Graphical Vector Addition
Adding two vectors A and B graphically can be visualized
like two successive walks, with the vector sum being the
vector distance from the beginning to the end point.
Representing the vectors by arrows drawn to scale, the
beginning of vector B is placed at the end of vector A. The
vector sum R can be drawn as the vector from the
beginning to the end point.
The process can be done mathematically by finding
the components of A and B, combining to form the
components of R, and then converting to polar form.
N – North
W – West
E - East
S- South
NW – North of
West
WN – West of
North
E - East
EN – East of North
NE – North of East
S – South
SE – South of East
ES – East of South
WS – West of
Find the resultant vector of an
object that travelled 53 meters
200 NE then preceded to 34
meters 630 NE.
NE
NE
E
Note the angle 200 NE
Note the angle 630 NE
Activity 3. Give the magnitude and direction of the resultant vector of the following using the
Parallelogram or Graphical Method of a car travelling in the following directions:
1. 10 km 400NE and continued to 9 km 150 WN
2. 8 km 250 SW and continued to 10 km 350ES
3. 7 km 150 NW and continued to 8 km 50 NE
4. 9 km 200 SE and continued to 10 km 350 WS
5. 6 km 200 WS and continued to 7 km 100 SE
Example of Vector Components
Finding the components of vectors for vector
addition involves forming a right triangle from each
vector and using the standard triangle trigonometry.
The vector sum can be found by combining these
components and converting to polar form.
Polar Form Example
After finding the components for the vectors A and
B, and combining them to find the components of
the resultant vector R, the result can be put in polar
form by
Some caution should be exercised in evaluating the
angle with a calculator because of ambiguities in the
arctangent on calculators.
Activity 4. solve the following by Polygon method and check by Polar form calculation:
Scale: 1 kilometer = 1 centimeter. You need ruler and protractor in solving this.
1. Give the magnitude and direction of the resultant vector of the distance travelled by the car 8 km at 250NE and
preceded to 11 km 1200NW.
2. Find the magnitude and direction of the resultant vector of the distance travelled by the car 10 km at 1200NW and
goes towards 9km at 1900SW.
Finding Resultant Vector of three or more vectors:
or
Activity
Give the resultant vector of the following given vectors:
Scale: 1km = 1 cm.
1. 4km at 220 NE, 8km at 800NE and 6km at 1200NW
2. 8km at 1000NW, 5km at 350NE, 9km at 600NE and 7km at 1500NW
3. 9km at 1400NW, 5km at 350NE, 6km at 600NE and 7km at 1500NW
Speed and Velocity
Answer the following:
1. How far did the object travelled after five
seconds?
2. How far did the object travelled after three
seconds
3. How long it took for object to travel for four
meters?
4. At what distance did the object stopped?
5. How long did the object stopped?
6. Give the velocity of the object at the distance of
four meters.
7. Give the velocity of the object at the distance of
five meters.
8. Give the velocity of the object at twelve
seconds.
9. At what position did the object reached after
three seconds?
10. At what position did the object reached after
twelve seconds?
11. Compare the velocity of the object in one to
five meters with that of ten to twelve meters.
12. At what time did the object had gone back to
where it came from.
13. Compare the object’s speed in distance 0-5
with that of the speed in the distance 5-0.
1.
An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before
takeoff.
Given: a = +3.2 m/s2; t = 32.8 s; vi = 0 m/s Find: d or distance
d= X0 + V0 x T + .5 x at2
2.
d = viXt + 0.5XaXt2
d = 0 + (0 m/s)X(32.8 s)+ 0.5X(3.20 m/s2)X(32.8 s)2
d = 1720 m
A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.
Given: d = 110 m; t = 5.21 s; vi = 0 m/s; Find: a or acceleration
d = v X t + 0.5 X a X t2
110 m = (0 m/s) X (5.21 s)+ 0.5 X (a) X (5.21 s)2
110 m = (13.57 s2) X a
a = (110 m)/(13.57 s2)
a = 8.10 m/ s2
3. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance
traveled.
Given: vi = 18.5 m/s; vf = 46.1 m/s; t = 2.47 s; Find: a and d
a = (Delta v)/t
a = (46.1 m/s - 18.5 m/s)/(2.47 s)
a = 11.2 m/s2
d = vi*t + 0.5*a*t2
d = (18.5 m/s)*(2.47 s)+ 0.5*(11.2 m/s2)*(2.47 s)2
d = 45.7 m + 34.1 m
d = 79.8 m
(Note: the d can also be calculated using the equation vf2 = vi2 + 2*a*d)
Activity. Solve for the following:
1. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of
the bike.
2. An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate
is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the
minimum allowed length for the runway?
3. A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a
distance of 0.0621 m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform
acceleration.)
4. A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform)
of the dragster.
5. acceleration (assume uniform) of the dragster.
Sample Problem Sample
Activity: Actual illustration of free fall.
1. Get a ball or any light object let it fall from two
meters from your floor.
2. Toss the light object or a ball upwards let it fall to the
floor.
