SUBJECT: PHYSICS
DATE: AUGUST 25 TH , 2023
CLASS: YEAR 10 INTGRATED
TERM: FIRST
WEEK: ONE
TOPIC: MEASUREMENT
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
ii.
iii.
iv.
v.
Explain the term measurement.
Describe how to use rules for measuring cylinders, to find a length or volumes
Explain measurement of mass and time
Describe how to use Vernier calipers and micrometer screwguage to measure length.
Describe different between mass and weight.
CONTENT
MEASUREMENT OF LENGTH OR DISTANCE
Distance is the length between two points. The S.I unit of length is the meter (m). Different
equipments are used to measure length depending on the distance involved.
Long distances are measured with tapes and metre rules graduated in centimeters, millimeters
and metres. The length of a metre rule is 1 metre or 100cm. each centimeter is subdivided
into 10 equal parts. The smallest division on the metre rule is 1mm (0.1cm).The reading
accuracy of a metre rule is 1mm (0.1cm).
The Vernier Calipers measures length with greater precision than the metre rule.Smaller
distances like the diameter of a coin, the diameter of a rod or the diameter of a pendulum bob
are measured with vernier calipers and the reading accuracy is 0.01cm or 0.1mm. The
uncertainty or accuracy of the vernier calipers is ± 0.01cm which is smaller than that of the
metre rule.
The vernier calipers have two scales: the main (M) scale and the vernier (V) scale.
Main scale (M):
it is the same as that of metre rule.
It is divided into centimetres and millimetres. Each division on the main scale represents
0.1cm (1.0 mm).
Vernier Scale:
The vernier or moving scale slides beside the main scale.One division on the vernier scale is
0.09 cm (0.9mm).The addition of the main scale and the vernier scale reading gives the total
length of object measured.
Uncertainty = one division on the M-scale – one division on the V-scale
= 0.10cm – 0.09 cm
= 0.01cm (0.1mm).
Note: The vernier calipers can measure lengths correctly to 2 decimal places in centimetres.
USES OF VERNIER CALIPERS.
i.
ii.
iii.
iv.
To measure the external diameters of a pipe
To measure the internal diameter of a pipe or hollow tube
To measure the depth or cavity of a hollow object like test tube
To measure the thickness of a disc (e.g. a coin)
Micrometer screw gauge
The micrometer screw gauge is used to measure small lengths with greater precision than the
vernier calipers. The uncertainty or the accuracy is 0.001 cm (0.01mm).It has two scales main
scale and vernier scale.
Uses of micrometer screw gauge:
i.
ii.
To measure the external diameters of pipes
To measure the thickness of a very thin wire, metal sheets, sheet of paper, disc and
pendulum bobs.
MEASUREMENT OF MASS, WEIGHT AND TIME
The mass of a body is the quantity of matter or material in the body .It is a scalar
quantity and the S.I unit is Kilogram .The instruments for measuring mass is beam
balance and chemical balance.
Time is measured with stopwatch, stop clock, ticker tape timer and other instruments which
are repetitive.The SI unit of time is seconds. Time-measuring devices rely on some kind of
constantly repeating oscillation. A
swinging pendulum controls a pendulum clock. A stopwatch is adequate for finding the
period in seconds of a pendulum. Ticker tape timers or data-loggers are often used to record
short time intervals in motion experiments
Weight is the force of gravity acting on a body .It is a vector quantity and the S.I unit
is Newton. The weight of a body is measured with a spring balance.
W = mg
Where,
M= mass
g- acceleration due to gravity.
W – weight
DIFFERENCES BETWEEN MASS AND WEIGHT
Mass
Weight
1. Mass is the amount of
matter in a body
Weight is the gravitational
force which attracts every
object towards the centre of
the earth
2. Mass is constant
everywhere in the
universe
Weight varies from place to
place depending on gravity
3. Mass is a scalar
Weight is a vector quantity
quantity
4. Mass is measured with Weight is measured with a
a beam balance or other
spring balance
balances
5. The SI unit of mass is
kilogram (kg)
The SI unit is Newton (N)
Frequency and period of oscillation
Frequency is the number of vibrations ( oscillations) completed in one
second.
The unit of frequency is the Hertz( Hz)
Period: period is the time it takes to complete one vibration.
The unit of period is second (s).
Using symbols
T = t/N
Where T = period of oscillation or vibration
t = time to complete N vibrations
N = number of vibrations completed in t seconds.
The period of oscillation is related to frequency by:
f = 1/T or T = 1/f
EVALUATION:
i.
ii.
iii.
iv.
v.
Explain the term measurement.
Explain how to use rules for measuring cylinders, to find a length or volumes
Briefly explain measurement of mass and time
Describe how to use Vernier calipers and micrometer screwguage to measure length.
In a tabular form, what are the different between mass and weight?
ASSIGNMENT
WORKSHEET ON VERNIER CALIPERS AND MICROMETER SCREW
GAUGE.
1.
SUBJECT: PHYSICS
DATE: AUGUST 25 TH , 2023
CLASS: YEAR 10 INTGRATED
TERM: PHYSICS
WEEK: TWO
TOPIC: MOTION
SUB-TOPIC: SPEED, SPEED TIME GRAPH/ DISTANCE TIME GRAPH, VELOCITY,
ACCELERATION AND EQUATION OF MOTION
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
ii.
iii.
iv.
v.
