This force is the centripetal force. The centripetal force pulls an object toward the centre of the circle.
An object moves in a circular motion and the centripetal force acts towards the centre of the circle.
Centripetal force does not exist in its own right, but is provided by the action of other forces. For example, imagine whirling a conker on a piece of string around in a circle. The centripetal force is the result of tension within the string.
For a vehicle turning a corner, the centripetal force is provided byfriction [friction: A force that opposes or prevents movement and converts kinetic energy into heat.] between the tyres and the tarmac.
Two motorcycles racing on track
For objects in orbit, for example the Earth orbiting the Sun, the centripetal force is provided by gravity [gravity: The force of attraction between all objects. The more mass an object has, the larger the force of gravity it exerts.] .
The Earth orbiting the Sun caption
Acceleration due to centripetal force
An object moving in a circle is constantly changing direction. This means that, even if its speed stays the same, its velocity is constantly changing. (Remember that velocity is speed in a particular direction.)
If the object’s velocity is changing, it must be accelerating. The centripetal force [centripetal force: Force, needed for circular motion, which acts towards the centre of a circle.] is the resultant force [resultant force: The overall force acting on an object, taking into account the sizes and directions of all other forces.] that causes this acceleration, and it is always directed towards the centre of the circle.
How centripetal force fights against velocity
Without the resultant centripetal force, an object would travel at a constant velocity (constant speed and direction). It would move off in a straight line, as is the case when a hammer-thrower lets go of the hammer.
Factors affecting centripetal force
The centripetal force needed to keep an object moving in a circle increases if:
the mass [mass: The amount of matter an object contains. Mass is measured in 'kg'.] of the object increases
the speed of the object increases
the radius [radius: A straight line from the centre to the circumference of a circle or sphere.] of the circle in which it is travelling decreases
Mass
Remember: force = mass × acceleration
To maintain a particular circular motion, there will be a particular acceleration. An object with more mass must have more centripetal force acting upon it.
Speed
An object travelling faster covers more distance per second. It will change direction by a bigger angle each second compared to slower object. A greater centripetal force is needed to achieve this bigger acceleration toward the centre.
Radius
A circle with a smaller radius has a smaller circumference. Therefore, an object travelling in a circle with a smaller radius has less distance to travel per orbit. It will complete more of the orbit per second, changing direction by a greater angle each second. A greater centripetal force is needed to achieve this bigger acceleration toward the centre.
A magnetic field is created when an electric current flows through a wire. Electromagnets have strong magnetic fields due to the coiling of wire around a soft iron core. Electromagnets are used in many appliances including electric bells and relay switches. When a magnetic field from a wire is placed into another magnetic field, it causes the wire to move. This principle is utilised in electric motors and loudspeakers.
Electromagnetism
When an electric current [current: Moving electric charges, for example, electrons moving through a metal wire.] flows through a wire, it produces amagnetic field [magnetic field: Region of space where a magnetic force acts.] around the wire. This magnetic field is only present while the current is flowing.
This effect is used in electromagnets. Wire is wrapped around a soft iron core, and an electric current passed through it. The electromagnet behaves as if it were a bar magnet, except that it can be switched on and off.
Applications of electromagnets
The ability of electromagnets [electromagnets: Magnets made by wrapping a coil of wire around an iron bar and passing an electric current through the coil.] to attract magnetic materials (iron, steel, nickel and cobalt) makes them useful in many ways. For example, electromagnets are used on cranes to lift and drop iron and steel in scrapyards, recycling centres and steel works.
Metal scrap heap
You should be able to explain how electromagnetic appliances work by interpreting diagrams. Three examples of appliances that use electromagnets are given below.
The electric bell
Electric bells work due to the action of electromagnets.
When the current [current: Moving electric charges, for example, electrons moving through a metal wire.] flows through the circuit [circuit: A closed loop through which current flows - from a power source, through a series of components, and back into the power source.] , the electromagnet makes amagnetic field [magnetic field: Region of space where a magnetic force acts.] .
The electromagnet attracts the springy metal arm.
The arm hits the gong, which makes a sound.
The circuit is broken now the arm is out of position.
The electromagnet is turned off and the springy metal arm moves back.
The circuit is complete again.
The cycle repeats as long as the switch is closed.
The circuit breaker
The circuit breaker does the same job as a fuse [fuse: An electrical component that protects circuits and electrical devices from overload by melting when the current becomes too high.] , but it works in a different way.
A spring-loaded push switch is held in the closed position by a spring-loaded soft iron bolt.
An electromagnet is arranged so that it can pull the bolt away from the switch.
If the current increases beyond a set limit, the electromagnet pulls the bolt towards itself, which releases the push switch into the open position.
The loudspeaker
Loudspeakers transform electrical signals into sound. Inside a loudspeaker there is a permanent magnet. An electromagnet attached to the speaker cone is inside the magnet field of the permanent magnet.
