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Physics
Unit 1- Mechanics
Module 1- Motion
-Physical Quantities and Units
Below are the SI Units used across the world:
Quantity
Unit
Abbreviation
Mass
Kilogram
kg
Length
Metre
m
Time
Second
s
Temperature
Kelvin
K
Electrical Current
Ampere
A
Amount of Substance
mole
mol
Module 1- Motion
-Physical Quantities and Units
Below are the Unit prefixes:
Prefix
Name
Abbreviation
10-12
pico
p
10-9
nano
n
10-6
micro
μ
10-3
milli
m
10-2
centi
c
103
kilo
k
106
mega
M
109
giga
G
1012
tera
T
Module 1- Motion
-Scalar and Vector Quantities
A scalar quantity is one that has magnitude (size) but not a direction.
A vector quantity is one that has magnitude (size) and direction.
Scalar
Vector
Density
Displacement
Temperature
Velocity
Pressure
Acceleration
Potential Difference
Force
Frequency
Impulse
Wavelength
Momentum
Power
Electric Current
Magnetic Field
Electric Field
Module 1- Motion
-Vector Component Forces
Here is a triangle which trigonometry can be used to find unknowns:
Fcos𝜃
F
𝜃
Fsin𝜃
Module 1- Motion
-Definitions in kinematics
Speed is distance per unit time.
Displacement is distance
moved in a stated direction.
Acceleration is the rate of
change of velocity.
Speed is the distance
travelled per unit time- it is
a scalar
Velocity is the displacement
per unit time- it is a vector
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
Average speed =
𝑡𝑖𝑚𝑒
𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
Average acceleration =
𝑡𝑖𝑚𝑒
=
𝑣−𝑢
𝑡
Instantaneous speed is the speed at a given instant of time (it is the gradient
of the graph of displacement against the against time at that instant)
Module 1- Motion
-Graphs of Motion
Displacement/ Time graphs:
• A straight line indicates constant velocity
• The gradient of a straight line gives the velocity
• The gradient at any point is the velocity, and this is called
instantaneous velocity
Velocity/ Time graphs:
• The gradient represents acceleration
• The area beneath a velocity/ time graph represents the
displacement
Module 1- Motion
-Equations of Motion
Symbol
Quantity
Alternative Quantity
SI Unit
S
Distance Moved
Displacement
Metre
U
Speed at the start Velocity at the start
Second
V
Speed at the end
m s-2
A
Acceleration
m s-1
T
Time interval
m s-1
Velocity at the end
Summary of the equations of motion for constant
acceleration:
v = u + at
Term not included: s
v2= u2 + 2as
Term not included: t
s=(
𝑢+𝑣
)
2
t
s = ut + ½ at2
s = vt - ½ at2
Term not included: a
Term not included: v
Term not included: u
Module 1- Motion
-Free Fall
An object undergoing free fall on the Earth has an acceleration of g =
9.81 m s-2. Acceleration is a vector quantity- and g acts vertically
downward.
Remember, when answering questions on free fall, make sure you deal
with the horizontal and vertical components separately, and watch out for
negative values.
Module 1- Motion
-Measurement of g
Below is a diagram on the ‘trap door and electromagnet method for
determining g’.
There will be a degree of uncertainty
in this experiment because:
1. If the electromagnet’s current is too
strong there will be a delay in
releasing the ball after the current is
switched off and the clock is
triggered.
2. If the distance of fall is too large, or
the ball is too small, air resistance
might have a noticeable effect on its
speed.
3. You need you make sure you
measure from the bottom of the ball
when it is held by the electromagnet.
Module 2- Forces in Action
-Force and the Newton
-Types of Force
Generally, a force is push or pull, but can be others such as drag, tension, friction,
weight and thrust. Thrust, for example, is the term used for the driving force
provided by a jet engine.
Outside the nucleus of an atom, there is just three types of force, which are:
• Gravitational force between two objects with mass. (Only one I will need is
between the object and the Earth: The weight).
• Magnetic force between two magnetic objects. At an atomic level this is a force
between moving charges, and will only concern you in examples using
magnetised forces.