Define speed and calculate average speed
Sketch, plot and interpret distance- time and speed –time graphs
Explain the term velocity and acceleration.
Calculate acceleration from the gradient of speed-time graph
Describe the motion of object falling in a uniform gravitational field with and without
air/liquid resistance.
CONTENT
MOTION
SPEED, VELOCITY AND ACCELERATION.
SPEED
This can be defined as the distance per unit time. Speed is defined as the distance travelled
per unit time. It is a scalar quantity and the S I unit is m/s.
Speed = distance/Time
Average speed = distance moved
time taken
VELOCITY
This can be defined as the distance per unit time in a specified direction. Velocity is the
distance travelled in unit time in a stated direction. It can also be defined as displacement
per unit time. It is vector quantity and the SI unit is m/s. Displacement (m) – how far
something has moved from its starting position.
Velocity = Displacement/ Time
ACCELERATION
This can be defined as the change in velocity per unit time. ². Acceleration is the change of
velocity in unit time.It is a vector quantity and the SI unit is m/s².
Acceleration = Change in velocity/time
a = V – U/ t
Where,
a = acceleration, V = final velocity, U = initial velocity, T = time
S = Distance.
EXAMPLES
Example of speed calculation questions
Q1.1 A train was timed to take 2.5 seconds when passing between two posts 100 m apart.
(a) What is the speed of the train in m/s?
v = s ÷ t = 100/2.5 = 40 m/s
(b) What is the speed of the train in km/hour?
(I'm just deliberately asking a more arithmetically awkward question of a sort you may have
to deal with)
100 m = 100/1000 = 0.1 km
v = s ÷ t = 0.1/2.5 = 0.04 km/s
Since 1 hour equates to 60 x 60 = 3600 seconds
In 1 hour the train will travel 0.04 x 3600 km, so speed = 144 km/hour
Q1.2 How far will a car travel in 15 seconds at a speed of 20 m/s?
v = s ÷ t , so s = vt = 20 x 15 = 300 m
MOTION GRAPHS
DISTANCE – TIME GRAPHS
The gradient (slope) at any point on the graph gives you the speed at that point.
Since speed = distance ÷ time, then for graphical work
speed = (change in vertical y axis for distance) ÷ (change in horizontal x axis for time)
speed = ∆d / ∆t
The steeper the gradient the greater the speed
1.Distance - time graphs - acceleration - speeding up :Graph curves upwards, showing
increasing speed/velocity with time (acceleration), for each incremental time unit (e.g. minute
or second) there is an ever increasing (larger) distance (∆d) covered in the same time (∆t).
speed = ∆d/∆t = the gradient of graph (∆d/∆t) is continuously increasing.
(2) Distance - time graphs - motionless – stationary: Graph is flat/horizontal, indicating
zero speed/velocity, there is no increase in distance with time, and object has stopped moving.
(3) Distance - time graphs - deceleration - slowing down: Graph shows the curve is leveling
off, steadily decreasing speed/velocity with time (deceleration), for each incremental time
unit (e.g. minute or second) there is an ever decreasing (smaller) distance covered in the same
time.
(4) Distance - time graphs - constant speed: Graph is linear, showing constant
speed/velocity, the distance covered in any equal time increment is the same.
The four graphs above illustrate of what you might see at any point on a distance-time graph,
SPEED/VELOCITY – TIME GRAPHS
Acceleration is about change in speed or velocity of an object and is not the same as speed
or velocity.
The interpretation of the seven graphs above, by considering the gradient - positive, negative
or zero, and their mathematical sign if the values of acceleration (+) or deceleration (-) are
used in calculations.
Acceleration is the rate of change of velocity with time
Acceleration = change in velocity ÷ time taken to effect the velocity change
a (m/s2) = Δv (m/s) ÷ Δt (s) (actual numerical calculations are dealt with further down the
page)
A comparison of speed/velocity - time graphs
1
2
3
4
5
6
7
Graph curves upwards, velocity is increasing (+ve), but also shows increasing
acceleration, speeding up at an increasing rate.
Graph is flat, shows constant velocity/speed (+ve), zero acceleration.
Graph shows decreasing acceleration (+ve), BUT not slowing down! Still speeding up
but at a decreasing rate.
Graph is linear, shows constant or uniform acceleration (+ve), constant rate of
increasing velocity.
Graph is linear, shows constant or uniform deceleration (-ve), velocity decreasing,
constant rate of deceleration.
Graph shows decreasing deceleration (-ve), velocity decreasing, but decelerating at an
increasingly slower rate.
Graph shows increasing deceleration (-ve), velocity decreasing, but slowing down at
an increasingly faster rate!
UNIFORM AND NON- UNIFORM ACCELERATION
A stone is dropped from a height with no air resistance. The velocity – time graph for the
stone would be as shown below:
The acceleration would be uniform i.e. the acceleration of free fall (g).
In practice, there is air resistance on the stone and this affects its motion producing a non
uniform acceleration.
At the point when the stone is dropped, it has no velocity. This means that its initial
acceleration is 0m/s² because there is no air resistance on it. However, as the velocity
increases, air resistance also increases.
Eventually, the air resistance is so great that the velocity reaches its maximum constant value
called the terminal speed and the acceleration falls to zero.
