IGCSE PHYSICS
2023-2025 syllabus – 0625
1 Motion, Forces & Energy
Physical Quantities and Measurement Techniques
• Measuring Physical Quantities
- Ruler
Used to measure lengths accurately, view ruler perpendicular to eye
level and make sure its stable when taking readings to avoid errors
in reading. SI unit of length is metres (m)
- Set-Square
Set squares are often used to ensure something is vertical or
perpendicular
- Stopwatch
Used to time or measure the duration of something
- Electronic Balance
Used to measure mass of an object accurately. SI unit of mass is
Kilograms (kg). if the object is wet it should be dried before mass is
measured. The balance should be reset to zero before reading is
taken. Can be used to measure weight as well if mass is multiplied
with gravitational field strength
- Thermometer
Used to measure the temperature accurately. SI unit of Temperature
is Celsius (C). thermometer should not touch the sides of the
container when measuring the temperature of a substance in a
container to avoid measuring the temperature of the container.
Reading should be taken perpendicularly for accuracy. You should
wait for temperature to stop changing before reading is taken
- Newton meter
Used to measure weight. SI unit of weight
Are newtons (N)
-Measuring Cylinder
Used to measure the volume of a substance, SI
Unit of volume is cubic metres (m3), can be used
To measure volume of irregular objects by adding
Object to a cylinder with a known volume of water
Or any other liquid and adding the object and
Calculating the difference in volume or rise in
Volume. Reading should be taken at lower
Meniscus perpendicularly to increase accuracy
- Measuring Tape, Trundle wheel
Used to measure length
- Micrometre Screw Gauge
Used to measure thickness
- Vernier Calliper
Used to measure diameter
Pendulums
-
-
-
-
The length of the pendulum is measured from the centre of the bob
to the lowest point of support or where the string attaches to
The length l is usually given on a scale in questions (the question
will specify this with “one tenth to actual size”, you can calculate
actual size from this by multiplying the length of the diagram by 10
in this example)
The bob is let go from a point and the number of a known value of
oscillations are timed
This usually uses about 20 oscillations, as it is much easier to
measure the time for 20 oscillations than one
The time period for a single oscillation can be calculated from this
by dividing the total time by number of oscillations
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑇=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛𝑠
If very few oscillations are used it will be harder to measure time
and increases chances of error due to reaction time, however if very
large number of oscillations such as 200 is used you may lose
count of the number of oscillations
Using more oscillations increases accuracy as time errors become
less significant
Scalar and Vector Quantities
The main difference between scalar and vectors is that vector quantities
have a direction, so when deciding if something is a vector or scalar,
determine whether the quantity has a direction
Scalars
Vectors
A scalar quantity is one that
only has magnitude (size)
A vector quantity is one that
has both magnitude and
direction
Distance
Displacement
Speed
Velocity
Time
Force
Energy
Acceleration
Mass
Weight
Temperature
Momentum
Electric field strength
Gravitational field strength
Vector Diagrams
(Limited to forces or velocities only, where the vectors are at right angles
to each other)
500 N
Resultant force
(b)
(a)
500 N
(b)
700 N
(c)
-
To calculate the resultant force, apply Pythagoras theorem
𝑐 2 + 𝑏 2 = 𝑎2
To calculate graphically, decide a suitable scale such as 1cm: 100N
Draw the forces perpendicular to each other using the scale used
Place the pointy end of the compass at the point of intersection and
extend to edge of the line drawn
Place the extended compass on the edge of the other line and
make an arc
Place the edge of the compass at intersection once again, and
extend to edge of second line
Place extended compass at edge of the opposite line and make
another arc
Measure the distance from the intersection of the lines to the
intersection of the arcs made (this is shown with the green lines)
Use the scale to calculate resultant force
Motion
• Speed, Velocity & Average Speed
-
-
Speed is the distance travelled per unit time
Velocity is the speed in a given direction
Speed and velocity are both calculated using the same formula
𝑣⁄ = 𝑑
𝛿 𝑡
Average speed is calculated by dividing total distance travelled and
total time taken
SI unit for both is metre per second (m/s)
• Sketching and Interpreting a Distance-Time graph
- The graph below shows when a person is no longer moving or at
rest on a Distance time graph, when a person is at rest both speed
and acceleration is at zero.