• Electrical force between charged objects, which is responsible for all
interactions between objects. When two atoms collide, they exert an electrical
force on one another, and may chemically bond as a result of the electrical
attraction between them.
This list of the three basic forces outside a nucleus can be reduced to two by
treating the electrical and magnetic forces as a single electromagnetic force. This
is because the theory of electromagnetism establishes the connection between
electrical and magnetic effects.
Module 2- Forces in Action
-Force and the Newton
The link between these three terms was first established by Newton, when he
discovered that when an object has no resultant force on it, the object won’t
accelerate; it will stay at a constant velocity. Once Newton established this, he
found that:
• Acceleration is proportional to force, if the mass is constant
• Acceleration is inversely proportional to mass, if the force is constant.
Putting this algebraically:
1
a ∝ F and a ∝ , so F=ma
𝑚
A resultant force always causes
acceleration.
Zero resultant force implies a constant
velocity, which may also be zero (it will
be in equilibrium).
Remember, forces cause
acceleration, and not the
other way round!
One Newton is the force that causes a mass of one kilogram to have an
acceleration of one metre per second every second.
Module 2- Forces in Action
-Motion with non-constant acceleration
Weight:
• Weight is a force, so is measured in newton's.
• The mass of an object is measured in kg.
To work out mass or weight, we can use the
equation W=mg
Weight is the gravitational
force on a body
Non-constant (non-linear) acceleration
When an object travels through a fluid (liquid or gas), it experiences a resistive force,
known as drag, which depends on several factors, such as velocity, roughness of
surface, cross-sectional area and shape (how it is streamlined)
Terminal Velocity:
This is when the drag (upwards) becomes equal to the weight of the object
(downwards) so the resultant force is zero, so it is travelling at a constant velocity.
This is called terminal velocity.
Module 2- Forces in Action
-Equilibrium
The triangle of forces:
Here are some examples of triangular forces:
Equilibrium: When there is
zero resultant force acting on
an object.
3N
2.8N
4N
R= 5.7N
4N
R=5N
4N
B
A+B=C
C+D=E
A+B+D=E A
C
4N
5N
5N
R=1.4N
D
E resultant A+B+D
Resultant
(almost)
zero
Module 2- Forces in Action
-Centre of Gravity
Whenever mass is used, the position of the weight of the object has to be
considered. For all objects there is a point where the entire weight of the object
can be considered to act as a single force, and this is called the centre of gravity
of an object. Although the weight of an object does not act through just the centre
of gravity, it does simply calculations.
Finding the centre of gravitySupport the piece freely on a wire passed
through a small hole.
Hang a string with a small weight at the bottom.
Repeat the procedure with a different hole, and
the centre of gravity is where the lines meet.
Module 2- Forces in Action
-Turning Forces
This is needed when doing things like designing building, to make sure it
can support itself and will not collapse.
Loading forces are usually vertically downwards, and need to be
balanced by vertically upward support forces. We need to establish
equilibrium when working with forces that are parallel.
Module 2- Forces in Action
-Turning Forces
Terms associated with Turning Forces:
Couple- A couple occurs when two forces are equal and
opposite to each other, but are not in a straight line. No
linear acceleration can be produced, as the upward and
downward forces cancel. The resultant of theses forces is
zero, however they can produce rotation.
Torque- This can be applied to a couple and describes a
turning effect of the couple. The formula for torque is:
Y
X
Torque = one of the forces x perpendicular distance between the forces
So torque is measured in newton metres, and
produces rotation rather than linear motion, so
the term is used in drills etc.
A couple is a pair of equal
and parallel but opposite
forces, which tends to
produce rotation only.
Module 2- Forces in Action
-Turning Forces
Moment of force = Fx
X
Moment of a force:
The moment of a force is the turning effect of a single
force shown to the right. Moments are also measured
in Newton metres. The principle of moments states
that: For a body in rotational equilibrium, the sum of the
clockwise moments equals the sum of the
anticlockwise moments. (CW=ACW).
P
F
F
P
X
The moment of a force is
the force multiplied by the
perpendicular distance
from the stated point.