3. While doing it record it in your phone and send it to
me.
4. Solve for the following problems:
a. The bullet was fired from the noozle of the gun
with the initial velocity of 125 meter/sec. find the
following:
a. How long will it take for the bullet to reach the
highest point?
b. How high will the bullet go?
c. At what time will the bullet be 90 meters from
the ground?
b. The ball was dropped from the window sill 150
meters from the ground. Find the following:
a. time before the ball hits the ground.
b. velocity upon hitting the ground.
c. At what time will the bullet be 90 meters from
the ground?
Defining Projectiles
A projectile is an object upon which the only force acting is gravity. There are a variety of examples of projectiles. An object dropped
from rest is a projectile (provided that the influence of air resistance is negligible). An object that is thrown vertically upward is also a
projectile (provided that the influence of air resistance is negligible). And an object which is thrown upward at an angle to the horizontal
is also a projectile (provided that the influence of air resistance is negligible). A projectile is any object that once projected or dropped
continues in motion by its own inertia and is influenced only by the downward force of gravity.
By definition, a projectile has a single force that acts upon it - the force of gravity. If there were any other force
acting upon an object, then that object would not be a projectile. Thus, the free-body diagram of a projectile
would show a single force acting downwards and labeled force of gravity (or simply Fgrav). Regardless of
whether a projectile is moving downwards, upwards, upwards and rightwards, or downwards and leftwards, the
free-body diagram of the projectile is still as depicted in the diagram at the right. By definition, a projectile is
any object upon which the only force is gravity.
Sample Problem:
Activity. Solve the problem: A bullet was fired at an angle of 400 above the horizontal with the velocity of 800
meter/ second. Find the following: a. range b. time before it returns to th same
level c. position of the bullet d. velocity of the bullet 50 seconds aftr it was fired
e. at what other angle of elevation could this bullet be fired to give the same range
f. what is the maximum possible range of the bullet.
Activity. Solve the problem: A ball was thrown at the top of the building horizontally with a velocity of 80
m/sec. find the following: a.) position and speed after 5 seconds if the ball hits
the ground 300 meters from the base of th tower, how tall is the building?
Newton’s Laws of Motion
Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless
compelled to change its state by the action of an external force. This is normally taken as the definition of
inertia.
Activity. Write you observations in the following
1. When riding a vehicle and it suddenly stops.
2. When vehicle at rest suddenly moves.
3. Try putting a smooth cloth with a book on top of it in the smooth table. Abruply pull the smooth cloth with book on
top of it. what happens. ( book should not fall on the floor after pulling the cloth beneath it.
4. If you will throw a paper while riding in the the running vehicle what hppends to the paper? In what direction will the
paper be thrown?
5. Explain the function of inflatable baloons in cars.
Newton’s Second Law of Motion states that acceleration is inversely proportional to mass and directly proportional and
towards the force acting on it.
Formula for Newton’s Second Law of Motion is Force = Mass X Acceleration
Activity
1. Get a piece of small plastic ball. If you have no plastic ball crumple a paper into a ball like shape.
2. Get other four objects having greater mass than a crumpled paper having two of which differ its masses from each
other also. Arrange the five objects (including the crumpled paper) you got from least to greatest mass.
3. Specify the approximate mass of the objects you have in grams. Push with the flip of your finger the crumpled paper
then the other three objects which has masses lesser than the next. Measure the time and distance when and where
each objects stopped moving after you pushed it by flipping it with your finger.
4. Fill the table below with the results of the activity.
Object
Approximate Mass
Distance
Time
Acceleration
Arranged from least to
in grams
travelled
Distance/ time elapsed
greatest mass
1 least mass cumpled
paper
2
3
4
5 object having
greatest mass
5. Plot the mass of the objects with the acceleration in the graph.
6. How is mass related to acceleration?
7. Using only the crumpled paper in this part of the activity, push the crumpled paper by flipping it with your finger from
least to greatest force.
8. Specify the approximate force in dynes your finger is excerting on the object. Measure the time and distance when
and where each objects stopped moving after you pushed it by flipping it with your finger.
Push applied on the
crumpled paper
1 least force
2
3
4
5 greatest force
Approximate Force
in dyne
Distance
travelled
Time
Acceleration
Distance/ time elapsed
9. Plot the force applied on the objects with the acceleration in the graph.
10. How is force related to acceleration?
A force is a push or pull acting upon an object as a result of its interaction with another object. There are a
variety of types of forces. A variety of force types were placed into two broad category headings on the basis of
whether the force resulted from the contact or non-contact of the two interacting objects.
Formula of is Force is Force = Mass X Acceleration
Unit of force:
Metric scale
Mass
Acceleration
Unit
MKS
Kilogram
Meter/ second2
Kilogram x Meter/ second2 or Newton
cgs
Gram
Centimeter/ second2
Gram x Centimeter/ second2 or Dyne
Contact Forces
Action-at-a-Distance Forces
Frictional Force
Gravitational Force also called weight
Tension Force
Electrical Force
Normal Force
Magnetic Force
Air Resistance Force
Applied Force
Spring Force
Friction is a force that opposes motion. When a force is applied to a body resting on a rough plane so that the body moves or tends to
move, a frictional force acts on the body in opposition to the applied force.