-
The graph below fig A shows when an object is moving at constant
speed, when an object moves at constant speed the acceleration is
zero. The steeper the graph is the greater the speed is, hence the
object is moving at a greater constant speed in fig B than fig A as
the graph is much steeper, however both have the same
acceleration of zero m/s2
Fig A
Fig B
-
The graph below shows non-uniform acceleration on a distance
time graph, here the acceleration is increasing or positive and so is
the speed. Acceleration is indicated by the upward facing graph on
distance-time graph
-
The graph below shows non-uniform deceleration on a distancetime graph, here acceleration is decreasing (decreasing speed) so it
is called deceleration(negative). Deceleration is indicated by the
downward facing graph on a distance-time graph
-
To calculate average speed between two points from a distance
time graph, use gradient
Gradient = (y2 – y1) / (x2- x1)
•
sketching and Interpreting a Speed or Velocity – time graph
-
Distance travelled is calculated using area under the curve on a
speed or velocity-time graph
Equilateral Triangle area
A = base x height
Right Angle Triangle Area
A= ½ x Base x height
a
h
Area of a Trapezium
A= ½ x (a + b) x height
b
b
a
h
-
The graph below shows constant speed on a speed or velocity time
graph, acceleration is zero at this point
-
The graph below shows increasing speed or constant acceleration
on a speed/velocity-time graph, at this part acceleration increases
constantly
-
The graph below shows decreasing speed or constant deceleration
on a speed/velocity – time graph, at this part rate at which speed
decreases or deceleration is constant
-
The graph below shows the speed-time graph for when an object is
at rest, here the acceleration, speed, and velocity are all zero
-
The graph below shows non-uniform acceleration on a speed time
graph, here the rate at which the speed changes is no longer
constant and is increasing
-
The graph below shows non-uniform deceleration on speed/velocity
time graph, here the rate at which the speed changes is no longer
constant and decreasing
-
Calculating acceleration from a speed-time graph, gradient is used
here, you may draw a tangent to your graph
Gradient = (y2 – y1) / (x2- x1)
•
Acceleration
-
Acceleration is the change in velocity per unit time
Acceleration is a positive value, deceleration is negative
Both are calculated using the formula below, the SI unit is m/s2
𝒂=
•
𝜟𝒗
𝜟𝒕
Free fall
-
-
•
free fall is the acceleration near the surface of earth due to gravity,
at this point acceleration is 9.8m/s2. Immediately after jumping off a
plane for skydiving there is no air resistance initially so you
accelerate downwards at 9.8m/s2 until air resistance or upward
forces start acting
The same happens where air resistance may be ignored, the
objects will fall with a constant acceleration of 9.8m/s2
Since acceleration is constant speed will increase as time increases
Speed is not constant, speed increases while acceleration remains
constant.
Terminal Velocity
-
the graph below shows the changes in speed as a skydiver jumps
from a hot air balloon
-1 initially speed increases or the skydiver accelerates as there is no
air resistance acting on him, so he falls while accelerating at
9.8m/s2 (freefall)
-2 however, as his falls air resistance starts to increase causing him to
slow down
3- and once the upward force due to air resistance increases and
becomes equal to the downward force due to his weight, the
skydiver reaches terminal velocity and he starts to fall at a constant
speed
4- once he opens his parachute the upward force due to air resistance
increases and becomes greater than the force due to his weight,
causing him to fall slower
5- eventually both forces equalize again and he reaches a second
terminal velocity
-
The graph below is shown for the changes in speed of a swimmer
as he pushes himself away from the end wall of the pool, he is
swimming in
-1
Initially his speed increases as he pushes himself away from the
end wall, so the force due to that causes him to accelerate
However due to the frictional force or opposing force of water the
force he used to push himself away with is equalised
Once the forces are balanced there is no resultant force and he
moves with terminal velocity (constant speed)
-
2
-
3
Mass & Weight
-
-
Mass is the measure of the quantity of matter in an object at rest,
relative to the observer
Mass is the property of an object that resists motion
The SI unit for mass is Kg (kilograms)
Weight is the effect of gravitational force on an object that has mass
The SI unit for weight is N (newtons)
Weight can be described as the effect of a gravitational force on a
mass
Gravitational field strength is the force (weight) per unit mass
𝒘
𝒈=
𝒎
the gravitational field strength is equal to the acceleration of freefall
gravitational field strength has the SI unit N/kg (Newton per
kilogram)
both weight and mass can be compared using a balance
the diagram below shows that mass never changes, however in different
gravitational fields, the strength can vary hence the weight is also affected.