Equilibrium of an extended object
A large object may have many forces acting on it.
These forces may provide a resultant force, which will
cause acceleration, and a resultant moment, which will
cause rotation. For a large object to be in equilibrium,
both the resultant force and the resultant moment
must be zero.
Module 2- Forces in Action
-Density
𝑚𝑎𝑠𝑠
Density = 𝑣𝑜𝑙𝑢𝑚𝑒, and density has the SI unit kg m-3.
1m3 = (100 cm)3 = 1 000 000 cm3.
The volume of water has a mass of 1000kg, so the density is 1000 kg m3.
Material
Density
Material
Density
Density is defined as
kg m-3
kg m-3
mass per unit volume.
Hydrogen 0.0899
Silicon
2300
Helium
0.176
Concrete
2400
Oxygen
1.33
Iron
7870
Air
1.29
Copper
8930
Ethanol
789
Silver
10500
Olive oil
920
Gold
19300
Water
1000
Platinum
21500
Mercury
13600
Osmium
22500
Aluminium
2710
Module 2- Forces in Action
-Pressure
𝑓𝑜𝑟𝑐𝑒
Pressure =
, and the SI unit for pressure is the Pascal (Pa). 1 pascal represents
𝑎𝑟𝑒𝑎
the force of 1N spread uniformly over an area of 1 m2 and is a comparatively small
unit of pressure.
Pressure in a liquid is given by hpg, where
h is height, p is density and g is 9.81m s-2.
Pressure is defined as
force per unit area.
Eg) An oil tanker has a total mass of 400 000 tonnes (ship + oil). It has a width of
40m and a length of 500m.
Force upward = Weight downward = mg = 400 000 000 kg x 9.81m s-2= 3.92 x 109N.
Upward force due to water = pressure x area of base of ship, so
3.92 x 109 = hpg x 40 x 500
p = density of sea water = 1030 kg m-3.
h= distance from the bottom of the ship to the surface, so
h=
3.92×109
1030 ×9.81 ×40 ×500
= 19.4m
Module 2- Forces in Action
-Car stopping distances
Force x distance gives the work done by a vehicle against its braking force. This
quantity is called the kinetic energy of a vehicle. The table below shows a car
(which including passengers and luggage is 1200kg) and its breaking distance.
Braking force/ N
Braking Distance/m at
15m/s (k.e. = 135000J)
Braking Distance/m at
30m/s (k.e. = 540000J)
100
1350
5400
1000
135
540
10 000
13.5
54.0
100 000
1.35
5.4
1 000 000
0.135
0.54
If you double the speed, the kinetic energy quadruples. So, for every given braking
force, the braking distance is always four times larger when the car is travelling at
twice the speed.
Module 2- Forces in Action
-Car stopping distances
Thinking Distance + Braking Distance = Stopping Distance
Thinking Distance = speed x reaction time
Reaction time is increased by tiredness, alcohol/ other drug use, illness, and
distractions such as children and phones.
Braking distance depends on the braking force, friction between the tyres
and the road, the mass and the speed.
• Braking force is reduced by reduced friction between the brakes and the
wheels (worn or badly adjusted brakes)
• Friction between the tyres and the road is reduced by wet or icy roads,
leaves or dirt on the road, worn out tyre treads, etc
• Mass is affected by the size of the car and what you put in it.
Module 2- Forces in Action
-Car stopping distances
Thinking, braking and stopping distances:
Stopping distance = thinking distance + braking distance
Thinking distance = Time taken to see the need to stop and apply the brakes
Braking distance = The time taken from hitting the brakes to coming to a stop
Eg) A car of mass 1000kg has brakes that are 75% efficient. It is travelling at 40ms-1
and it’s daylight and the road is dry. The driver takes 0.25 seconds to respond to an
incident that requires an emergency stop. What’s the shortest possible distance for
stopping?