An electromagnetic loudspeaker cross-section
1. The electrical current from the amplifier [amplifier: Component which changes a small input (current, voltage, force or movement) into a larger output (current, voltage, force or movement).] is continually changing direction which, in turn, causes the magnetic field around the electromagnet to continually change.
The changing attraction and repulsion between the permanent magnet’s magnetic field and the electromagnet’s magnetic field make the electromagnet move back and forth.
In turn, the speaker cone vibrates back and forth, which generates sound waves. The frequency [frequency: A measurement of how many cycles of repetition (eg waves) occur in one second. The unit of frequency is the hertz, 'Hz'.] at which the current changes direction is the frequency of the sound that the speaker produces.
The motor effect
A simple electric motor can be built using a coil of wire that is free torotate [rotate: To spin on an axis.] between two opposite magnetic poles [magnetic pole: Either of two variable points on the Earth where the magnetic field of the Earth is most intense and toward which the needle of a compass points.] . When an electric current flows through the coil, the coil experiences a force [force: A push or a pull. The unit of force is the newton, 'N'.] and moves. This is called the motor effect.
This size of the force is greatest when the wire isperpendicular [perpendicular: At right angles to.] to the magnetic field [magnetic field: Region of space where a magnetic force acts.] of the permanent magnet. In other words, it cuts through the magnetic field at 90°. If the wire is parallel to the magnetic field, it will not experience any force.
Working out the direction of the force
The direction of the force - and therefore the movement of the wire - can be determined using Fleming’s left hand rule.
To do this, spread out your left thumb, forefinger (index finger) and second finger so they are all at 90° to one another:
point your forefinger (index finger) in the direction of the magnetic field (north to south)
point your second finger in the direction of the electric current (positive to negative)
Your thumb will point in the direction of movement.
Fleming’s left-hand rule
Remember:
thuMB – Movement
Forefinger – magnetic Field
seCond finger – Current
Note that the direction of the force is reversed if either the direction of the current is reversed, or if the direction of the magnetic field is reversed.
Electric motors
Electric motors use the motor effect [motor effect: The effect that occurs when a current-carrying wire in the presence of a magnetic field experiences a force.] . A simple electric motor can be built using a coil of wire that is free torotate [rotate: To spin on an axis.] between two opposite magnetic poles [magnetic pole: Either of two variable points on the Earth where the magnetic field of the Earth is most intense and toward which the needle of a compass points.] .
When an electric current [current: Moving electric charges, for example, electrons moving through a metal wire.] flows through the coil, the coil experiences a force [force: A push or a pull. The unit of force is the newton, 'N'.] and moves. One side moves up and the other side moves down (based onFleming’s left hand rule).
The direction of the current must be reversed every half turn, otherwise the coil comes to a halt again. This is achieved using a conducting ring split in two, called a split ring or ‘commutator’.
The animation shows a simple electric motor, with the arrowheads showing the direction of the current.
Increasing the size of the force
The size of the force on a wire carrying a current in a magnetic field [magnetic field: Region of space where a magnetic force acts.] can be increased by:
increasing the size of the current
increasing the strength of the magnetic field
The speed of a motor can be increased by either increasing the size of the current or by increasing the strength of the magnetic field.
In the animation below, the size of the current can be changed by changing thevoltage [voltage: The potential difference of a cell, electrical supply or electric component. It is measured in volts, 'V'.] .
The direction in which an electric motor turns can be reversed by reversing the direction of the current, or by reversing the direction of the magnetic field.
A wire moving in a magnetic field can induce an electric current. This principle is used in electricity generation, but it is also used in transformers to change the potential difference of the electricity. Modern electronic devices tend not to use 230 V mains electricity, and therefore switch mode transformers allow the potential difference to be reduced.
Electromagnetic induction
If an electrical conductor [conductor: An electrical conductor is a material which allows an electrical current to pass through it easily. It has a low resistance. A thermal conductor allows thermal energy to be transferred through it easily.] such as a wire cuts through a magnetic field [magnetic field:Region of space where a magnetic force acts.] , a potential difference [potential difference: The voltage between two points that makes an electric current flow between them.] is induced (made to happen) across the ends of the conductor. If the conductor is part of a complete circuit [circuit: A closed loop through which current flows - from a power source, through a series of components, and back into the power source.] , an electriccurrent [current: Moving electric charges, for example, electrons moving through a metal wire.] will flow in the circuit.
For induction to happen, the conductor must cut through the magnetic field. This can be achieved in two ways:
a conductor can be moved in a magnetic field
a magnet can be moved in a coil of wire
Induction does not happen if the conductor moves in the same direction as the magnetic field.
The induced potential difference can be increased by:
moving the magnet or wire faster
using a stronger magnet
increasing the number of turns, or loops, on the coil
increasing the area of the coil
Transformers
A transformer changes the potential difference [potential difference: The voltage between two points that makes an electric current flow between them.] of electricity. It only works with a.c. (alternating current) electricity:
a step-down transformer reduces the potential difference
a step-up transformer increases the potential difference
The structure of a transformer
A transformer consists of a soft iron core with two coils of insulated wire wrapped separately around it. Each coil has a different numbers of turns, or loops.