The overall mass of the two Astronauts and
the satellite near earth’s surface is 1500kg,
but have a weight of 14,700N (this is
because there is a gravitational force acting
on the mass)
The overall mass of the two
Astronauts and the satellite in
space is 1500kg, but have a
weight of zero newtons (this is
because there is no gravitational
force on the mass in space)
Density
-
-
density is the mass per unit volume
the SI unit of density is kg/m3 (kilogram per metre cube)
less dense objects will float above more dense objects
differences in density may cause some liquids that do not mix to
float above each other, (fresh water is less dense than sea water so
it floats above sea water, oil is less dense than water so it floats
above oil)
density is calculated using the formula given below
𝝆=
𝒎
𝒗
Density of an irregular shaped object
-
find the volume of the irregular shaped object using displacement
method
add a known volume of water such as 20cm3 to a measuring
cylinder and record as V1
gently place the irregular shaped object in the water
measure the rise in volume and record V2
find the difference between V2 and V1 to get the volume
dry the object
place the object on an electronic balance and measure its mass
use the formula for density with the recorded measurements
Density of a regular shaped object
-
-
find the volume of the regular shaped object
use the formula Volume = base area x height to calculate the
volume of the object
the base of the object is considered as the cross sections from the
object which gives the same face no matter where the sections are
taken from (do not include this part in your answer)
place the object on an electronic balance
record its mass
use the density formula to calculate (write the formula in answer
space as it carries a mark)
Density of a liquid
-
use a measuring cylinder to measure certain volume of the liquid
place an empty beaker on an electronic balance and record the
mass
pour the measured volume of the liquid in to the beaker
find the difference in mass to get the mass of the liquid
use the formula for density to calculate the density of the liquid
(include the formula in your answer)
Floating
-
some objects can float in water or any other substance though they
be made from something more dense
similarly, a steel ship with a density of 7200kg/m3 is able to float in
water of density 1000kg/m3
this is because there are air spaces in the ship making the overall
density of the ship to be lower than water
Effect of forces
•
What is a force?
-
•
A push or a pull that acts on an object due to the interaction with
another object
A force can change the direction, velocity, size and shape of an
object
Resultant/Net Forces
-
A single force which describing all the forces acting on a single
body is known as resultant or net force
If the forces are in the same direction, then they should be added
If the forces acting are in different directions, they should be
subtracted
The resultant force is what determines the magnitude and the
direction of the force as a result of all the forces
The direction is the side with largest total force
4 N, Right
10 N, left
Resultant force = 10N – 4N
=6N to left
-
In the example above the net force or resultant force is 6N, the
forces are subtracted as they are in opposing directions and the
direction of the net force is to the left as the individual force is
greater towards the left than right
4 N, Right
4 N, Right
4 N, Right
Resultant force = 4N + 4N + 4N
=16N to right
-
Here the resultant force or net force is 16N to the right, all the
forces are added here as they are acting in the same direction so
the direction remains same, but the total resultant force is greater
than the individual forces acting on the object
4 N, left
4 N, Right
4 N, Right
4 N, left
4 N, Right
Resultant force on left Total Resultant force Resultant force on right
= 4N + 4N
= 16N – 8N
= 4N + 4N + 4N
=8N
=8N to the right
=16N
-
-
Here there is more than one force acting on either side, so find the
resultant force acting towards each side and then subtract the total
from each side to calculate the resultant force acting on the object
Sometimes the resultant force may be zero, this is when the forces
acting on the object are balanced (equal)
Only unbalanced forces can create a resultant force greater than
zero with a direction
Upthrust
Drag (air resistance)
Thrust (Driving Force)
Weight
Drag (air
resistance)
Friction
Friction
Weight
•
Types of forces
-
The force present when a string or rope is pulled or stretched is
known as tension (T)
Solid friction is the force between two surfaces that may impede
motion and produce heating
Friction (drag) acts on an object moving through water and gases
(water and air resistance), these forces usually oppose the direction
of motion
Hooke’s Law
-
•
Hooke’s law states that the extension of a spring is proportional to
the applied force
Limit of proportionality
-
Limit of proportionality is the point at which a spring stops obeying
Hooke’s law and no longer returns to its original size when
stretched. This is known as the point up to which extension is
directly proportional to the load.
Extension or
Length/ cm
Limit of proportionality
Load/N
•
Spring Constant (k)
-
Force per unit extension (x) is defined as the spring constant
The spring constant has an SI unit of Newton per centimetre (N/cm)
𝒌=
•
𝑭
𝒙
Extension
-
The SI unit for extension in centimetre
Extension = stretched – Unstretched length
Hooke’s Law: worked examples
(a)
Where height and load are given
Load/ N
Height/ cm
(I)
Keep in mind that height
and length are the same!
0
5
2
9
4
13
Calculating the spring constant
-
Take any sets of values and insert it to the formula
When substituting the value for “x” or extension, if the values given
are Height, make sure to subtract the stretched height from the
height at when a load of zero newtons is used as this is the initial
height before being stretched
Extension = stretched – Unstretched length
X = 13 – 5
X =8cm
𝒌=
𝑭
𝒙
K= 4N / (13-5) cm
K= 4N / 8cm
K= 0.5N/cm
(II)
Calculating the Height when a force of 8N is used
-
Always double check if the question is asking for length(height) or
extension!
If the question asks for height, first insert the springs constant and
the force (if you haven’t calculated the springs constant in a
previous part of the question calculate it using the formula as shown
in part (I)). Then calculate and you will get the value for “x” or the
extension. Substitute the values to the formula for extension
correctly! (Or just add the extension calculated to the unstretched
length)
𝒌=
𝑭
𝒙
𝟎. 𝟓 =
𝟖
𝒙
Here you’ve calculated “X” or the extension,
however the question asks for Height, so this is
not the final answer
0.5x = 8
X = 8 / 0.5
X = 16cm
Extension = stretched – Unstretched length
X=S–U
16(X or extension) = S (height or stretched)- 5(unstretched)
16 = S – 5
S – 5 = 16
S= 16 + 5
S= 21cm
(b)
Where Extension and Load are given
Load/ N
Extension/ cm
0
0
2
4
6
8
-
In this situation, you do not have to do any calculations to get
-
extension, as its already given!