𝑚
Thinking distance= 40 × 0.25s = 10m
𝑠
75
Acceleration while braking= −
× 9.8 = −7.35𝑚 𝑠 −2
100
2
2
Since, for braking: v = u + 2as
02 = 402 + 2 x (-7.35)s
1600
s=
= 109𝑚
109m + 10m = 119m
14.7
Module 2- Forces in Action
-Car Safety
You can stop a moving vehicle with less braking force if you increase the braking
distance, because kinetic energy = braking force x breaking distance. This becomes
more relative when thinking of someone involved in a car crash. In a crash, you want
to reduce the force, and you can do this by increasing the crash time, or the distance
your body moves in a crash. A good car does this with crumple zones, seat belts and
airbags.
Crumple zones: These are meant to collapse during a
collision (usually the front end). The crumple zones slightly
decrease collision speed, which increases the collision
time, so the average force you endure is less.
Seat Belts: The distance in which a force can act is also
increased by wearing a seatbelt, as it stretches during an
incident. However, the main advantage of a seatbelt is to
keep you kept in the car, as without one your body would
be most likely stopped by the windscreen or another rigid
part of the car.
Module 2- Forces in Action
-Car Safety
Airbags: These work well with seatbelts, as they should
be fully inflated when you hit them, which they most likely
won’t be without the aid of seatbelts. Airbags are
designed to inflate in 0.05 s, and deflate in 0.3s, which is
sufficient to slow you down. An airbag consists of three
parts:
• A flexible nylon bag that is folded into the steering
wheel or dashboard
• A sensor know as an accelerometer. When the front
end of the spring is suddenly stopped, the mass on
the end of the spring continues to move forward and
makes contact with a switch, starting a chemical
reaction. This occurs when the acceleration is
around -10g, an acceleration that only occurs during
an incident.
• An inflation system in which a spark ignites a violent
chemical reaction in which nitrogen gas is produced (it
may sometimes be air, but usually Nitrogen gas)
Module 2- Forces in Action
-Car Safety
Global Positioning System (GPS): A GPS in cars enable you to know
where you are on the worlds surface within a distance of about 1m,
using satellites orbiting Earth at the height of about 20 000km. At any
one point, there will always be at least four satellites available for any
GPS receiver. The system relies on accurately measuring time
differences between the arrival of signals sent simultaneously from
several satellites, and on the precise position of these satellites. The
satellites clocks are synchronised with clocks on the ground and are
accurate to one second in 100 million years.
Module 2- Forces in Action
-Car Safety
Global Positioning System (GPS): The method used for determining the position
of the GPS receiver in a car is called trilateration. If satellite A sends out a signal
and it arrives after a known time ay the GPS receiver then, given the speed of travel
of electromagnetic radiation, the distance of the receiver from the satellite can be
found. We now repeat this for the other satellites, which gives your current location;
where all the spheres meet! The in-car computer then plots this position on its map,
and can guide the car along a suitable route to the requested destination. Although
trilateration only needs 3 satellites, GPS systems actually use at least four
satellites.
You are
here
Module 3- Work & Energy
-Work and the joule
Work, is defined by the equation:
work = force x distance moved in the direction of the force
Since the definition has a direction for the force, you would think it is a vector but in
fact it is a scalar. It defies the general rule of Vector x Scalar = Vector.
The SI Unit for work is the joule, and 1 joule = 1 newton metre.
Eg) Picking up a pen = 0.2N x 0.1m = 0.02Nm = 0.02J
1 joule is the work done when a force
of 1 newton moves its point of
application 1 metre in the direction of
the force.
Module 3- Work & Energy
-Work and the joule
Force at an angle to the direction of movement:
Eg) A barrel of weight 200N is raised by a vertical distance of 1.8m by being moved
along the ramp. The work done against gravity will be 200N x 1.8m = 360J
If the ramp is at an angle of 25o to the horizontal, then the force required will be less
but the total work done must, if the friction is negligible, be the same, so:
1.8𝑚
Distance moved along the ramp =
= 4.26
360𝐽
4.26𝑚
𝑠𝑖𝑛25°
Force required =
= 84.5N
A simpler way is to use the vertical component of the distance moved along the
slope:
Work done = 200N x 4.26m x cos65o
= 360J
o
65 is the angle between the force and the distance moved. In other words:
Work done = force x distance moved in the direction of the force
= F d cos𝜃
Where d is the distance travelled and 𝜃 is the angle between the force and the
direction of travel.