The primary coil is connected to an a.c. supply. It acts like anelectromagnet [electromagnet: A magnet made by wrapping a coil of wire around an iron bar and passing an electric current through the coil.] . The secondary coil is where an alternating potential difference is induced.
A transformer
How transformers work
This is the basis of how a transformer works:
An alternating current passes through the primary coil.
The alternating current produces a magnetic field [magnetic field: Region of space where a magnetic force acts.] that continuously changes direction. The soft iron core increases the strength of the magnetic field.
The secondary coil cuts through the changing magnetic field, inducing an alternating potential difference [potential difference: The voltage between two points that makes an electric current flow between them.] across the ends of the coil.
An alternating current flows if a circuit is connected to the secondary coil
It is important to note that there is no electrical connection between the primary and the secondary coils.
Calculating the potential difference across the coils
The potential difference [potential difference: The voltage between two points that makes an electric current flow between them.] across the primary and secondary coils of a transformer [transformer: A device used to increase or decrease the voltage of an electricity supply.] can be shown in the following equation:
where:
Vp is the potential difference across the primary coil in volts, V
Vs is the potential difference across the secondary coil in volts, V
np is the number of turns in the primary coil
ns is the number of turns in the secondary coil
This means that:
step-up transformers have more turns on their secondary coil
step-down transformers have more turns on their primary coil
Worked example
A transformer has 400 turns on its primary coil and 20 on its secondary coil. Calculate the potential difference across the primary coil if the potential difference across the secondary coil is 12 V.
which can be written as Vp ÷ Vs = np ÷ ns
This can be rearranged as:
Vp
= Vs × np ÷ ns
Vp
= 12 400 ÷ 20
= 240 V
This is an example of a step-down transformer, as the potential difference is reduced (from 240 V to 12 V).
Check your understanding by having a go at this activity.
Conservation of energy in transformers
P = V × I
where:
P is the power in watts, W
V is the potential difference in volts, V
I is the current in amperes (amps), A
This equation can be used to work out the power for the primary coil and the secondary coil of a transformer [transformer: A device used to increase or decrease the voltage of an electricity supply.] .
Assuming that the transformer is 100% efficient (no energy is lost between its primary coil and secondary coil), the power output from the secondary coil will be the same as the power input to the primary coil. This can be shown by the equation:
Vp × Ip = Vs × Is
Where:
Vp is the potential difference across the primary coil in volts, V
Ip is the current in the primary coil in amperes (amps), A
Vs is the potential difference across the secondary coil in volts, V
Is is the current in the secondary coil amperes (amps), A
Note that, in reality, the assumption that transformers are 100% efficient is not a valid one. Some energy will be lost to the surroundings as heat from the iron core and the coils.
Worked example
A current of 0.2 A is supplied to the primary coil of a transformer at a potential difference [potential difference: The voltage between two points that makes an electric current flow between them.] of 230 V. The secondary coil has a 4.0 A current flowing through it. Calculate the potential difference across the secondary coil, assuming that the transformer is 100% efficient.
Step 1: Work out the power for the coil where the p.d. and current are given
In this example, you know the potential difference and current for the primary coil.
P
= Vp × Ip
P
= 230 × 0.2
= 46 W
Step 2: Work out the p.d. for the other coil
Assuming that the transformer is 100% efficient, the power output of the secondary coil is also 46 W. Rearrange the equation to find the potential difference:
P
= Vs × Is
Vs
= P ÷ Is
Vs
= 46 ÷ 4.0 = 11.5 V
Switch mode transformers
Switch mode transformers are often found in the power supplies of electronic devices such as laptop and mobile phone chargers.
Phone Charger
Devices like these need a smaller potential difference [potential difference:The voltage between two points that makes an electric current flow between them.] than the 230 V from the mains electricity. Therefore, they need a step-down transformer to reduce the potential difference, built into the plug or power supply.
Switch mode transformers achieve this by using complex electronic circuits.These rapidly switch the current on and off, allowing the alternating current to be changed to a higher frequency. This is often between 50 Hz and 200 Hz.
At these frequencies, a much smaller and lighter transformer than normal is able to reduce the potential difference. As a result, these transformers are suited for use in power supplies such as mobile phone chargers.
When the device is plugged in and the batteries are recharging, a load is being applied (the transformer is drawing power).
Switch mode transformers use very little power when the plug is left switched on but no load is applied (such as when the device’s batteries are not charging). This is another advantage for using switch mode transformers in applications such as mobile phone chargers.
Comparing switch mode transformers with iron core transformers
| Switch mode transformers | Iron core transformers | |
|---|---|---|
| Frequency | Operate at a high frequency, often between 50 Hz and 200 Hz | Operate at 50 Hz (UK mains frequency) |
| Size | Relatively small and light | Relatively large and heavy due to the iron core) |
| Power usage when no load is applied | Very little | Same as if a load was being applied because a current continues to flow through the primary coil |