Symbol • Ff  Units • Newtons (it’s a force!)  Depends on • Weight of object (normal force) • Nature of the surfaces between the
moving object and the supporting surface
Friction • Two types • Static friction (pushing the piano but no motion) • Sliding (kinetic) friction (piano moves!!!) • Static force > kinetic
force
Formula • where • μ = coefficient of friction, • values usually between 0 and 1 • Note: • Low μ = slippery • High μ = sticky • FN = normal
force dependent on weight vector
Examples of μ Surfaces Static Sliding Hardwood on hardwood 0.5 0.25 Rubber on dry concrete 1.0 0.75 Rubber on wet concrete 0.75
0.5 Steel on steel 0.74 0.6 Steel on steel (lub’d) 0.15 0.06 Human joints 0.01 0.003.
When friction acts between two surfaces that are moving over each other, some kinetic energy is transformed into heat energy.
Friction can sometimes be useful.
Activity.
1. Make a force measurer as shown in the photo.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
As illustrated in the photo below drag the object (here object used is stapler) in smooth (here the smooth
surface is the cloth) and rough surface (here the rough surface is the towel).
Choose an area in your place where it is really rough in sandy safe road nearby. Drag an object a small bottle or
tin can could be.
Measure the passing of the arrow in the force measurer in the rough and smooth surface.
In what surface is the passing of the arro0ow greater in rough or in smooth surface?
What is that force that happen in the set up
Define friction.
In what instance does friction happen?
Is friction always needed or not needed? Expound answer by giving examples.
Give advantages of friction.
Give disadvantages of friction.
Why is it that you feel hot in your palm if continue rubbing your hands together.
Why is it that meteors burn while falling from space to the ground.
Is friction a kind of force.
What is the unit for friction?
Work done on a system by a constant force is defined to be the product of the component of the force in the direction of
motion times the distance through which the force acts.
Work = Force x distance
Work = Force x distance cos θ
W = Fdcosθ
• W is Work • F is the force doing the work on the object • d is the displacement of the object • θ is the angle between F and d • When
using this equation use the Magnitude of F and d
Instances where work is done: walking up stairs, lifting heavy objects, pulling a sledge and pushing a shopping trolley.
Whenever work is done, energy is transferred from one place to another.
Instances where work is not done: carrying heavy bag in place
Making work done the easier way
Following is the table of units and dimensional formula:
SI unit
N.m
Joule
CGS unit
dyne-cm
Erg
Dimensional formula
ML2T-2
–
Activity. Give 5 examples in each of instances where work is done and not done.
Work is done
Reason why work is done
Worrk is not done
Reason why work is not done
What is power
Power is defined as the ability to act or have influence over others. An example of power is the strength needed to run five miles.
An example of power is the authority a local government has to collect taxes. The number of times a number or expression is
multiplied by itself, as shown by an exponent.
Energy, in physics is the capacity for doing work.
The SI unit of energy/work is the joule (J), named for English physicist James Prescott Joule (1818 1889). Joule discovered the relationship between heat and mechanical work, which led to the development of the laws of
thermodynamics.
Joule managed the family brewery from 1837 to 1856 which enabled him to experiment on the relationships
between heat and electricity in a laboratory built in the cellar of his father’s home. His earliest experiments explored
the relationships between electricity and work and in 1840, he published a paper in the Proceedings of the Royal
Society describing the first of the eponymous laws which predicts the heat generated by a conductor from its resist ance
and the current applied.
In 1843, Joule showed that heat was a form of energy and determined the physical constant now used as the S.I. unit
for energy, the Joule (J). He demonstrated the mechanical equivalent of heat by measuring change in the tempe rature
of water caused by the friction of a paddlewheel attached to a falling weight.
This concept was further tested on his honeymoon in 1847 with his patient new bride Amelia Grimes, when Joule
measured the temperature difference above and below the Sallanches waterfall in Switzerland!
James Prescott Joule, an ‘amateur’ scientist and inventor, combined brilliant scientific thinking and innovation with the
brewer’s interest in highly accurate measurements. His findings and publications greatly improved the efficiency of
many 19th century industrial machines and processes including steam engines, electric motors and transmission of
electrical power.
The principles that Joule described directly led to the important developments of arc welding and refrigerati on. Joule’s
best known legacy is the eponymous unit that was officially adopted as the S.I. unit for energy by the ‘Bureau
International des Poids et Mesures’ in 1948.
Potential Energy
An object can store energy as the result of its position. For example, the heavy ball of a demolition machine is storing
energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a
drawn bow is able to store energy as the result of its position. When assuming its usual position (i.e., when not drawn),
there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to
store energy by virtue of its position. This stored energy of position is referred to as potential energy. Potential energy is
the stored energy of position possessed by an object.