The extension at zero newtons is zero cm as there would be no
extension if no load is added
(c)
Where a graph is given
-
Sometimes you may be asked to plot a graph with a set of data
given
In this case take Extension as the Y axis, and Load or Force as
your X axis
Extension or
Length/ cm
Load/N
(I)
Using data from the graph below, calculate the springs constant
-
This graph shows the length (height) and weight (load), so to
calculate you should start by taking a set of data
Draw a table like the one shown below and fill the data using the
graph
Force/N
Height/m
Height at zero
newtons/m
Extension/m
-
-
2
0.2
0.16
0.2-0.16
=0.4
Note that you will not have to calculate the extension (grey shaded
boxes in table drawn above) if it is given as the y axis, then you
may directly insert the values to your formula
Sometimes they may give length in metres as opposed to
centimetres
In that case, take the extension in meters, but keep in mind this will
affect the SI unit of the spring’s constant. The unit will be N/m
And make sure when you take a set of values from the graph that
the values are prior to the limit of proportionality being reached
𝒌=
𝑭
𝒙
K= 2N / 0.4m
K= 5N/m
(d)
Where you are asked to measure the length of a spring
-
When asked to measure the length of a spring the height shown as
l0 on the diagram should be measured
Newtons Laws of Motion
•
1st Law: The Law of Inertia
-
•
An object at rest remains at rest unless acted upon by another force
An object moving at constant speed will continue to move at
constant speed unless acted upon by a force
Inertia is what causes you to move forward on a moving bus when it
suddenly stops
2nd Law: The Law of Acceleration
-
•
The acceleration of an object is directly proportional to its force and
inversely proportional to its mass
This is shown by the formula F=ma
When the force acting on an object increases, the object
accelerates and vice versa
When the mass of the object decreases the object accelerates and
vice versa
If acceleration is to be calculated and velocity and time are not
given, this formula is to be used
Example; rockets accelerate when the engines expel the fuel, due
to this the overall mass of the rocket decreases and the rocket
accelerates forward
3rd Law: “Action Reaction”
-
for every action there is an equal and opposite reaction
Example; when you swim forward by applying a forward force, the
water applies the same force back on you
Circular Motion
-
-
When a force acts at 90 degrees or perpendicular to the direction of
motion of an object, the object changes direction, but the speed at
which it moves remains at a constant
This is what happens in circular motion, the resultant force acting
on the moving object known as the centripetal force acts
perpendicular to the direction of motion of the object. So, it moves
at constant speed with changing velocity (due to changing direction)
The diagram above shows the motion of Jupiter in 5 different
positions of its circular orbit around the sun
Centripetal Force (resultant force)
Direction of motion of Jupiter
Tangent taken by Jupiter if removed
from circular path
-
If another force acts an object in circular motion it takes a tangent
(moves out of the circular path) along its direction of motion
-
The circular motion of an object is affected by mass, speed, force
and radius
For a greater mass, a greater force is required where speed and
radius are constant
A faster moving object requires a greater force when mass and
radius are constant
A smaller radius requires a greater force
Jupiter has a greater mass than earth and Venus, so there has to
be a greater force to keep it in its circular motion
Venus has a faster speed than earth and Jupiter, so the centripetal
force needed to keep it in circular motion is greater when mass and
radius are constant
And since Venus has a smaller radius, a greater centripetal force
exists between the sun and Venus to ensure it stays in its circular
path.
-
-
Turning Effect of Force
•
Moment
-
The turning effect of force can be described as moments
Moment of force is defined as the product of force and
perpendicular distance to pivot
The SI unit of moment of force is Newton metre (Nm)
Moment of force = Force x Perpendicular Distance to Pivot
•
Equilibrium / Principle of Moments
-
The total clockwise moment is equal to total anticlockwise moment
The total upward force is equal to total downward force
the net/resultant moment and force is equal to zero
the formula used to calculate the forces or distances where an object in
equilibrium is;
F1d1=F2d2
Where on one side of the formula is clockwise moments and the other
side, the anticlockwise moments
This formula relates to the principle “total clockwise moment is equal to
total anticlockwise moment”. Every force acting on an object will have a
moment about its pivot. So, the direction (clockwise or anticlockwise) of
the moment is determined and the total of all clockwise moments is
represented on one side and the total of all anticlockwise moments is
represented on the other side
Moment of Force, Equilibrium: Worked Example
F
A
0m
15m
50m
80m
65m
0m
50m
40m
40N
20N
A
C
-1 Draw the arrows of all the forces acting on the object, arrows are
usually not given but the direction of force is included. If the
question states weight or mass know that it will always be a
downward force, however if it specifically says upward then draw an
arrow facing upwards at the distance mentioned or to be calculated.