At terminal speed, air resistance = weight of the body or object.
EQUATIONS OF A UNIFORMLY ACCELERATED MOTION
If a body is moving with uniform acceleration and its velocity increases from u to v in time (t)
then,
V = U + at------ i
V² = U² + 2as ----- ii
S =ut + ½ at² ------- iii
S = (V+ U/2)t ---------iv
Where,
V = Final velocity, U = Initial velocity, S = Distance, a = Acceleration
t = Time
EXAMPLE
A car starts from rest and accelerates at 2m/s²for 10s. Calculate:
i) The final velocity
ii) The distance travelled
ACCELERATION DUE TO GRAVITY
The acceleration of objects due to the earth’s gravitational attraction is
called acceleration due to gravity. It is represented by a symbol whose
average value is given by 9.8m/s².
The equations of a body moving under gravity are obtained by replacing (s)
and (a)with (h) and (g), h is the highest distance of the object above the
ground level and g is the acceleration due to gravity.
When the object moves upward a = -g and when it moves downward a =
+g. Thus, the equations of motion under gravity are given below gravity
are given below:
V
u
, h
u
,
u
When a body is released from a height above the ground, the initial
velocity (u)is zero , but when it is thrown upwards its velocity at the top is
zero .It has its maximum velocity when it hits the ground again.
1. EXAMPLES
A cricket ball is thrown vertically upwards with an initial velocity of
40m/s. Find: i. it’s velocity after 3 sec.
ii. The maximum height attained and time taken to reach
2. An orange drops from a tree at a height of 100m. Calculate: i. the
velocity with which it hits the ground.
ii. The time taken to strike the ground.
EVALUATION:
i.
ii.
iii.
iv.
v.
Explain speed and average speed
Describe how to sketch, plot and interpret distance- time and speed –time graphs
Explain the term velocity and acceleration.
Describe acceleration from the gradient of speed-time graph
Describe the motion of object falling in a uniform gravitational field with and without
air/liquid resistance
WORKSHEET /ASSIGNMENT
3.
SUBJECT: PHYSICS
CLASS: YEAR 10 INTGRATED
DATE: AUGUST 25 TH , 2023
TERM: FIRST
WEEK: THREE
TOPIC: DENSITY
SUB-TOPIC: REGULAR SHAPED SOLID, IRREGULAR SHAPED SOLID, FLOATING
BASED ON DENSITY
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
ii.
iii.
iv.
v.
Explain the term density
Solve simple question on density
Describe density of regular and irregular shape of solid
Describe the density of liquid and gas (air)
Explain floating and sinking.
CONTENT
DENSITY
This is defined as the mass per unit volume.
Mathematically, Density = mass / volume
The S.I unit of density is kg/m³. Note that 1g/cm³ = 1000kg/m³
MEASURING THE VOLUME OF A LIQUID
The volume of a liquid of about 1 liter can be measured using a measuring cylinder.
MEASURING OF A REGULAR SOLID
If an object has a simple shape .It’s volume can be calculated e.g. a cylinder, a cuboid, a cube
etc.
MEASURING OF AN IRREGULAR SOLID
If a shape is irregular, for the volume to be calculated or determined the solid can be lowered
into a partly filled measuring cylinder and the rise in the level of the volume of water gives
the volume of the solid. If the solid floats it can be weighed down with lump of metal, the
total volume is found. The volume of the metal is measured in a separate experiment then
subtracted from the total volume, to give the volume of the floating object.
Measuring the volume of an irregular solid: method 1
Measuring the volume of an irregular solid: method 2
MEASURING DENSITY
The density of material can be found by calculating the mass and the volume.
RELATIVE DENSITY
The relative density of a substance tells how the density is compared with that of water that is
relative density of the substance to that of the water. Relative density has no unit.
SUBSTANCE
DENSITY g/cm³
Copper
8.9
Iron
7.9
Kerosene
0.87
Mercury
13.6
Water
1.0
EXAMPLE
Calculate the density of a long cuboid shape wood 10cm by 6cm by 4cm
with mass 100g.
Liquid
The mass of an empty beaker is found on a balance. A known volume of
the liquid is transferred from a burette or a measuring cylinder into the
beaker. The mass of the beaker plus liquid is found and the mass of liquid
is obtained by subtraction.
Air
Using a balance, the mass of a 500 cm3 round-bottomed flask full of air is
found and again after removing the air with a vacuum pump; the difference
gives the mass of air in the flask. The volume of air is found by filling the
flask with water and pouring it into a measuring cylinder.
Floating and sinking
An object sinks in a liquid of lower density than its own; otherwise it
floats, partly or wholly submerged. For example, a piece of glass of
density 2.5 g/cm3 sinks in water (density 1.0 g/cm3) but floats in mercury
(density 13.6 g/cm3). An iron nail sinks in water but an iron ship floats
because its average density is less than that of water, due to the lowdensity air enclosed in the hull.
EVALUATION:
i.
ii.
iii.
iv.
v.
Define density
State the formula used to calculate density
Describe density of regular and irregular shape of solid
Explain the density of liquid and gas (air)
Explain why float object and sink.