Gravitational Potential Energy
The two examples above illustrate the two forms of potential energy to be discussed in this course - gravitational potential
energy and elastic potential energy. Gravitational potential energy is the energy stored in an object as the result of its
vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object. The
gravitational potential energy of the massive ball of a demolition machine is dependent on two variables - the mass of the
ball and the height to which it is raised. There is a direct relation between gravitational potential energy and the mass of
an object. More massive objects have greater gravitational potential energy. There is also a direct relation between
gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the
gravitational potential energy. These relationships are expressed by the following equation:
PEgrav = mass • g • height
PEgrav = m *• g • h
In the above equation, m represents the mass of the object, h represents the height of the object and g represents the
gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.
To determine the gravitational potential energy of an object, a zero height position must first be arbitrarily assigned.
Typically, the ground is considered to be a position of zero height. But this is merely an arbitrarily assigned position that
most people agree upon. Since many of our labs are done on tabletops, it is often customary to assign the tabletop to be
the zero height position. Again this is merely arbitrary. If the tabletop is the zero position, then the potential energy of an
object is based upon its height relative to the tabletop. For example, a pendulum bob swinging to and from above the
tabletop has a potential energy that can be measured based on its height above the tabletop. By measuring the mass of
the bob and the height of the bob above the tabletop, the potential energy of the bob can be determined.
Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the
height will result in a doubling of the gravitational potential energy. A tripling of the height will result in a tripling of the gravitational
potential energy.
Use this principle to determine the blanks in the following diagram. Knowing that the potential energy at the top of the tall platform is 50
J, what is the potential energy at the other positions shown on the stair steps and the incline?
Elastic Potential Energy
The second form of potential energy that we will discuss is elastic potential energy. Elastic potential energy is the energy stored in
elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee
chords, trampolines, springs, an arrow drawn into a bow, etc. The amount of elastic potential energy stored in such a device is related
to the amount of stretch of the device - the more stretch, the more stored energy.
Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching. A force is
required to compress a spring; the more compression there is, the more force that is required to compress it further. For certain
springs, the amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known
as the spring constant (k).
Fspring = k • x
Such springs are said to follow Hooke's Law. If a spring is not stretched or compressed, then there is no elastic potential energy stored
in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when
there is no force applied to it. In terms of potential energy, the equilibrium position could be called the zero-potential energy position.
There is a special equation for springs that relates the amount of elastic potential energy to the amount of stretch (or compression) and
the spring constant. The equation is
PEspring = 0.5 • k • x2
where k = spring constant
x = amount of compression
(relative to equilibrium position)
To summarize, potential energy is the energy that is stored in an object due to its position relative to some zero
position. An object possesses gravitational potential energy if it is positioned at a height above (or below) the
zero height. An object possesses elastic potential energy if it is at a position on an elastic medium other than
the equilibrium position.
Types of Potential Energy
 Chemical energy
 Stored mechanical energy
 Gravitational energy






Nuclear energy
Elastic potential energy
Chemical potential energy
The
combustion
engine
converts
potential
chemical
energy
into
kinetic
energy.
In the case of chemical potential energy, we refer to the way in which atoms and molecules are structured in
chemical bonds capable of storing energy, as occurs in the body of animals with glucose, the compound from
which
we
obtain
energy
to
supply
our
metabolism.
The latter is given by the oxidation of the glucose molecule, whose bonds, when broken, release the potential
chemical energy contained in them. The same is true, for example, with fossil fuel (hydrocarbons) in the car’s
gas tank, before being subjected to combustion in the engine that will convert its potential chemical energy into
kinetic energy to start the vehicle.
Examples of matter containing chemical energy include:
Coal: Combustion reaction converts chemical energy into light and heat.
Wood: Combustion reaction converts chemical energy into light and heat.
Petroleum: Can be burned to release light and heat or changed into another form of chemical energy, such as
gasoline.
Batteries, food, plants
Elastic potential energy
The elastic energy potential has to do with the property of the elasticity of matter, which is the tendency to
regain its initial shape abruptly after having been subjected to deformation forces greater than its force. This
abrupt movement is the one that operates on the springs, which are compressed and decompressed, or gives
meaning to old weapons of war, such as catapults, or bows that shoot arrows.
In this last example, the potential elastic energy reaches its maximum level as the arch is tightened by pulling
the elastic fiber, slightly bending the wood, but still with a speed equal to 0. The next moment, the potential
energy is it becomes kinetic and the arrow is thrown forward at full speed.
Gravitational potential energy
This type of potential energy is defined on the basis of the gravitational pull of the earth or between masses of
different magnitudes located close to each other. These masses can be those of the sun and orbiting planets,
or
those
of
a
roller
coaster
when
it
reaches
the
top
of
the
hill.
In this last example, the potential energy that the Earth’s gravitational pull accumulates in the car reaching the
top is as large as possible on its planned route, and is then transformed into kinetic energy to release the car
as it falls onto the rails. At this point of maximum energy accumulation, its speed will be 0 and there will be no
movement.