-2 Bend the direction of the arrows towards the pivot, and mark it is a
clockwise (C) or anticlockwise (A) moment
-3 Calculate the distance of each force to the pivot
- Insert it to the formula, know that for each arrow you have to
4 multiply the force the certain arrow represents and the distance its
from the pivots, and then finally add the arrows that have moments
going in the same direction and insert this to one side of your
equation, and the moments from the opposite moment in the other
side of your equation
F1d1=F2d2
(20 x 50) + (F x 15) = (40 x 40)
1000 + 15F = 1600
15F = 1600 – 1000
15F = 600
F = 600/15
F= 40N
•
Moment: Additional Notes & Examples
-
To increase the size of the moment, move the object further away
from the pivot, as distance from pivot increases
Example;
-
In the diagram above, the moment due to the 200N on the spanner
is not strong enough to turn the wheel nut, and the mechanic
cannot increase the force, so instead he can move the point at
which he applies the 200N further to the right so the moment
becomes greater.
-
Sometimes to ensure that an object is in equilibrium or stable a
counterweight is added, this usually cancels out the effect of the
opposing moment that can disturb the equilibrium or the stability of
an object
Example;
-
-
Here the counterweights downward force creates an anticlockwise
moment that is equal to the size of the clockwise moment created
due to the block making the resultant moment zero. This prevents
the crane from toppling over.
-
When there is a resultant moment or force that is greater than zero
(unbalanced), the object will move in accordance to the direction of
the resultant moment or force
-
Example;
-
This example shows the forces acting on a two-person spanner,
here both moments act in the same anticlockwise direction, hence
the resultant moment is in an anticlockwise direction and will turn in
that direction. Keep in mind that there may be an opposing moment,
and in that situation the object will turn to the direction with the
greater moment about the pivot
-
When the pivot is not at the centre of mass always remember the
weight of the object will have a downward force at the centre, and
this force will also have a moment which must be taken in to
account in calculations. Remember to convert the mass in to
newtons!
-
Total upward force = total downward force, this can be used to find
the upward or downward forces acting on an object in equilibrium
when asked. Find the sum of forces on the side where all the forces
are given and that will be equal to the force on the opposing side.
This only applies to an object in equilibrium
-
Example;
80N + 80N (upward forces) = 160N (downward force)
Centre of Gravity
-
the point at which the weight of the object may be considered to act
symmetrical objects with uniform densities will have their centre of
gravity at the point of symmetry
Point of symmetry
•
Finding the centre of gravity of a plane lamina
-
Set up the apparatus as shown above
Suspend the plane lamina from the pin from point A and allow it to
hang freely
Suspend the plumb line from the same point and allow to hang
freely
Draw a line along the string
Repeat the procedure by suspending the lamina from other points
(B and C), and draw a line along the string each time
The point of intersection is the centre of gravity of the plane lamina
(irregular shaped object)
Put the pin at the point of intersection and see if it will balance on
the pin to confirm if the centre of gravity has been found
-
Stability
-
-
An object is considered to be stable when its centre of gravity lies
exactly above its base
If the centre of gravity falls outside the object, the object will fall
over (topple)
In the diagram above, the stability of the bus is being tested and the
platform is tilted to an angle. This causes the bus to start toppling
The bus starts toppling as its centre of gravity does not fall below its
base and falls outside the bus.
