Centre of mass
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.
1. Drill a small hole in the object and hang it up so
that it is free to swing without obstruction.
2. 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.
3. Drill another hole at a different location within
the object.
4. Again hang a plumb line to determine the vertical
and mark it on.
5. 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
Moments
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
A see-saw has a pivot [pivot: A
point around which rotation occurs.] in the middle:
·
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.
Hydraulics
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
Circular
motion
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.
The motor effect
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.
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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.
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1.
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.] .
2.
The electromagnet attracts the
springy metal arm.
3.
The arm hits the gong, which makes a
sound.
4.
The circuit is broken now the arm is
out of position.
5.
The electromagnet is turned off and
the springy metal arm moves back.
6.
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.
1.
A spring-loaded push switch is held
in the closed position by a spring-loaded soft iron bolt.
2.
An electromagnet is arranged so that
it can pull the bolt away from the switch.
3.
If the current increases beyond a set
limit, the electromagnet pulls the bolt towards itself, which releases the push
switch into the open position.
Use this simulation to see how
circuit breakers work.
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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.
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.
2.
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.
3.
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.
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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'.] .
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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.
Transformers
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.
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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
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Conservation of energy in transformers
In Physics Unit 2 you learnt that
electrical power can be calculated using this equation:
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
|
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