Electrostatic potential energy
In terms of electricity, the concept of potential energy also applies, especially when it comes to electrical
circuits (where electricity is conserved) or current storage methods, which can be converted to other forms of
energy, such as kinetics, thermal or light, given the enormous versatility of electricity.
The electric potential is calculated through the energy of the electrostatic potential, which can be repulsive (if
the charges are the same) or attractive (if they are of a different signal), giving rise to positive or negative
potential energy, as the case may be.
Nuclear energy
Nuclear energy is the P.E of the particles such as neutrons and protons which are present in the nucleus of the
atom. This energy holds neutrons and protons together to form the nucleus of an atom. The particles of the
nucleus like protons and neutrons are held together by the strong nuclear force.
Activity give reason why is it that the following are examples of Potential Energy
Stretched Rubber
Raised Brick
Wound Spring
Stretched Bow
Balloons
An apple on a tree branch
A kite
Pendulum
The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form
of energy to another. This means that a system always has the same amount of energy, unless it's added from the outside. ... The
only way to use energy is to transform energy from one form to another.
The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In
essence, energy can be converted from one form into another. ... In the process of energy transfer, some energy will dissipate as
heat.
Activity. Label the kind of energy transformed in the picture below – potential or chemical – electrical – light, sound…
Activity. Give your own illustration of transformation of energy in both Chemical energy and Potential energy.
Give other sources of energy environmentally friendly or renewable source of energy and illustrate its transformation to a
useful one.
Kinds of Transfer of Energy
There are three methods of energy transfer that we need to learn: conduction, convection, and radiation.
1. Conduction:
Heat is thermal energy, and in solids it can be transferred by conduction. Heat is passed along from the hotter end of an object to the
cold end by the particles in the solid vibrating. The hotter particles vibrate a lot and cause the particles next to them to vibrate as they
gain heat energy too. Solids are heat conductors due to how tightly packed their particles are.
For example: When a saucepan is put on a hob, overtime the handle will get hot too. Due to conduction -> the heat from the bottom of
the pan will cause the particles to vibrate and then cause all the surrounding particles to vibrate until the handle is hot too.
2. Convection:
Fluids, that is both gases and liquids, can transfer heat energy by convection. It is easiest to explain this while thinking of an example:
Imagine a beaker of water being heated from the bottom. As the water particles at the bottom get hot, they expand and become less
dense. This means they will rise to the top of the beaker, and other colder water particles will fall to replace them. After a while, the
'new' cold particles at the bottom will be heated and they will then rise to the top as they will be less dense. The water at the top which
was first heated will have slightly cooled by then, so will sink down to the bottom, but then will be reheated and the same process will
happen again.
This constant flow of the fluid due to the expansion / change in density of the particles is called a convection current. Over time all the
fluid reaches a constant temperature.
3. Radiation:
Radiation is different to the other two processes as it doesn't require particles in its transfer of energy. Instead, infra-red radiation is a
type of electromagnetic radiation. This means that the energy is transferred by waves rather than particles.
Radiation is how we feel the heat from the sun on Earth, as waves can pass through the vacuum of space where there are no particles.
Activity. Give 5 examples of each kind if transfer of energy – conduction, convection, radiation.
Electricity
Volts (V)
Volt is the SI unit of measuring electrical voltage. Voltage is the potential difference between two points between which current is
flowing. Current flows from higher potential difference to the lower potential difference. Voltage is the pressure from an electrical
circuit's power source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating
a light. In brief, voltage = pressure, and it is measured in volts (V).
V=IXR
Using the power equation of 1 watt = 1 ampere × 1 volt and translating that formula to find volts, you end up with 1 volt = 1 watt ÷ 1
ampere. Divide 1000 watts by 10 amperes and the resultant voltage would equal 100 volts.
Ampere or Amps (I)
Ampere or Amps is the SI (an international system of measurements) unit of measuring current. In simple terms, flow of electrons
through a circuit is called current. If you want to be more accurate, rate of flow of electrons at any given point in the circuit at any given
point of time is called current. It is denoted by capital I.
I = V/R
1 ampere = 1 coulomb/sec, where coulomb measures the amount of electrons
Ohms (R)
Ohm is the SI unit of electrical resistance. When current flows through any electrical circuit, some of the electrons can collide with
atoms of the wires and produce heat. This heat resists the flow of current and is measured in terms of ohms.
R = V/I
Watts (W)
Watts is the SI unit of power (P). 1 watt measures the amount of electrical power consumed when a current of 1 ampere flows through
a potential difference of 1 volt. Our electricity bills are measured in Kilowatt-hour, i.e. how many kilowatts (1000 Watts) of electricity we
have consumed in an hour.
P=VXI
Using the power equation of 1 watt = 1 ampere × 1 volt and translating that formula to find volts, you end up with 1 volt = 1 watt ÷ 1
ampere. Divide 1000 watts by 10 amperes and the resultant voltage would equal 100 volts.
