Sample Ratio Problems

Introduction for sample ratio problems:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Example: For every Spoon of sugar, you need 2 spoons of flour (1:2) (Source: Wikipedia)

In our daily life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are equal, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.

Sample Ratio Definition and Example Problems:

Definition of ratio:

The learning ratio is a comparison by division method. We compare the two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote ratio-using symbol ‘:’

Examples of sample ratio problems:

Sample problem 1:

Length and breadth of a rectangular field are 75 m and 25 m respectively. Find the ratio of the length to the breadth of the field.

Solution:

Length of the rectangular field = 75 m

Breadth of the rectangular field = 25 m

The ratio of the length to the breadth is 75: 25

The ratio can be written as

= 75 / 25 = 3:1

Thus, the required ratio is 3:1

Sample problem 2:

There are 60 persons working in an office. If the number of females is 25 and the left over are males, find the ratio of,

(a) The number of females to number of males.

(b) The number of males to number of females.

Solution:

Number of females = 25

Total number of workers = 60

Number of males = 60 – 25 = 35

Therefore, the ratio of number of females to the number of males

= 35: 25 = 7: 5

And the ratio of number of males to the number of females

= 25: 35 = 5: 7.

(Notice that there is a difference between the two ratios 7: 5 and 5: 7).I have recently faced lot of problem while learning Electric Field Definition, But thank to online resources of math which helped me to learn myself easily on net.

Sample Practice Problem for Ratio:

Problem 1:

In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:5. If the bag contains 150 green sweets, how many red sweets are there?

Answer: There are 90 red sweets.

Problem 2:

A fence post in Tina's garden is 6 feet tall.  When she measured the fence post’s shadow, she found that it was 12 feet long.  A tree in Tina’s yard had a shadow of 72 feet.  How tall is the tree?

Answer: 36 tall is the tree

Problem 3:

The ratio of Kate's stickers to Jenna's stickers is 7:5.  Kate has 21 stickers. How many stickers does Jenna have?

Answer: 15 Stickers

Problem 4:

Chef Pillsbury's secret recipe requires 8 eggs for every 4 cups of flour. How many eggs will he need if he uses 6 cups of flour?

Answer: 12 eggs

Problem 5:

The ratio of the length of a rectangle to its width is 5:6. Its length is 25 inches. What is its width?

Answer: 30 inches

Introduction to Physics in Daily life

Physics is  a science based on experimental, observative and quantitative measurement. It is the study of nature and the laws governing the nature and how energy and matter are related to each other.

Physics in Daily Life Examples

Physics forms an inevitable part of all branches of life. It has numerous applications in all fields of life. If we consider our daily life, whatever we do can be directly or indirectly connected to one or the other principle of Physics. Our walking, our eating. our talking all involves Physics. Physics is the backbone of many daily life example like electricity, computer, wrist watch, Car, refrigerator and so on.Understanding Definition of Gravitational Potential Energy is always challenging for me but thanks to all math help websites to help me out.

some of the very few  examples from our daily life which illustrates the principles of Physics are

i. We walk, walk fast, run, jog, jump into a bus etc. All these or any type of motion is associated with Newton's law of motion.

ii. When we talk, our vocal cords vibrate producing sound.

iii. When we eat food, the chemical energy of the food is being converted into mechanical energy which we use to do different types of work.

iv. The electricity is our house is a gift of Physics. Hydroelectric project is the method in which water is used to generate electricity.  The mechanical energy of the water is converted into electrical energy using dynamo.



Physics in Daily Life, Examples Continued

v. refrigerator works on the principles of thermodynamics

vi. Pressure cookers, washing machines, music system, computers all work on the principle of Physics.

vii. Automobiles, trains, aircraft all work on the concepts of Physics.

viii. While you are reading this article the working of your eye is similar to the working of a camera which again belongs to Physics.

ix. Mobile phones working on microwaves also uses Physics to connect people from different parts of the world.

x. Writing using Pen, writing on whiteboard using marker all are the sole properties of Physics.

xi. Rain, snowfall, lightening, thunder, wind, sea breeze etc all owe their existence to the laws of Physics

As mentioned in the beginning, the above list is endless. Any phenomenon of our daily life you consider, we an surely bring Physics in it.

Physics Adding Vectors

Introduction to number of star activities:

Stars are the heavenly bodies like the sun that are extremely hot and have light of their own. They are made up of vast clouds of hydrogen gas, some helium and the dust. Hydrogen atoms are being continuously converted into helium atoms and a large amount of nuclear energy in the form of heat and light is released. The stars are not permanent. Some activities are continuously occurring in the core of the stars. Here we discuss the activities inside the stars.Please express your views of this topic Permanent Magnet Motor Free Energy by commenting on blog.

Activities Inside the Stars

As we know that the stars are not permanent, they have some internal activities. The activity begins with the gathering of hydrogen gas and helium gas present in galaxies to form the dense clouds of these gases. These stars are then formed by the gravitational pull and it becomes the protostar. It is a highly condensed cloud of gases, mainly hydrogen and some amount of the helium gas, formed by the gravitational contraction of gases present in the galaxy. It looks like a huge dark ball of gases. The formation of protostar is only a stage in the formation of the complete star. A protostar does not emit any light. The protostar continues to contract further due to the large gravitational gas cloud collide with one another very frequently. So, that the temperature of the protostar raises from - 173°C to 107 °C. At this high temperature, the nuclear fusion of hydrogen starts.Is this topic Examples of Electromagnets hard for you? Watch out for my coming posts.