Assignment
SUBJECT: PHYSICS
CLASS: YEAR 10 INTGRATED
DATE: AUGUST 25 TH , 2023
TERM: FIRST
WEEK: FOUR
TOPIC: FORCES: EFFECTS OF FORCE
SUB-TOPIC: EFFECTS OF FORCE, HOOKE’S LAW, FRICTION, APPLICATIION OF
FORCE =MA. CENTRIPETAL FORCE
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
ii.
iii.
iv.
Explain the effect of force
Explain the term elasticity of a material
State Hooke’s law and recall use the of formula
Describe the significance of the limit of proportionality for an extension – load graph.
v.
Explain friction as the forces between two surfaces.
CONTENT
FORCE
A force can be defined as a pull or push that tends to change the state of a body or the
uniform motion in a straight line.
EFFECTS OF A FORCE
The following are the effects of a force:
i.
ii.
iii.
iv.
It changes the shape of a body.
It changes the size of a body.
It changes the direction of a body.
It makes a body to slow down or stop.
ELASTICITY
This is the ability of a body or substance to regain its original shape or size after being
distorted by an external force.
ELASTIC MATERIAL
An elastic material is one that regains its original shape and size after the distorting force has
been removed.
HOOKE’S LAW
It states that provided the elastic limit of an elastic material is not exceeded the extension of
the object is directly proportional to the applied force or load.
Mathematically, F = k e
Where, f= Applied force
e extension measured in metre.
k- force constant measured in metre.
Example
A force of 0.8N stretching an elastic spring by 2cm. Find the constant of the spring.
GRAPH OF HOOKE’ S LAW
DIAGRAM
PO – Proportionality limit
E- Elastic limit
Y – Yielding point
B –Breaking point
OE – Elastic region
EB – Plastic region
PROPORTIONALITY LIMIT: This is the limit at which the extension is proportional to
the force applied.
ELASTIC LIMIT: This is the limit of beyond which the stretched wire does not return to its
original length when the force is removed.
YIELD POINT: This is the point beyond the elastic limit in which the elastic material has
yielded it’s elasticity permanently and has become a plastic.
BREAKING POINT: This is where the material may finally snap or break.
Limit of proportionality the point at which the load-extension graph becomes non-linear
EXAMPLE
A spring is stretched 10mm (0.01m) by a weight of 2.0N. Calculate:
(a) the force constant k, and
(b) the weight W of an object that causes an extension of 80mm (0.08m)
SOLUTION.
(a)
f = kx
k = f/x
k = 2.0N/0.01m
k =200 N/m
W = stretching force F
=K×x
= 200N/m × 0.08m
FRICTION
Friction occurs when there is a relative motion of one body over the other body thereby
opposing the motion of the sliding body on the other body.
TYPES OFFRICTION
I. Static friction
II. Dynamic friction
F = UR
F = Frictional force
R = Normal reaction
W = Weight
U = Coefficient of friction
EVALUATION:
i.
ii.
iii.
iv.
v.
Describe the effect of force
Explain the term elasticity of a material
State Hooke’s law
Describe the significance of the limit of proportionality for an extension – load graph.
Explain friction as the forces between two surfaces.
ASSIGNMENT
SUBJECT: PHYSICS
DATE: AUGUST 25 TH , 2023
CLASS: YEAR 10 INTEGRATED
TERM: FIRST
WEEK: FIVE
TOPIC: FORCES: EFFECTS OF FORCE
SUB-TOPIC: NEWTON’S FIRST LAW OF MOTION, NEWTON’S SECOND LAW OF
MOTION, INTRODUCE EQUATION F=MA, NEWTON’S LAW OF MOTION,
MOMENTUM, PRINCIPLE OF CONSERVATION OF MOMENTUM
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
ii.
iii.
iv.
State Newton’s law of motion
Apply Newton’s law of motion to solve problem
Explain the concept of momentum and impulse
Describe the use of momentum equation
v.
vi.
Apply the principle of the conservation momentum to solve problem
Explain the term collision
CONTENT
NEWTON’S LAWS OF MOTION
NEWTON’S FIRST LAW OF MOTION
It states that every object continues in the state of rest or uniform motion in a straight line
unless acted upon by an external force.
NEWTON’S SECOND LAW OF MOTION
It states that the time rate of change of momentum is proportional to the force and takes place
in the direction of the force.
F = change in momentum / time
Momentum = mass x velocity
F = mv – mu / t
F =m (v – u) / t
But a = v – u / t
F=mxa
F = ma
NEWTON’S THIRD LAW OF MOTION
It states that for every action there is an equal but opposite reaction.
MOMENTUM
The momentum of a moving object is defined as the product of the mass and velocity.
Note that it is not just the speed, rather the velocity. Remember, the difference between the
speed and the velocity is that velocity is a vector; it has a direction associated with it. This
means that momentum is a vector quantity. It has both a magnitude (mass x speed) and a
direction (the direction the object is moving).The formula for momentum is:
p=mv
Where p stands for momentum, m stands for mass (in kilograms), and v stands for velocity
(in meters/sec). This means that momentum has units of kgm/s (kilogram-meter per second).
Example: A runner has a mass of 75 kg and is running at 6 m/s (about 13.5 mph). The
runner's momentum would be:
p=mv
p = (75 kg) x (6 m/s)
p = 450 kgm/s
IMPULSE
The product of the force and the time the force acts is known as the impulse given to the
object. This impulse produces a change in the object's momentum.