(If the centre of gravity does not fall below the base, and falls
outside the object, it will start to topple and fall over)
In the diagram below the bus is stable as centre of gravity falls
below the base of the bus
-
-
Objects which are wider will have a lower centre of gravity
The narrower an object, the higher its centre of gravity (less stable)
The closer to the surface the centre of gravity is, the more stable an
object is
Increasing the mass near the base of an object can also lower the
centre of gravity, this is usually done on cargo ships. The heavier
containers are loaded near the base to lower the centre of gravity
and make the ship more stable
In the diagram above C is most stable as it has the widest base and
a low centre of gravity
Since A narrows towards the top, it is likely to topple
B is uniformly narrow and its centre of gravity is highest making it
most likely to fall over
G has a high centre of gravity and a narrow base, making it
unstable
Momentum & Impulse
-
Momentum is defined as the product of mass and velocity
An object moving at a great speed may be described to have a
great momentum
The SI unit for Momentum is kilogram metre per second (kg m/s)
Momentum = mass x velocity
𝒑 = 𝒎𝒗
-
Impulse is defined as the product of force and the time for which a
force acts on an object
The SI unit for impulse is Newton Second (Newton second)
When the same force is applied for the same time, a larger object
would gain a lower velocity than a smaller object
Impulse = Resultant force x Time = Change in Momentum
𝑰 = 𝒇𝜟𝒕= mv-mu
Hence impulse can be found with two formulas
𝑰 = 𝒇𝜟𝒕
I= mv-mu
If the question has given impulse and momentum and either one of
the velocities, and asks to calculate the second velocity, you should
consider the second formula
If either impulse, force or time is given you should opt to use the
first formula
-
Resultant force can also be calculated using impulse or momentum
Resultant force is defined as the change in momentum per unit time
𝒎𝒗 − 𝒎𝒖
𝑭=
𝒕
𝑰
𝑭=
𝒕
Momentum & Impulse: Worked Examples
(a) Calculations
2kg
the cart shown above has a mass of 2kg and moves at a velocity of
5m/s. find its momentum
𝒑 = 𝒎𝒗
𝒑=𝟐𝑿𝟓
𝒑 = 𝟏𝟎 𝒌𝒈 𝒎/𝒔
after a few seconds the cart speeds up and moves at 9m/s. find the
resultant momentum
𝝆 = mv-mu
𝒑 = (2 x 9) – (2 x 5)
𝒑 = 8 Kg m/s
What is the impulse acting on the object
I= mv – mu
I = 8N s
Calculate the resultant force acting on the object (the time for when
speed increases is 0.5s
𝑭=
𝒎𝒗−𝒎𝒖
𝒕
𝑭=
𝟖𝒌𝒈 𝒎/𝒔
𝟎.𝟓𝒔
= 𝟏𝟔𝑵
Below shows cart B, a resultant force of 50N acts on it for 2s, calculate its
impulse
3kg
𝑰 = 𝒇𝜟𝒕
𝑰 = 𝟓𝟎 𝑿 𝟐
𝑰 = 𝟏𝟎𝟎 𝑵 𝒔
cart B was initially travelling at 4m/s until the resultant force acted on it, calculate
its final velocity
I= mv-mu
100= (3 X v) – (3 X 4)
3v – 12 = 100
3v = 100 + 12
V= (112)/3
V= 37.3 m/s
Principle of Conservation of Momentum
-
The principle of conservation of momentum states that the
momentum before a collision is equal to the momentum after a
collision, provided that no external forces act on it (if collision occurs
in a closed system)
Momentum before collision = momentum after collision
m1v1 = m2v2
-
-
when calculating the resultant momentum prior to or after a collision
you must be careful with the masses. if the objects join up and
move together you must add the masses and consider it as one
object
if the objects lose any mass during collision, you must subtract it
from the initial mass
Calculations: Conservation of momentum
Before collision
2m/s
3m/s
Sticky substance
4kg
1kg
After collision
V?
1kg
4kg
Step 1: calculate the resultant momentum before collision
Momentum of 1kg cart = 1 x 2 = 2kg m/s
Momentum of 4kg cart = 4 x -3 = -12kg m/s
Resultant momentum = 2 + (-12) = -10kg m/s
(Here the velocity for the 4kg cart is negative as its moving backwards, velocity can be
positive or negative as it has a direction)
Step 2: Calculate the resultant moment after collision
(Here since both carts are connected after collision you have to add the masses and
consider it as one object)
Momentum of connected carts= (1+4) x Xm/s = 5x m/s
Step 3: m1v1 = m2v2
5x = -10
x= -10/5, x= -2m/s
Energy & Work Done
• Energy
-
-
-
Energy may be stored in different forms, though the main types are
potential and kinetic
Moving objects have kinetic energy, the faster the object moves the
more kinetic energy the object has and vice versa
Non-moving objects have gravitational potential energy, potential
energy increases as height increases. When a non-moving object
starts moving this energy is converted to kinetic energy and vice
versa
Chemical energy is the energy stored in the bonds of chemical
compounds, when new bonds are formed during chemical reactions,
energy is released. Energy is stored in this form in batteries, biomass,
wood, petroleum (when burnt releases energy). This is a form of
potential energy
Electrostatic energy is a potential energy resulting from the
interaction between electric charges
Nuclear energy is the energy present within the nucleus of an atom
Internal energy (thermal energy), the total energy of a closed system
of molecules
The energy stored in a stretched rubber band, spring or rope is
known as Elastic Energy
• Law of Conservation of Energy
-
The law of conservation of energy states that energy cannot be
created nor destroyed, but changes from one form to another
• Work-done
-
Work done is the change in energy of an object
Mechanical work done or electrical work done is equal to the energy
transferred
It has the SI unit Joules (J)
Work done = Force x Distance which the object is moved for
W=F x d
-
Example;
-
The diagram above shows the work done by a worker pushing up a
wheel burrow up a plank
W=F x d
W=290 x 2
W= 580 J
-
The distance is taken as 2.0m instead of 0.60m, as for work done to
be calculated the distance for which the force is applied to an object
is considered
• Sankey Diagrams
- Sankey diagrams are flow diagrams used to visualise the
transfer of energy
- The width of the arrows in a Sankey diagram correlates
with the amount of energy transferred
- The diagram below shows the transfer of energy in an old
electric kettle
- The missing values can be calculated from the diagram by
subtracting the total energy input from the wasted energy
- Since more energy is wasted than is useful the arrow
representing wasted energy is wider.