4 1H1   `->`      2 He 4 + huge amount of energy

Now, the protostar begins to glow and become a complete star. It continues as a star for thousands of millions of years. In all the fusion reactions continues to liberate energy.

Conclusion for the Activities Inside the Stars

As in the star, the fusion reaction continues again in the interior of the star. Then it becomes the red giant star. At that time, it becomes red in color. After that, the future of the star depends on the mass of the star. If the mass of the star is same as that out sun it lose its expanding shell. The energy liberated by the fusion of helium would make this small core glow as white dwarf star. The matter is highly condensed. If the mass of the star is more than the mass of our sun, it continues to contracts and explodes, called the supernova. After that, it becomes the neutron star and then it becomes the black hole.

Define Electromagnetism

Define Electromagnetism
Advancement of modern physics is related to putting electricity and magnetism together to
get electromagnetism. It is governed by the fact that electric current has capacity to produce a
magnetic field. According to Faraday’s law, a change in electric field produce magnetic field and
change in magnetic field produces electric field. Scottish physicist Maxwell gave the complete
mathematical explanation of electromagnetism.I like to share this Definition of Electric Current with you all through my article.

Biot Savart Law Example
The electro magnet is the example of the Biot Savart Law. As we know that as the variable
current passes through a wire it produces a magnetic field. It can be observed in any household
by using a coil of wire connected to the AC source and put a magnetic or ferro magnetic material
near it. We will observe that the magnetic or ferromagnetic material is attracted towards the
coil until the coil is carrying the current. The attraction cease to exists as soon as current is
disconnected from the coil.

Mutual inductance formula
Mutual inductance is defined as production of electromotive force in a close coil due to change in
current in the coupled coil.
The induced electromotive force (Emf2) in coil 2 due to change in current (I1) in coil 1is given by
following formula:

Here M is mutual inductance.

Induction Heating Circuit
Induction heating circuit includes a work coil in which alternating current is induced using a high
frequency electricity. This induced alternating current produces intense and quickly changing
magnetic field within the work coil. This object or work-piece that is to be heated is then placed
under this alternating magnetic field. When placed within the alternating magnetic field, a current
flow is induced in the work-piece. These currents are eddy current that flow in small circles.

What is Induction Heating
Induction heating is the process of heating an electrically conductive material using alternative
magnetic field. It is a non-contact process of heating that use high frequency electricity to heat
the material. As mentioned, it is a non-contact process, hence the heating process does not
contaminate the heated material. As compare to other heating processes in which heat is
generated in heating element and then is used to heat the material, induction heating involves
generation of heat in the material, to be heated, itself. Hence induction heating is an efficient
process of heating.Having problem with Electrical Resistance Definition keep reading my upcoming posts, i will try to help you.

Electromagnetism Equations

Electromagnetism is governed by four basic formulas that are represented by Maxwell
Equations. These four Formulas are Gauss Law, Gauss Law in Magnetism, Faraday’s Law and
Amperes Maxwell Law.
These formulas are given below.
1. Gauss’a Law: it is given below
= Q/0

2. Gauss’s law in magnetism is given below:

=0

3. Equation for Faraday’s Law is given below:
= - (d

4. Ampere-Maxwell law formula is given below:
= µ0I+e0µ0 (d

The Relationship between Electricity and Magnetism

Electricity is related to both electrons and protons both carry a charge. Electrons carry positive charge
and protons carry positive charge. Protons concentrated in a small area called nucleus and placed in
the centre of atom. The motion of electrons is outside of nucleus in orbital. So, the moving of electrons
is response of Electricity. When an object is placed in magnetic field called magnet, it is due to motion
of electrically charged particles. Magnet has two poles called North poles and South poles. Two
magnets of same poles are repel each other while magnets of different poles are attracted each other.
Magnetism is a force of attraction or repulsion that acts at a distance. Electromagnetism definition is
correlated with electricity and magnetism each other.Please express your views of this topic Define Second Law of Thermodynamics by commenting on blog.

According to Dutch physicist Hendricks Anton Lorentz, Lorentz force law is the electric current applied
on a charged particle is parallel to the local electric field. The magnetic force, however, is perpendicular
to both the local magnetic field and the particle’s direction of motion. According to lenzs law, when an
electric force applied on a conductor then due to current it induced electromotive force. Lenz found a
way of direction of electromotive force and current of electromagnetic field. The direction of current
induced in magnetic field is opposite to direction of magnetic flux changes. The formula of Lenz law
shows negative sign to opposition of magnetic flux from the electric current.Is this topic Electric Flux Symbol hard for you? Watch out for my coming posts.