• A barrel of weight 200N is raised by a
vertical distance of 1.8m by being moved
along the ramp.
• A) what is the work done?
• B) what force is required?
Module 3- Work & Energy
-Work and the joule
The picture that was used in the example previously:
1.8m
25o
200N
Module 3- Work & Energy
-Work and the joule
Note that if the force and direction of travel are at right angles to one
another, then no work is done as cos 90o is zero. This may seem rather
irrelevant, as at first sight a force at right angles to the direction of travel
seems impossible, however the force of gravity on the Moon as it orbits
Earth is at right angles to the Moon’s direction of travel. So, despite the
large gravitational force the Earth is exerting on the Moon, the Earth is not
doing any work on the Moon, and so the Moon moves at a constant speed
for a very long time.
Module 3- Work & Energy
-The conservation of Energy
Energy is the stored ability to do work.
•
•
Total energy in = Total energy out
Energy cannot be created or destroyed.
Energy can be transferred from one form to another but the total amount of
energy in a closed system will not change.
At a basic level, energy is either kinetic energy or potential energy.
• Kinetic Energy: where movement is taking place
• Potential Energy: Regions where electric, magnetic, gravitational and nuclear forces
exist. Regions such as these are called fields.
Below are different forms of energy together with some details of how the energy is
stored:
Chemical Energy: energy can be released when the arrangement of atoms is altered
Electrical potential energy: Eg) A positive charge is pushed close to another positive
charge. This will often be called electrical energy.
Electromagnetic energy: includes all the waves that travel at the speed of light in a
vacuum (gamma rays, X-rays, ultraviolet, light, infrared, microwaves, radio waves).
These waves hold their energy in electric and magnetic fields.
Module 3- Work & Energy
-The conservation of Energy
Gravitational potential energy: where an object is at a high level in the Earth’s
gravitational field.
Internal energy: the molecules in all objects have random movement and have
some potential energy when they are close to one another.
Kinetic energy: when an object has speed.
Nuclear energy: energy can be released by reorganising the protons and neutrons
in an atom’s nucleus. This form of energy is also known as atomic energy.
Sound energy: in the movement of atoms
Conservation of energy describes the
situation in any closed system, where
energy may ne converted from one from
into another, but cannot be created or
destroyed.
Module 3- Work & Energy
Potential and Kinetic energies
Gravitational potential energy (GPE): this is the energy stored in an object (the work
an object can do) by virtue of its position in a gravitational field. The formulae is:
GPE = mgh
Kinetic energy (KE): this is the work an object can do by virtue of its speed. The
1
formulae is: kinetic energy (k.e.) = 𝑚𝑣 2 . Also, the kinetic energy of a moving body
2
equals the work it can do as a result of its motion.
Falling objects: An object of mass m, falling from rest, loses gravitational potential
energy. From the principle of conservation of energy, it gains an exactly equivilant
amount of kinetic energy as a result of the work being done on it by gravity, so:
1
Mgh = 𝑚𝑣 2 , where v is its speed and h is the distance fell, m cancels to give:
2
2gh = v2 or v= √2𝑔ℎ
Module 3- Work & Energy
Power and the Watt
To power a 100 watt light bulb, an
electric current must be flowing
through the filament of the bulb. It
supplies energy at the rate of 100
joules per second, so to power it
for one hour it would be:
Power is the rate of doing work.
𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒
Power = 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
One watt (W) is equal to one joule per
second.
1kW = 1000 W
1MW = 1000kW = 1 000 000 W
100J s-1 x 3600s = 360 000 J. Electrical energy is sold to domestic users in units
called kilowatt- hours (kWh), which is equivalent to the use of 1000 W of power for
an hour.
Eg) 1kWh could be supplied to a 100W lamp over 10 hours.
1kWh = 1000J s-1 x 3600s = 3 600 000 J. Today one kWh of energy costs about
15p.