The formula for Impulse is: I = F t
where I stands for impulse, F stands for the force acting on the object, and t stands for the
time the force acts on the object. To give an object an impulse means that you are applying a
force for a given period of time to change the object's motion or momentum.
In fact, an impulse given to an object is equal to the change in momentum of the object.
Examples:
1. A 1000 kg car is at rest initially. A 500 Newton force is applied to the car in the
forward direction for 10 seconds. How fast is the car going at the end of the 10
seconds?
Solution
Given: m=1000 kg ; F=500 N ; t=10 sec ; initial u = 0 m/s
Want: final v
Eqn: F t = m v; (since initial v=0)
v = (F t)/m = (500N x10s)/ (1000 kg) = 5 m/s.
So the final speed of the car is 5 m/s.
2. A force of 1000 N acts to stop a 1000 kg car moving at 20 m/s. How much time
does it take the car to stop?
Solution
Given: F = -1000 N; Change in v = -20m/s ; m=1000 kg
Want: Time (t)
Eqn: F t = m (change in v)
t = m (change in v)/F = (1000kg)(-20m/s)/(-1000N) = 20 sec.
So time required to stop the car is 20 seconds.
COLLISIONS
There are two types of collisions:
a. Elastic collision
b. Inelastic collision
ELASTIC COLLISION: In this collision, both kinetic energy and momentum are
conserved.
Momentum: M1U1 + M2U2 = M1V1 + M2V2
Kinetic energy: 1/2M1 (U1)² + 1/2M2 (U2)² = 1/2M1 (V1)² + 1/2M1 (V2)²
INELASTIC COLLISION: In this collision, only momentum is conserved. Kinetic energy
is not conserved.
PRINCIPLE OF CONSERVATION OF MOMENTUM
When two or more bodies act on each other, their total momentum remains constant,
provided there is external force acting.
That is:
Total momentum before collision = Total momentum after collision
EXAMPLE
A bullet of mass 0.01Kg, is fired into a block of wood, of mass 390g, lying on a smooth
surface. The wood then moves at a velocity of 10m/s.
a. What was the velocity of the bullet?
b. What is the kinetic energy before and after the collision?
EXPLOSIONS
An explosion is the opposite of a collision - objects move apart instead of coming together.
Examples are:
a. A ROCKET: A rocket uses a controlled explosion. The rocket moves one way while
the hot gases move the opposite way. The gain of momentum of the rocket is equal
and opposite to the momentum of the hot gases that are ejected.
b. A GUN: A gun firing a bullet is like a rocket ejecting fuel. The bullet gains
momentum in one direction, while the gun recoils with momentum in the opposite
direction.
EVALUATION:
i.
ii.
iii.
iv.
State Newton’s law of motion
Apply Newton’s law of motion to solve problem
Explain the concept of momentum and impulse
Explain the use of momentum equation
v.
vi.
Explain the principle of the conservation momentum
Describe the term collision and its type
ASSIGNMENT
SUBJECT: PHYSICS
CLASS: YEAR 10 INTGRATED
DATE: AUGUST 25 TH , 2023
TERM: FIRST
WEEK: SIX
TOPIC: TURNNIG EFFECT: MOMENT
SUB-TOPIC: MOMENT OF A FORCE, PRINCIPLE OF MOMENT
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
ii.
iii.
iv.
v.
Describe the moment of a force as a measure of its turning effect
Define the moment of force
State the principle of moment
Apply the principle of moments situation with one force each side of the pivot,
including balancing of a beam.
State that, when there is no resultant force and no resultant moment, an object is in
equilibrium.
CONTENT
MOMENT OF A FORCE
The turning effect of a force is called the moment of the force. It depends on both
the size of the force and how far it is applied from the pivot. It is measured by
multiplying the force by the perpendicular distance of the line of action of the
force from the pivot. The unit is the newton metre (Nm).
moment of a force = force × perpendicular distance from the pivot
Moment of a force about a point is defined as the product of the force and the perpendicular
distance of the line of action from that point. The S.I unit of moment is Nm and its is a vector
quantity.
Principle of moments
The law of moments (also called the law of the lever) is stated as follows: When a body is in
equilibrium, the sum of the clockwise moments about any point equals the sum of the
anticlockwise moments about the same point. There is no resultant moment on an object in
equilibrium.
The law of moments is an equivalent statement to the principle of moments. If the clockwise
moments are regarded as positive and the anticlockwise moments are regarded as negative,
then the sum of the moments is zero when the body is in equilibrium.
BALANCING A BEAM ABOUT A PIVOT
A metre rule is placed on a knife edge and is then moved to the right and to the left until it is
balanced horizontally.
At equilibrium, with loads f1 and f2 at the extremes of the metre rule, total clockwise
moment is equal to the total anticlockwise moments.
CONDITIONS OF EQUILIBRIUM UNDER THE ACTION OF COPLANAR FORCE
1. The sum of the forces in one direction equals the sum of the forces in the opposite
direction.
2. The sum of the clockwise moment about a point equals the sum of anticlockwise
moment about the same point.
EVALUATION:
1.
2.
3.
4.
5.
Describe the moment of a force as a measure of its turning effect
Define the moment of force
State the principle of moment
Describe the principle of moments situation with one force each side of the pivot,
including balancing of a beam.
State that, when there is no resultant force and no resultant moment, an object is in
equilibrium.