• Kinetic Energy
- Kinetic energy is the energy present in moving objects
- The SI unit for kinetic energy is Joules (J)
Kinetic Energy = ½ x mass x Velocity2
𝑬𝒌 =
𝟏
𝒎𝒗𝟐
𝟐
• Potential Energy
- The energy present in non-moving objects
- The SI unit for potential energy is Joules (J)
Potential Energy= Mass x Gravity x Vertical Distance
𝑬𝒑 = 𝒎𝒈𝒉
Where potential energy is being converted to kinetic energy, and kinetic
energy to potential energy, and you are not provided with mass and
asked to find either the vertical height or velocity, the formula below
should be used
Loss in Potential Energy = Gain in Kinetic Energy
𝟏 𝟐
𝒈𝒉 = 𝒗
𝟐
Energy Resources
• Geothermal Energy
- The diagrams above show a geothermal power station
- Water is pumped down to hot rocks, which gets converted
to steam and goes up a pipe and turns a turbine which
turns a generator
- This generator has a coil inside which turns in a magnetic
field hence producing an electric current
- The steam is then condensed and cooled and sent back
to the hot rocks making this process sustainable
• Fossil Fuels
- Coal, methane (natural gas) and crude oil are all fossil
fuels
- There are many different types of fossil fuels
- First the fossil fuels are burnt in a boiler, where
combustion takes place releasing a lot of energy
- This energy heats up cold water and converts it to steam,
which flows out of the boiler to a turbine
- The steam causes the turbine to turn
- The turbine is connected to a generator which has a coil
inside that turns along with turbine
- When the coil is turned inside the magnetic field present
in the generator, an electric current is produced
• Hydroelectric Dams
- Hydroelectric dams block the natural flow of water in
rivers, causing the water levels to rise in the reservoir or
behind the dam
- When the watered is stored in the reservoir it has
Gravitational Potential Energy
- The water is sent through a penstock
- Within the penstock is a turbine, which is turned as water
enters
- When the turbine is turned, the generator is also turned
- Due to this the coil connected to the turbine turns inside
the magnetic field present in the generator producing
electricity
• Tidal Energy
-
Instead of damming water on one side like a conventional
dam, a tidal barrage allows water to flow into a bay or
river during high tide, and releases the water during low
tide
- When the water flows through a turbine is turned
- The turbine turns a generator
- The generator has coil with a magnetic field present
inside, which is turned as the coil is connected to the
turbine, hence producing an electric current
• Wind Energy
- Wind energy is generated using wind turbines
- The turbines are turned due to the winds flow
- When the turbines are turned, the generator to which they
are connected are also turned
- So, the coil present in a magnetic field within the
generator connected to the turbine is turned and an
electric current is produced
• Solar Cells
- Solar cells work by absorbing light energy coming from
the sun
- This light energy is used to generate an electric current
• Solar Panels
- Solar panels absorb the radiations coming from the sun
and heat up metal tubes carrying water, this in turn heats
up the water inside the pipes
• Nuclear Energy via Nuclear Fission
- Inside nuclear reactors, nuclear fission takes place
releasing vast amounts of energy
- Nuclear fission is the splitting up of the nuclei of the atoms
to form smaller nuclei
- This causes water to vaporize and form steam which
flows through a pipe and turns a turbine
- The turbine then turns a generator which turns a coil in a
magnetic field, producing an electric current
(*you do not need to know how to label a nuclear reactor*)
- currently research is being done on how nuclear fusion can
be carried out on earth to produce energy, it is not possible
right now due to the high temperatures it requires. Nuclear
fusion is where two small nuclei join together to form a larger
nucleus and lots of energy. This occurs in stars.