Module 3- Work & Energy
Power and the Watt
You need to be careful when distinguishing between rates and totals. For example, you
cannot buy a kW of power; you pay for energy. You can pay 1 kW used for 6 hours6kWh. Below is a table showing the relationship between rates and totals for several
units.
Rate
Example of rate
Time
Total
Example of total
Speed
80 km h-1
4h
Distance
320km
Power
3 kW
200s
Energy
600kJ
Current
25 mA
1000s
Charge
25C
Human Power and Horse Power:
176W is a high rate of work that only a fit person could sustain for any length of
time. Most people would find it difficult to work continuously at a rate of 70W.
Horse power is still used to express some power ratings. 1 horse power is
equal to 746W- though this isn’t really what horses achieve.
Module 3- Work & Energy
Efficiency
Efficiency is expressed as:
𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦
Efficiency =
× 100%
𝑡𝑜𝑡𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦
To convert electrical energy into
heat, you just need resistance.
Device
Energy Input
Energy Output
Typical
Efficiency (%)
Electrical motor
Electrical
Kinetic/ Potential
85
Solar cell
Light
Electrical
10
Rechargeable battery
Electrical
Electrical
30
Electric radiator
Electrical
Internal
100
Power station
Nuclear
Electrical
40
Car (petrol)
Chemical
Kinetic/ Potential
45
Car (diesel)
Chemical
Kinetic/ Potential
55
Steam engine
Chemical
Kinetic/ Potential
8
Module 3- Work & Energy
Sankey Diagrams
Useful output
energy
Input energy
The width of the arrows should
relate to how much is wasteddon’t use fat arrows for things
with small loss!
(Do it to scale)
Wasted output energy
split into different types
Module 3- Work & Energy
Deformation of materials
The word elastic can be applied to a collision. In an elastic collision no kinetic energy
is lost. This can only happen when there is no permanent distortion of the objects
colliding, because if there is permanent distortion some energy must have been used
to create the distortion. Collisions which are not elastic collisions are not usually called
plastic collisions but inelastic collisions.
A stretch can be Elastic or Plastic…
Elastic
If a deformation is elastic, the material returns to
its original shape once the forces are removed.
1) When the material is put under tension, the
atoms of the materials are pulled apart from
one another.
2) Atoms can move small distances relative to
their equilibrium positions, without actually
changing position in the material.
3) Once the load is removed, the atoms return
to their equilibrium distance apart.
For a metal, elastic deformation happens as long
as Hooke’s law is obeyed.
Plastic
If a deformation is plastic, the
material is permanently
stretched.
1) Some atoms in the material
move position relative to one
another.
2) When the load it removed, the
atoms don’t return to their
original position.
A metal stretched past its elastic
limit shows plastic deformation.
Module 3- Work & Energy
Deformation of materials
Tensile and compressive forces
Forces that stretch objects like wires, springs and rubber bands are called tensile
forces, because they cause tension in the object. Therefore, for there to be tension in
a fixed stretched wire, there must be equal and opposite forces on it at either end.
With a spring, it is possible to reduce its length by squeezing it, and in this instance
the forces applied are called compressive forces. Unless the spring is accelerating,
equal and opposite forces must be applied.
Once the elastic limit has been passed,
the stretch becomes permanent.
Plastic deformation- the object will not
return to its original shape when the
deforming force is removed, it becomes
permanently distorted.
Module 3- Work & Energy
Hooke’s Law
Hooke’s Law- the extension of
an elastic body is proportional
to the force that causes it.
The equation is F= kx,
where F is the force causing extension x, and k is known as the force constant
(stiffness constant). The force constant is expressed in newton's per metre. k tells us
how much force is required per unit of extension.
Eg) A k of 6N mm-1 means it takes 6N to cause an extension of 1mm. Note that the
force constant can only be used when the material is undergoing elastic deformation.
When deformation become plastic, the force per unit extension is no longer constant.
Graphs- When extension is plotted on the x-axis, the area beneath the line is equal to
the work required to stretch the wire.