ASSIGNMENT
SUBJECT: PHYSICS
INTGRATED
DATE: AUGUST 25
TH
CLASS: YEAR 10
, 2023
TERM: FIRST
WEEK: EIGHT
TOPIC: CONDITION FOR EQUILIBRUM AND CENTRE OF MASS
SUB-TOPIC :CONDITION FOR EQUILIBRUM, POSITION OF CENTRE
MASS ,EFFECT OF THE POSITION OF THE CENTER MASS
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
State what is meant by centre of gravity
ii. Describe an experiment to determine the position of the centre of gravity of an irregular
shaped lamina.
CONTENT
CENTRE OF MASS OR GRAVITY
The centre of mass or gravity of a body is defined as the point through which the
line of action of the weight of the body always passes irrespective of the position
of the body.An object behaves as if its whole mass were concentrated at one point,
called its centre of gravity even though the Earth attracts every part of it. T
It is also the point at which the resultant weight in the body appears to be
concentrated.
CENTRE OF GRAVITY OF SOME REGULAR OR UNIFORM BODIES
1. The C O G of a uniform metre rule is at the 50cm mark.
2. The C O G of a circular object is at the centre of the circle.
3. The C O G of a square or a rectangle is at the intersection of the diagonals.
TYPES OF EQUILIBRIUM
There are three types of equilibrium:
1. Stable equilibrium
2. Unstable equilibrium
3. Neutral equilibrium.
STABLE EQUILIBRIUM
When there is a small movement of the ball, the line of action of the
weight will remain inside the base on which it is balanced. This will cause
it to fall back to its starting point.Its centre of gravity rises when it is
displaced. It rolls back because its weight has a moment about the point of
contact that acts to reduce the displacement.
UNSTABLE EQUILIBRIUM
An object is in unstable equilibrium if it moves further away from its previous position when
slightly displaced and released.A small movement of the ball will take the line of action of
the weight outside the base of the ball on it is balanced. This will cause it to rotate and toggle
out.Its centre of gravity falls when it is displaced slightly because there is a moment which
increases the displacement.
NEUTRAL EQUILIBRIUM
If there is a small movement of the ball the line of action of its weight remains above the
point of contact with the ground, so it will remain in its new position.Its centre of gravity
does not rise or fall because there is no moment to increase or decrease the displacement.
EVALUATION:
1. Explain what is meant by centre of gravity
2. Describe an experiment to determine the position of the centre of gravity of an
irregular shaped lamina.
ASSIGNMENT
SUBJECT: PHYSICS
DATE: AUGUST 25 TH , 2023.
CLASS: YEAR 10 INTEGRATED
TERM: FIRST
WEEK: NINE
TOPIC: SCALARS AND VECTORS
SUB -TOPIC : SCALARS AND VECTORS ,RESULTANT VECTOR
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
Explain scalar quantity and vector quantity
ii. Mention example of scalar and vector quantity
iii. Determine by calculation or graphically, the resultant of two vectors at right angles.
CONTENT
POSITION, SCALAR, AND VECTOR
POSITIONS
When two points are plotted on a plane, we are locating the position. To be able to locate
the position of objects on a plane, we should be able to know the distance of the object
from a point of origin along each of the two axes that make up the plane.
The position of an object ( p) is the distance x1 along the x-axis and the distance y1
along the y- axis, the point is described as p( x1,y1).
DIAGRAM
SCALARS
A scalar quantity is one which has magnitude only. For example temperature, volume,
distance, speed, etc In order to specify a scalar quantity completely, the magnitude and
the unit must be stated e-g The distance from Lagos to Minna is 1500Km.
VECTORS
A VECTOR QUANTITY HAS BOTH MAGNITUDE AND
DIRECTION .EXAMPLES ARE DISPLACEMENT, VELOCITY,
ACCELERATION, MOMENTUM, ETC
EXAMPLE OF A COMPLETELY SPECIFIED VECTOR IS:
i. Velocity of a bus is 20Km/hr, N60W.
ADDITION AND SUBTRACTION OF VECTORS
Considering two vectors of magnitude p=30N, q = 40N acting on a body:
a. If the two vectors are acting in the same direction , the resultant force will be
R= q + p = 30 + 40 = 70N
b. If the two vectors are acting in the opposite directions, the resultant force will
be R = q – p = 40 – 30 = 10N
c. If the equal forces q and q are acting directly opposite to each other , the
resultant force will be ,R = q – q = 40 – 40 = 0N
VECTORS AT AN ANGLE OF INCLINATION
RESULTANT VECTOR
A resultant vector is that single vector which would have the same effect in
magnitude and direction as the original vectors acting together.
PARALLELOGRAM LAW OF VECTORS
It states that if two vectors are represented in magnitude and direction by the
adjacent sides of a parallelogram, the diagonal of the parallelogram drawn
from the point of intersection of the vectors represent the resultant vector in
magnitude and direction.
DIAGRAM
Example
Find the resultant of two vectors of magnitudes 30N and 40N acting at a point
and are inclined to each other at an angle of 45.
A vector can be represented by a straight line whose length represents the
magnitude of the quantity and whose direction gives its line of action. An
arrow on the line shows which way along the line it acts.
In the case of two vectors FX and FY acting at right angles to each other at a
point, the magnitude of the resultant F, and the angle θ between FX and F can
be calculated from the following equations:
The resultant of two vectors acting at right angles to each other can also be
obtained graphically.