• Biofuels
-
-
(*you do not need to know how to label a fermenter nor
how biofuels are produced*)
To a fermenter yeast and plant crops are added. Along
with this a suitable pH and temperature for the yeast to
thrive in is provided
The yeast feed on the sugars in the plant crops producing
ethanol and carbon dioxide
The remaining products at the end of the fermenter are
then distilled and pure ethanol is collected
This ethanol can be burnt and used as a fuel (in burners,
to produce heat to vaporize water to steam to turn
turbines and generators)
• Advantages and Disadvantages of Energy Resources
Type of energy
resource
Fossil Fuels (Coal,
crude oil, natural gas;
methane)
Advantages
Available
Reliable for large scale
energy production
Geothermal (heat from Continuous supply
Does not require fuel
earth)
No waste products
Wind (Turbines)
No fuel cost
Less air pollution
No greenhouse gases
produced
Tidal and Hydroelectric No pollution
Reliable and can produce a
dams (water)
large amount of electricity at
short notice
Renewable energy resource
Solar Cells (light)
Solar Panels
(Radiation from sun)
Free fuel
Renewable
No air pollution
No greenhouse gases
Little maintenance
Quiet
Reduce cost of producing
hot water
Solar energy is renewable
Cut cost of household bills
Disadvantages
Non renewable
Decreasing supply
Produces atmospheric
pollutants when burnt
Produces greenhouse gases
Contributes to acid rain
Expensive to prevent release
of harmful gases in to
atmosphere via catalytic
converters and flue gas
desulfurizers
Only available in certain
areas
Thin crust
Rocks can cool
Limited lifespan
Noise pollution
Visual pollution
Harms birds
Deforestation
Expensive to install
Depends on weather
conditions (windy or not)
Expensive to build
Damages fragile habitats
Very few suitable locations
The technology is not
advanced enough for large
scale electricity production
Requires a lot of space
No energy produced at night
or in absence of sun
Less energy in winter
Produces DC
Need to be large scale to
produce high temperatures
Not regular, as sun doesn’t
shine regularly
Nuclear Energy
(Nuclear fission in
nuclear reactors)
No pollution
Reliable as produces energy
on larger scales
Biofuels (fermentation No atmospheric pollutant
produced
of crops)
Renewable resource
Carbon neutral
Uranium ore, fuel for fission
is finite in amount
Non renewable
Radioactive waste
Monocultures are setup to
grow crops
Releases carbon dioxide to
atmosphere
Takes time to grow crops
Efficiency
- Efficiency is defined as the ratio between the total energy
or power input and the useful energy or power output
- There are two equations used to calculate efficiency
- Efficiency does not have an SI unit, but is usually
calculated in percentage
𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 =
𝒖𝒔𝒆𝒇𝒖𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒐𝒖𝒕𝒑𝒖𝒕
𝑿 𝟏𝟎𝟎
𝒕𝒐𝒕𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 𝒊𝒏𝒑𝒖𝒕
𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 =
𝒖𝒔𝒆𝒇𝒖𝒍 𝒑𝒐𝒘𝒆𝒓 𝒐𝒖𝒕𝒑𝒖𝒕
𝑿 𝟏𝟎𝟎
𝒕𝒐𝒕𝒂𝒍 𝒑𝒐𝒘𝒆𝒓 𝒊𝒏𝒑𝒖𝒕
- The useful energy or power may be calculated by
subtracting the wasted power or energy from the total
input
Useful energy = total energy – wasted energy
Useful power = total power – wasted power
Power
- Power is defined as the rate at which energy is supplied
- Power is measured in watts (W)
- The equation to find power is as shown below
𝑷𝒐𝒘𝒆𝒓 (𝑷) =
𝑾𝒐𝒓𝒌 𝒅𝒐𝒏𝒆 𝒐𝒓 𝑬𝒏𝒆𝒓𝒈𝒚 (𝑾 𝒐𝒓 𝑬)
𝒕𝒊𝒎𝒆 𝒊𝒏 𝒔𝒆𝒄𝒐𝒏𝒅𝒔 (𝒕)
Solid Pressure
- Pressure is defined as the force per unit area
- Pressure is measured in the SI unit Pascals, or Pa
- This is only when the area is given in metre squared. If area
is given in centimetre squared or kilometre squared the SI
unit may be given as N/cm2 or N/km2
𝑷𝒓𝒆𝒔𝒔𝒖𝒓𝒆 (𝑷) =
𝑭𝒐𝒓𝒄𝒆 𝒐𝒓 𝑾𝒆𝒊𝒈𝒉𝒕 (𝑭 𝒐𝒓 𝑾)
𝑨𝒓𝒆𝒂 (𝑨)
- The larger the surface area is, the smaller the pressure will
be
- The smaller the surface area is the larger the pressure will
be
- This means that pressure inversely proportional to the area
- This is why tractors are usually fitted with large tyres, as the
large contact area with the ground reduces the pressure
and prevents it from sinking
Liquid Pressure
- The pressure of the same liquid at the same depth and
density is the same
- As density or depth of the liquid increases, the pressure will
also increase
- Liquid pressure is measured in the same SI unit as solid
pressure, Pascals (Pa)
𝑷𝒓𝒆𝒔𝒔𝒖𝒓𝒆 (𝑷) = 𝑫𝒆𝒏𝒔𝒊𝒕𝒚(𝝆) 𝑿 𝑮𝒓𝒂𝒗𝒊𝒕𝒚 (𝒈) 𝑿 𝒉𝒆𝒊𝒈𝒉𝒕 (𝒉)
- In the diagram above the stream of water flows furthest as
it is at the greatest depth, this is because the pressure is
greatest at greater depths
- So as depth decreases pressure decreases, and so does
the size of the water stream