Work done = area of triangle = ½ Fx
And since F=kx…
1
Work done = 𝑘𝑥 2
2
In the case of elastic deformations, the elastic potential energy E equals the work
done, giving:
1
1
E = 𝐹𝑥 = 𝑘𝑥 2 .
2
2
Module 3- Work & Energy
Hooke’s Law
Energy stored in plastic deformation:
The graph shown below could be produced by stretching a copper wire beyond its
elastic limit. The work done stretching the wire is given by the area A + B. If the tension
is then reduced to zero, the wire behaves elastically, contracting to a permanent
extension x. As the tension is reduced, energy equivalent to area B is released from
the wire. The net result of the wire having work A + B done on it, but only releasing
energy B, is that the wire becomes hot to the touch.
Module 3- Work & Energy
Young’s modulus
Stress and Strain:
• Stress is force per unit cross-section area, therefore is
Stress is force per unit
expressed in the SI Unit newton per square metre. N m-2. cross-sectional area.
This unit is called pascal (Pa), which is also used to
quantify pressure.
Strain is extension per
unit length.
• Strain is extension per unit length. As a result, strain
does not have a unit, since it is length divided by length;
sometimes it is quoted as a percentage. A strain of 2% is
the same as a strain of 0.02 and implies that a material
has extended 2cm for each metre of its original length.
Module 3- Work & Energy
Young’s modulus
Stress on a material causes strain. How much strain is caused depends on how
stiff it is. A stiff material, such as cast iron, will not alter its shape much when a
stress is applied to it, but a relatively small stress will cause a substantial strain in
a soft material, such as clay.
Young's Modulus is the ratio between stress and strain, measured in pascals
(Pa). The formulae is as follows:
stress
Young Modulus (E) =
strain
=
force
area
extension
length
=
force × length
area ×extension
Where, F = force in N, A = cross-sectional area, l = initial length in metres and
e = extension in m
Module 3- Work & Energy
Categories of materials
Material variety:
There are many materials now, all with different strengths and weaknesses.
Some of the properties materials may have are: Ductility, brittleness, stiffness,
density, elasticity, plasticity, toughness, fatigue resistance, conductivity, and fire
resistance.
The properties of individual material types can be illustrated clearly by sketching
graphs of stress against strain.
Ductile- materials that have a large plastic region (therefore they can be drawn
into a wire); for example, copper. The strain on a ductile material may be around
50%
Brittle- A material that distorts very little even when subject to a large stress and
does not exhibit any plastic deformation; for example, concrete.
Polymeric material- A material made of many smaller molecules bonded
together, often making tangled long chains. These materials often exhibit very
large strains (e.g. 300%) for example rubber.
Module 3- Work & Energy
Interpreting Stress-Strain Graphs
Stress-Strain graphs for Ductile materials curve
Stress (Nm-2)
Yield point
The material suddenly starts to stretch
without any extra load. The yield point is
the stress at which a large amount of
plastic deformation takes place with a
constant or reduced load.
Limit of Proportionality
Stops obeying Hooke’s
Law but would still return
to original shape
Strain
Elastic Limit
Starts behaving plastically, and would no
longer return to original shape once the stress
was removed.
Module 3- Work & Energy
Interpreting Stress-Strain Graphs
Stress-Strain graphs for Brittle materials don’t curve
•
Stress (Nm-2)
Material
fractures
•
•
Strain
Brittle materials obey Hooke’s
Law.
When the stress reaches a certain
point, the material snaps (it does
not deform plastically).
When stress is applied to a brittle
material any tiny cracks get bigger
and bugger until the material breaks
completely. This is called brittle
fracture.
Module 3- Work & Energy
Interpreting Stress-Strain Graphs
Rubber and Polythene are Polymeric Materials
Polythene
Rubber
Unloading
Strain
Rubber returns to its original length
when the load is removed- it behaves
elastically.
Stress (Nm-2)
Stress (Nm-2)
Loading
Loading
Unloading
Strain
Polythene behaves plastically- it has
been stretched to a new shape. It is a
ductile material.
DEFINITIONS
Acceleration (a)- the rate of change of velocity, measured in metres per second
squared (m s-2); a vector quantity
Sample- definition