Example
Calculate the resultant of two forces of 3.0N and 4.0N acting at right angles
to each other
The resultant is a force of 5.0N acting at 53° to the force of 3.0N
EVALUATION:
1.
Define scalar quantity and vector quantity
2.
Mention example of scalar and vector quantity
3.
Determine by calculation or graphically, the resultant of two vectors at right angles.
ASSIGNMENT
SUBJECT: PHYSICS
DATE: AUGUST 25 TH , 2023.
CLASS: YEAR 10 INTEGRATED
TERM: FIRST
WEEK: TEN
TOPIC: WORK, ENERGY AND POWER
SUB- TOPIC : ENERGY,WORK,POWER AND CONSERVATION OF ENERGY
LESSON OBJECTIVES:
By the end of the lesson, student will be able to;
i.
Define energy
ii. Explain mechanical or electrical workdone
iii. Describe the equation for mechanical working
iv. Describe energy resources and power
CONTENT
WORK, ENERGY AND POWER
ENERGY
This is the ability or capacity to do work. The S.I unit of energy is Joules.
KINETIC ENERGY
This is the energy possessed by a body virtue of motion .
K.E = 1/2mV²
M = mass (kg)
V= velocity (m/s)
POTENTIAL ENERGY
This is the ability of an object to do work by virtue of its position or shape.
P.E = mgh
M= mass(kg)
- g= acceleration due to gravity (10m/s²)
H= height(m)
Examples
1. An object of mass 5kg is moving at a constant velocity of 15m/s .
Calculate its K.E.
2. Find the potential energy of a body of mass 10kg standing on a building
floor 10m above the ground level. Also, calculate the velocity with which
it hits the ground.
CONSERVATION OF ENERGY
It states that in an isolated or closed system, the total amount of energy is
always constant, although energy may be changed from one form to
another.
TRANSFORMATION OF ENERGY
The transformation of mechanical energy is the changing of potential energy to kinetic
energy or vice versa.Examples of energy conservation are:
i. A falling body
ii. The simple pendulum
TYPES OF ENERGY
1. Elastic or strain energy
2. Sound energy
3. Wind energy
4. Light energy
5. Solar energy
6. Electrical energy
7. Chemical energy
EFFICIENCY
Efficiency is the proportion of the energy that is usefully transformed.
Efficiency = Useful output energy / Total input energy
= Useful output power / Total input power
ENERGY RESOURCES
An energy resource (sometimes called an energy source) is a natural
system (such as a waterfall) or store of energy (such as fuel) that we can use to
make electricity.
It is divided into Renewable & Non-Renewable.
Renewable energy sources are being constantly replenished by natural
systems in a short enough time scale that we will never run out of them.
Renewable energy resources are the oldest, cleanest and in most cases the
most efficient forms of energy humans have at their disposal. They will never
run and do not pollute the environment by emitting gases that cause global
warming effects or acid rain, nor do they produce radioactive waste.
Non-renewable energy sources will run out eventually because they are
not being replaced naturally at a fast enough rates for us to make use of them.
Non-renewable resources are widely used directly (as heat sources) or to
make electricity.
FOSSIL FUELS
Fossil fuels take millions of years to form. They are the product of the fossilized
remains of dead plants and animals that have been exposed to the heat and
pressure deep within the earth’s crust. There are many types of fossil fuels, such
as oil, natural gas, and coal.
Fossil fuels are arguably one of the most valuable natural resources in
modern times. It is estimated that 86 percent of the world’s energy comes
directly from burning fossil fuels. Fossil fuels are the source of energy for
almost every machine, including the generators that produce electric energy.
Because fossil fuels take so long to form, they are being consumed faster
than they can be produced. They are not renewable and can't be replenished,
unlike renewable energy sources like solar or wind energy.
DISADVANTAGES OF FOSSIL FUELS INCLUDE:
1. HEALTH RISKS
The particles released by burning fossil fuels contribute to air pollution,
which leads to numerous potential health problems like low lung functioning,
chronic asthma, cardiovascular disease etc.
2. CLIMATE CHANGE
Greenhouse gas emissions like carbon dioxide, or CO2, contribute to climate
change by affecting how the sun's radiation is retained and reflected in the
atmosphere (This is known as global warming). Consequently, sulphur dioxide
(SO2) increases acid rain.
ALTERNATIVE ENERGY RESOURCES (RENEWABLE ENERGY
RESOURCES)
Alternative energy is an interesting concept when you think about it. In
our global society, it simply means energy that is produced from sources other
than our primary energy supply i.e. fossil fuels. These energy resources include:
1.
WAVE ENERGY
The sea’s waves have kinetic energy. Using machines that bob up and
down in the waves, this energy can be turned into electrical energy which we
can
use
in
our
homes.
Though this energy source is cheap and does not constitute air pollution,
the machines used can be damaged by storms.
2.
GEOTHERMAL ENERGY
Deep underground, the Earth’s rocks are naturally very hot. We can turn
their heat energy into electrical energy to use in our homes. This is referred to as
‘geothermal
energy’
.
The processes involved include:
(a) Cold water is pumped below the ground.
(b) Hot rocks heat the water, turning it into steam.
(c) The steam is used to generate electricity.