What is the Relationship between Electricity and Magnetism

Electromagnetism is also known to be as a Relationship between Electricity and Magnetism. Electricity
is produces due to magnetic effect and magnetism produces due to electric effect. When an electric
field is constant would never produce magnetism. Similarly when a magnetic field has constant value,
is doesn’t produce electric field. In our daily life we use many appliances based on electromagnetism
like television, computer etc. When an electric current is carried by a circular wire then magnetic field
produced will be same as magnetic field of bar magnet with their poles. When a magnetic field is linear
then circular electric field produces. When the electric current is carried in a straight wire then magnetic
field produces in a circular manner. Electricity and Magnetism equations are used to solve problems
related to daily life. Dr. Robert Becker was regarded as most well renowned scientist whose work
involved in the healthful and harmful effects of electromagnetic fields on the human body.

Electricity and Magnetism

How Induction Heating Works

For this a high frequency source is connected to the induction coil which generates high frequency
current in the coil. This in turn generates high and frequently varying magnetic field inside the induction
coil. The changing magnetic field induces a current in the targeted conductor. As a result of this large
amount of current passes through the target and it is known as eddy current. High frequency current
causes the skin effect which causes the AC to pass into a thin layer. Because of this effect resistance of
the target gets increased and leads to heating of target material through induction. During this process
induction coil does not get heated.Having problem with Wavelength to Frequency Equation keep reading my upcoming posts, i will try to help you.

Gravity Electromagnetism

Electromagnetism and gravity are two different forces in nature. Electromagnetism concerns with the
forces between electrically charged particles. Gravity is the attraction force between all bodies having
mass. Gravity is always attractive but electromagnetic force can be attractive or repulsive.

lenz's law equation

This is given as: V=- N

V is the induced emf due to change in flux φ.

N is number of turns of wire. The minus sign tells which way the induced current flows, based on the law
that magnetic field due to the induced current opposes the change in the flux that produced it.Please express your views of this topic Examples of Doppler Effect by commenting on blog.

Laws of Electromagnetism

Biot-Savart law: magnetic field generated due to a current carrying conductor of infinitely small
length dl is:
dB=(μo I dl sinθ) / 4πr2
Ampere's law: current generates magnetic field and its equation is given as:
∑B.dl=μo I

Force law: force on a charge q moving in a magnetic field B with velocity v is:

F =q)

Faraday's law: voltage induced in a circuit by change in magnetic flux is:
V=-

Induction Heating Coils

These coils are used in induction heating process to generate alternating magnetic field. Induction
heating coils are connected to a source of high frequency electricity which could produce high
Alternating Current through the coil. Induction coils are used to heat target material and induction coils

Biot Savart Law Derivation

Consider a small current carrying element of length dL with current I. Let r be the position vector of a
point P from the current element dL and θ be the angle between dL and r.

As per this law, the magnetic field dB induced at a point P due to current element depends on following
factors.

dBI
dBdL
dBsinθ
dB(1/r2)

Combining these we get

dBIdLsinθ/r2

dB=K Idl sinθ/r2

K=μ0/4π

Concept of Induction Heating System

Induction heating has unique characteristics of radio frequency, that portion of the electromagnetic
spectrum below infrared and microwave energy. Induction Heating System was discovered by Michael
Faraday by using electromagnetism. Since heat is transfer in form of electromagnetic waves, the object
never comes into contact with any flame directly, the inductor itself does not get warm, and there is
no product distortion. Induction Heating System becomes very repeatable and controllable. When an
alternating electrical current applying to primary coil transformer, a magnetic field is induced. If the
secondary coil of transformer is located within magnetic field, an electric current will be produced.
Induction Heating Systems used in new manufacturing circuit with accuracy, persistency and high
speed. In the process of Electromagnetism heat loss occurs, this loss of heat is transferred in the form
of production. The loss is converted in the form of unusable heating production, it is called Induction
Heating.I like to share this Define Electromagnetic Induction with you all through my article.

According to Lenz’s law explanation when a bar magnet moves toward solenoid from north pole then
the magnetic field lines move from south to north pole and the induced current moves from left to right
in the coil. When a bar magnet moves away from solenoid then direction of induced current changes.
Similarly if a bar magnet placed from South Pole towards solenoid then direction of induced current will
be right to left and magnetic lines move from north to South Pole.

Lorentz Force Law is the electric force apply on a charge particle is parallel to the local electric field. The
magnetic force is perpendicular to both the local magnetic field and the direction of particle’s motion.
The Lorentz force equation ir related to electromagnetism and Maxwell equation. Electric field and
magnetic field are related to each other and it’s superimpose effect is Definition of Electromagnetism.
When electric current applied on iron core wound with a conductor, the strength of electromagnet
depend on applying current. The current can easily start and stopped as required for functioning to form
an electromagnet.Understanding Magnetic Moment of an Electron is always challenging for me but thanks to all math help websites to help me out.

According to Biot Savart Law, Biot describes the magnetic field effect on electric current, how magnetic
field induced electric current. The law is consistent for both Ampere’s law and Gauss’ law and also valid
for magneto static approximation. Biot Savart Law Examples are based on electromagnetism; they
are used to define direction of current, magnetic field and electric field. It used for finding direction of
current and magnetic field and also finding length and accuracy.