Ohm's Law
Ohm's law states that the voltage V across a conductor of resistance R is proportional to the current I passing through the resistor (see
circuit below). The relationship is written as.
V=RI
Example 1
Find the current (I) through a resistor of resistance R = 2 Ω if the voltage across the resistor is 6 V.
Solution Substitute R by 2 and V by 6 in Ohm's law V = R I.
6=2I
Solve for I
I = V/R
I = 6Volts / 2Ω = 3Amperes
Example 2
In the circuit below resistors R1 and R2 are in series and have resistances of 5 Ω and 10 Ω, respectively. The voltage across resistor
R1 is equal to 4V. Find the current passing through resistor R2 and the voltage across the same resistor.
Solution to Example 2
We use Ohm's law V = R I to find the current I1 passing through R1.
4V = 5 Ω x I1
Solve for I1
I1 = 4 / 5 = 0.8 A
The two resistors are in series and therefore the same current passes through them. Hence the current (I)2 through R2 is equal to 0.8
A.
We now use Ohm's law to find the voltage V2 across resistor R2.
V2 = R2 x I2 = 10 (0.8) = 8 V
Example 3
The current passing through a resistor in a circuit is 0.01 A when the voltage across the same resistor is 5 V. What current passes
through this resistor when the voltage across it is 7.5 V?
Solution to Example 4
Use Ohm's law V = R I to find the resistor R in this circuit.
5 = R (0.01)
Solve for R
R = 5 / 0.01 = 500 Ω
We now use Ohm's law V = R I and the value of R to find the current when the voltage is 7.5.
7.5 = 500 I
Solve for I
I = 7.5 / 500 = 0.0125 A
A wave is a disturbance that propagates through a medium.
Essential property
Waves transfer energy, momentum, and information, but not mass.
There are two basic types of wave motion for mechanical waves: longitudinal waves and transverse waves.
Features of Waves
Definitions
 Crest - the highest point in the wave.
 Trough - the lowest point in the wave.
 Wavelength - the horizontal distance between successive crests, troughs or other parts of a wave.
 Wave height - the vertical distance between the crest of a wave and its neighboring trough. This term is commonly used when
describing water waves where the undisturbed surface is not easily determined.
 Amplitude - the amount of displacement from the equilibrium or rest position. Equal to one half the wave height.
 Undisturbed surface - resting state or equilibrium position of medium in the absence of a wave.
 Period - the time it takes for successive crests or troughs to pass a specific point.
 Frequency - the inverse of period. The number of crests or troughs that pass a point during a set time interval.
Law of Reflection
When any wave, including light, hits a surface that is opaque, the light will mostly reflect off that surface. The law of reflection tells us
how it bounces off that surface. When a wave is moving toward the surface, it's called the 'incident ray.' When it bounces off, it's call the
'reflected ray.' If you were to draw a line perfectly in between the two rays, the law of reflection tells us that the incident angle is equal
to the reflected angle.
When you look in a mirror, what do you see? As long as the mirror is flat, the picture is nice and clear, and at the correct size, all the
parts of you are in the right place. This is because of the law of reflection. But does that mean it only applies to mirrored surfaces?
Types of Reflection
Reflection from the surface of a mirror, or any reflection where all the light rays reflect off a surface at the same angle, is
called specular reflection. But, in fact, the law of reflection is always true. When you go from a mirrored surface to a regular surface, it
isn't the law that changes, but the surface itself.
Take a look at the table on which your computer is sitting. Run your hand across it. Does it feel smooth? Although something might feel
smooth to our hands, the surface contains millions of tiny imperfections. Because of those imperfections, a light wave doesn't hit the flat
surface we see. Most of the time it hits an imperfection, and those imperfections could be pointed at any angle at all. Therefore, light
waves hit different imperfections and bounce off at different reflected angles. This is called diffuse reflection.
Specular reflection and diffuse reflection are two types of reflection. The more shiny and mirrored a surface, the more specular
reflection occurs, and the more dull a surface, the more diffuse reflection occurs.
Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the
bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves. ... Thus, if water waves are
passing from deep water into shallow water, they will slow down.
Diffraction is the bending of waves around obstacles and openings. The amount of diffraction increases with increasing wavelength.
We can define two distinct types of diffraction: (a) Fresnel diffraction is produced when light from a point source meets an obstacle,
the waves are spherical and the pattern observed is a fringed image of the object. (b) Fraunhofer diffraction occurs with plane wavefronts with the object effectively at infinity.