Geothermal energy is renewable, does not cause pollution but costs a lot
of money to drill deep into the ground.
3. HYDRO-ELECTRIC POWER
Hydro-electricity is generated from running water. Dams are built across
a lake or river in a valley to trap water. The water flows through tunnels and
turns the turbines which make electricity. HEP advantages include:
(a)
It is renewable.
It does not cause pollution, because nothing gets burned. On the
(b)
other
hand,
HEP
disadvantages
include:
(a) It costs a lot of money to build a dam.
(b) The dam can ruin the local environment, because it changes where the
water naturally flows. Some animals and plants may die.
4.
SOLAR ENERGY
The Earth gets heat and light energy from the sun all the time. The Sun’s
energy can either be:
(a) changed into electrical energy to use in homes, using solar cells;
(b) or
used
to
heat
water
for
homes,
using
solar
panels.
Solar energy is renewable, does not cause pollution; because
nothing gets burned. On the other hand, solar cells and solar panels are
expensive and they only work if it is sunny.
5.WIND ENERGY
Using wind turbines, we can turn the kinetic energy of the wind into
electrical energy which we can use in our homes or windmills to grind wheat
into
flour.
This
is
‘wind
energy’.
This energy source does not cause air pollution, because nothing gets
burned. Furthermore, wind turbines are quite cheap and easy to build, so they
can be used even in poor countries.
Wind turbines can be ugly and noisy and if the wind stops, you get no energy.
6.
BIOMASS ENERGY
Biomass uses the energy from burning plants and waste materials to make
electricity. For example, wood or animal droppings can be burnt to make steam
that turns turbines to make electricity.
It is renewable (as long as we keep planting trees to replace the ones we cut
down). It does not need any special equipment, so it can be used very easily,
even in poor countries and it does not add to the greenhouse effect.
The only disadvantage is that large areas of land are needed to grow enough
trees.
7.
TIDAL ENERGY
Tidal energy comes from the movement of water in the sea by the tides.
These tides happen twice a day. When the tide is high, the water has lots of
gravitational potential energy, which we can turn into electrical energy to use in
our homes.
Tidal energy does not cause pollution, because nothing gets burned. It is
cheap and reliable because there are always two tides every day.
The disadvantages of this energy source include:
(a) It Costs a lot to build the dam.
(b) The dam may cause local flooding.
CONCEPT OF WORK
Work is said to be done whenever a force moves its point of application through a distance in
the direction of the force.
W=fxs
Where,
F = force
S = distance
The S.I unit is Joules.
Example
A boy of mass 50kg runs up a set of stairs of total height 3m, find the work done against
gravity.
POWER
Power is the time rate of doing work or the time rate of energy transferred.
Power = W.D or Energy expended / time taken
P = w / t ------- 1
=fxs/t
= f x (s/t)
= F x v ------ 2
Where,
V = speed
F = force
P = power
The S.I unit of power is J/ s or Watts
1 hp = 746W
= 750W
= 0.75KW
Hp = horse power
EXAMPLE
A car travelling at 120m/s, produces a force of 400N.Calculate the power of the engine in
KW.
EVALUATION:
1. Define energy
2. Explain mechanical or electrical workdone
3. Describe the equation for mechanical working
4. Explain energy resources and power
ASSIGNMENT
1.
CBIS YEAR 10 INTEGRATED FIRST TERM SCHEME OF WORK
(PHYSICS).
WEEKS
TOPICS
1
MEASUREMENT
CONTENTS
MEASUREMENT
OF LENGTH,
MASS, WEIGHT
AND TIME.
FUNDANMENTAL
AND DERIVED
QUANTITES AND
UNITS.
2
MOTION
 SPEED, SPEED
TIME GRAPH/
DISTANCE TIME
GRAPH,
VELOCITY,
ACCELERATION
AND EQUATION
OF MOTION.
3.
DENSITY
 REGULAR
SHAPED SOLID
 IRREGULAR
SHAPED SOLID.
 FLOATING BASED
ON DENSITY
4.
FORCES: EFFECTS OF
FORCE
 EFFECTS OF
FORCE
 HOOKE’S LAW
 FRICTION
 APPLICATIION OF
FORCE =MA.
 CENTRIPETAL
FORCE
5.
 FORCES: EFFECTS
OF FORCE
 NEWTON’S FIRST
LAW OF MOTION
 NEWTON’S
SECOND LAW OF
MOTION
 INTRODUCE
EQUATION F=MA
 NEWTON’S LAW
OF MOTION
 MOMENTUM
 PRINCIPLE
OF
CONSERVATION
OF MOMENTUM
6
TURNNIG EFFECT:
MOMENT
 MOMENT
FORCE
OF
 PRINCIPLE
MOMENT
7
MID- TERM BREAK
8
CONDITION FOR
EQUILIBRUM AND
CENTRE OF MASS
A
OF
 CONDITION FOR
EQUILIBRUM
 POSITION OF
CENTRE MASS
 EFFECT OF THE
POSITION OF THE
CENTER MASS
9
SCALARS AND
VECTORS
 SCALARS
 VECTORS
 RESULTANT
VECTOR
10
WORK, ENERGY AND
POWER
 ENERGY
 WORK
 POWER
 CONSERVATION
OF ENERGY
11
REVISION AND
EXAMINATION