A sound wave, like any other wave, is introduced into a medium by a vibrating object. The vibrating object is the source of the
disturbance that moves through the medium. The vibrating object that creates the disturbance could be
the vocal cords of a person, the vibrating string and sound board of a guitar or violin, the vibrating tines
of a tuning fork, or the vibrating diaphragm of a radio speaker. Regardless of what vibrating object is
creating the sound wave, the particles of the medium through which the sound moves is vibrating in a
back and forth motion at a given frequency. The frequency of a wave refers to how often the particles of the medium vibrate when a
wave passes through the medium. The frequency of a wave is measured as the number of complete back-and-forth vibrations of a
particle of the medium per unit of time. If a particle of air undergoes 1000 longitudinal vibrations in 2 seconds, then the frequency of the
wave would be 500 vibrations per second. A commonly used unit for frequency is the Hertz (abbreviated Hz), where
1 Hertz = 1 vibration/second
Frequency, Pitch and Human Perception
The ears of a human (and other animals) are sensitive detectors capable of detecting the fluctuations in air pressure that impinge upon
the eardrum. The mechanics of the ear's detection ability will be discussed later in this lesson. For now, it is sufficient to say that the
human ear is capable of detecting sound waves with a wide range of frequencies, ranging between approximately 20 Hz to 20 000 Hz.
Any sound with a frequency below the audible range of hearing (i.e., less than 20 Hz) is known as an infrasound and any sound with a
frequency above the audible range of hearing (i.e., more than 20 000 Hz) is known as an ultrasound. Humans are not alone in their
ability to detect a wide range of frequencies. Dogs can detect frequencies as low as approximately 50 Hz and as high as 45 000 Hz.
Cats can detect frequencies as low as approximately 45 Hz and as high as 85 000 Hz. Bats, being nocturnal creature, must rely on
sound echolocation for navigation and hunting. Bats can detect frequencies as high as 120 000 Hz. Dolphins can detect frequencies as
high as 200 000 Hz. While dogs, cats, bats, and dolphins have an unusual ability to detect ultrasound, an elephant possesses the
unusual ability to detect infrasound, having an audible range from approximately 5 Hz to approximately 10 000 Hz.
The sensation of a frequency is commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency
sound wave and a low pitch sound corresponds to a low frequency sound wave. Amazingly, many people, especially those who have
been musically trained, are capable of detecting a difference in frequency between two separate sounds that is as little as 2 Hz. When
two sounds with a frequency difference of greater than 7 Hz are played simultaneously, most people are capable of detecting the
presence of a complex wave pattern resulting from the interference and superposition of the two sound waves. Certain sound waves
when played (and heard) simultaneously will produce a particularly pleasant sensation when heard, are said to be consonant. Such
sound waves form the basis of intervals in music. For example, any two sounds whose frequencies make a 2:1 ratio are said to be
separated by an octave and result in a particularly pleasing sensation when heard. That is, two sound waves sound good when played
together if one sound has twice the frequency of the other. Similarly two sounds with a frequency ratio of 5:4 are said to be separated
by an interval of a third; such sound waves also sound good when played together. Examples of other sound wave intervals and their
respective frequency ratios are listed in the table below.
Interval
Frequency Ratio
Examples
Octave
2:1
512 Hz and 256 Hz
Third
5:4
320 Hz and 256 Hz
Fourth
4:3
342 Hz and 256 Hz
Fifth
3:2
384 Hz and 256 Hz
The ability of humans to perceive pitch is associated with the frequency of the sound wave that impinges upon the ear. Because sound
waves traveling through air are longitudinal waves that produce high- and low-pressure disturbances of the particles of the air at a
given frequency, the ear has an ability to detect such frequencies and associate them with the pitch of the sound. But pitch is not the
only property of a sound wave detectable by the human ear. In the next part of Lesson 2, we will investigate the ability of the ear to
perceive the intensity of a sound wave.
Refraction of Sound
Red, Orange, Yellow, Green, Blue, Indigo, Violet
ROYGBIV
Electromagnetic radiation can be described by its amplitude (brightness), wavelength, frequency, and period. By the
equation E=h\nuE=hνE, equals, h, \nu, we have seen how the frequency of a light wave is proportional to its energy. At the beginning
of the twentieth century, the discovery that energy is quantized led to the revelation that light is not only a wave, but can also be
described as a collection of particles known as photons. Photons carry discrete amounts of energy called quanta. This energy can be
transferred to atoms and molecules when photons are absorbed. Atoms and molecules can also lose energy by emitting photons.
Earth Science
At these grade levels, students begin to appreciate the living and nonliving things that make up their surroundings.
Students learn that many things they use everyday come from the natural surroundings so that there is a need to
protect and use them wisely. They also become more conscious about some natural events (e.g., typhoons and
earthquakes), and the hazards associated with them. They observe changes in the weather, including when the rainy
season and dry season occur in their locality. They watch objects in the sky more often so that they can observe changes
in their appearance.
Specifically, students in Grades 1 and 2 observe the land around their homes and school and identify plants grown for
human consumption. They investigate where the water they use comes from and suggest ways to save them. They give
evidence or demonstrate that air is everywhere. They learn about the types of weather and the precautions to be
observed during a thunderstorm, especially if they are out of the house. They find out changes in the surroundings
before and during typhoons. Most children would have experienced earthquakes so they should be able to follow
instructions during an earthquake drill as well as decide what to prepare in case their families have to be evacuated to a
safer location. When they observe the sky, they realize that some objects are seen only during daytime, some objects
are observed only at night, while others can be seen both during daytime and at night. Finally, students are given
opportunities to share their experiences on how the natural events and objects in the sky affect them and their families.
The idea being promoted is to be prepared ahead of time in case a natural phenomenon results to a disaster that brings danger and
risks to people and property.
Catastrophism vs Uniformitarianism
Catastrophism is the Uniformitarianism is the
theory that Earth’s
theory that Earth’s
features
are mostly
features are mostly
accounted for by
accounted for by
gradual, small-scale
violent, large-scale
processes, that
events that occurred
occurred over long
in a relatively short
periods of time.
amount of time
“ the present is the key
to the past.”
James Hutton (1726-1797, Scottland) Expounded the principle of uniformitarianism. Charles Lyell (1797-1875) Published
"principles of geology" textbook (1833), wherein he espoused the principle of uniformitarianism. Geologists accepted this idea, and,
having accepted uniformitarianism, they generally agreed that vast amounts of time were needed to explain the earth's features and
particularly the sedimentary record.
Geologists haven't always agreed about the history of our planet. They have debated between catastrophism and uniformitarianism
over the last few hundred years. Catastrophism is the opposite viewpoint that teaches that a terrible crisis occurred at some earlier
time. It was a great catastrophe - the Flood - which within a few months laid down all the sedimentary rock strata, entombing the
animals contained within them, which became fossils. Geologic evidence on all sides is clear that it was a catastrophe of such gigantic
proportions that rocks were twisted, mountains were hurled upwards, water was pulled out of the earth, and the very atmosphere was
dramatically affected. As a consequence, thousands of volcanoes erupted and vast glaciers moved downward from the the poles which
had earlier been warm. Here is a quote from W.D. Thornbury, "Bretz has been unable to account for such a flood, but maintained that
field evidence indicated its reality. This theory represents a return to catastrophism which many geologists have been reluctant to
accept
Catastrophists believed that Earths landscapes had been developed primarily by great catastrophes.
So according to uniformitarianism, the way everything is occurring today is the way it has always occurred on our planet. It teaches that
"all things continue as they were from the beginning" (you will find II Peter 3:3-7 interesting reading).
The principle of uniformitarianism states that the physical, chemical and biological laws that operate today have also operated in the
geologic past.
The forces and processes that we observe presently shaping our planet earth have been at work for a very long time. to understand
ancient rocks, we must first understand present-day processes and their results. The present is the key to the past. The theory of
catastrophism was challenged by James Hutton in the late 18th century, who in his theory of uniformitarianism proposed that uniform
gradual processes (such as for example the slow erosion of the coast by the impact of waves) shaped the geologic record of the earth
over an immensely long period of time. He assumed that the acting processes were the same than those that we see in action at
present (rivers, volcanoes, waves, tides etc.). Darwin later on based his theory of the origin a species on Hutton's theory.
Main Topic: Geologic Time
SUBTOPICS
1.
2.
3.
4.
5.
Relative Dating
Absolute
Dating
Fossils
Stratigraphic
Correlation
Geologic Time
Scale
Catastrophism is the theory that Earth's features are mostly accounted for by violent, large-scale events that
occurred in a relatively short amount of time. So, a species that went extinct was probably killed off by a giant natural
disaster. An impressive mountain range was probably formed by worldwide earthquakes and eruptions.
Cuvier and other scientists believed that most major features of the land we see today were established a very long time
ago by very dramatic events. These events would not at all resemble the small-scale natural disasters we experience in our
time. The drama was over, immortalized in religious texts, never again to be seen on such a humongous scale.
In 1785, a geologist and physicist named James Hutton proposed another idea. He thought that most of the features on the surface of
the Earth were formed by slow, ongoing geologic processes, not by sudden catastrophic events. Hutton didn't believe that there was
anything happening long ago that wasn't still happening on Earth today. In other words, 'the present is the key to the past.' The erosion
of landforms, the deposition of sediments, the drifting of continents and the eruption of volcanoes - all of these were happening long
ago, on roughly the same scale and at roughly the same rate as they are today. . So, a brief definition of Uniformitarianism would
be: the natural laws that govern geologic processes have not changed over geologic time, but the rate at which certain
geologic processes operate can vary. Uniformitarianism also has been paraphrased as "The Present is the Key to the Past".
An appreciation for the immensity of geologic time
is essential for understanding the history of our
planet
Geologists use two references for time
A. Relative time: places events in chronological
order
- does not tell us how long ago events were
B. Absolute time: results in specific dates for rocks
- calculated from natural rates of decay
Which came first?
Relative dating means
placing rocks in their
proper sequence of
formation – which
ones formed first,
second, third and so
on.
Unraveling earth
history by placing
geologic events in
chronological
order.
NO ACTUAL
NUMBERS
APPLIED.
Principles of
Relative Dating
1. Principle of Original
Horizontality


Layers of
sediments are
generally
deposited in a
horizontal
position.
All sedimentary
rock layers were
originally
horizontal.