WORKSHOP CALCULATION & SCIENCE

1. Explain decimal fractions & lowest common multiple.

Ans. The decimal numeral system (also called base ten or occasionally denary) has ten as

itsbase. It is the numerical base most widely used by modern civilizations.[1][2]

Decimal notation often refers to a base-10 positional notation such as the Hindu-Arabic numeral

system; however, it can also be used more generally to refer to non-positional systems such

asRoman or Chinese numerals which are also based on powers of ten.

Decimals also refer to decimal fractions, either separately or in contrast to vulgar fractions. In this

context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a

notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently an Angstrom.

The contrast here is between decimals and vulgar fractions, and decimal divisions and other

divisions of measures, like the inch. It is possible to follow a decimal expansion with a vulgar

fraction; this is done with the recent divisions of the troy ounce, which has three places of

decimals, followed by a trinary place. In arithmetic and number theory, the least common

multiple (also called the lowest common multiple or smallest common multiple) of

two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is

a multiple of both a and b.[1] It is familiar from grade-school arithmetic as the "lowest common

denominator"[citation needed] that must be determined before two fractionscan be added.

If either a or b is 0, LCM(a, b) is defined to be zero.

The LCM of more than two integers is also well-defined: it is the smallest number that is an

integer multiple of each of them.

2. What do you mean by Square and square root ? explain the methods of finding

out the squire root of a number.

Ans. In mathematics, a square root of a number a is a number y such that y2 =a, or, in other

words, a number y whose square (the result of multiplying the number by itself, or y × y)

is a.[1] For example, 4 is a square root of 16 because 42 = 16.

Every non-negative real number a has a unique non-negative square root, called the principal

square root, which is denoted by , where is called radical sign. For example, the principal

square root of 9 is 3, denoted , because 32 = 3 × 3 = 9 and 3 is non-negative. The term

whose root is being considered is known as the radicand. The radicand is the number or

expression underneath the radical sign, in this example 9.

Every positive number a has two square roots: , which is positive, and , which is

negative. Together, these two roots are denoted (see± shorthand). Although the principal

square root of a positive number is only one of its two square roots, the designation "the square

root" is often used to refer to the principal square root. For positive a, the principal square root

can also be written in exponent notation, as a1/2.

Square roots of negative numbers can be discussed within the framework of complex numbers.

More generally, square roots can be considered in any context in which a notion of "squaring" of

some mathematical objects is defined (including algebras of matrices, endomorphism rings, etc.)

Square roots of positive whole numbers that are not perfect squares are always irrational

numbers: numbers not expressible as a ratio of two integers (that is to say they cannot be written

exactly as m/n, where m and n are integers). This is the theorem Euclid X, 9 almost certainly due

to Theaetetus dating back to circa 380 BC.[2] The particular case is assumed to date back

earlier to the Pythagoreansand is traditionally attributed to Hippasus

3. Give Introduction--properties of metal--types of metals

Ans. In printing, type metal (sometimes called hot metal) refers to the metal alloys used in

traditional typefounding and hot metal typesetting. Lead is the main constituent of these alloys.

Antimony and tin are added to make the character produced durable and tough while reducing

the difference between the coefficients of expansion of the matrix and the alloy. Cheap, plentifully

available as galena and easily workable, lead has many of the ideal characteristics, but on its

own it lacks the necessary hardness and does not make castings with sharp details because

molten lead shrinks and sags when it cools to a solid.

After much experimentation it was found that adding pewterer's tin, obtained from cassiterite,

improved the ability of the cast type to withstand the wear and tear of the printing process,

making it tougher but not more brittle.

Despite patiently trying different proportions of both metals, solving the second part of the type

metal problem proved very difficult without the addition of yet a third metal, antimony. Type metal

is an alloy of lead, tin and antimony in different proportions depending on the application, be it

individual character mechanical casting for hand setting, mechanical line casting or individual

character mechanical typesetting and stereo plate casting.

The proportions used are in the range: lead 50‒86%, antimony 11‒30% and tin 3‒20%. The

basic characteristics of these metals are as follows:

Introduce the term Algebra. Explain the Algebric formula & its equation with the

help of some examples.

4. What is Newton’s law of motion--space diagram--vector diagram?

Ans. Newton's laws of motion are three physical laws that form the basis for classical

mechanics. They describe the relationship between the forces acting on a body and itsmotion due

to those forces. They have been expressed in several different ways over nearly three

centuries,[2] and can be summarized as follows:

1. First law: The velocity of a body remains constant unless the body is acted upon by an

external force.[3][4][5]

2. Second law: The acceleration a of a body is parallel and directly proportional to the

net force F and inversely proportional to the mass m, i.e., F = ma.

3. Third law: The mutual forces of action and reaction between two bodies are equal,

opposite and collinear.

The three laws of motion were first compiled by Sir Isaac Newton in his work Philosophiæ

Naturalis Principia Mathematica, first published in 1687.[6] Newton used them to explain and

investigate the motion of many physical objects and systems.[7] For example, in the third volume

of the text, Newton showed that these laws of motion, combined with his law of universal

gravitation, explained Kepler's laws of planetary motion. Newton's Laws hold only with respect to

a certain set of frames of reference called Newtonian or inertial reference frames. Some authors

interpret the first law as defining what an inertial reference frame is; from this point of view, the

second law only holds when the observation is made from an inertial reference frame, and

therefore the first law cannot be proved as a special case of the second. Other authors do treat

the first law as a corollary of the second.[10][11] The explicit concept of an inertial frame of

reference was not developed until long after Newton's death.

In the given interpretation mass, acceleration, momentum, and (most importantly) force are

assumed to be externally defined quantities. This is the most common, but not the only

interpretation: one can consider the laws to be a definition of these quantities.

Newtonian mechanics has been superseded by special relativity, but it is still useful as an

approximation when the speeds involved are much slower than the speed of light

5. Write short note on :-

Work

Power

Energy

6. What is unit? classify it. Explain the interrelationship between Metric and British

System of units.

7. Explain the purpose & process of heat treatment.

Ans. Heat treating is a group of industrial and metalworking processes used to alter

the physical, and sometimes chemical, properties of a material. The most common

application is metallurgical. Heat treatments are also used in the manufacture of many

other materials, such as glass. Heat treatment involves the use of heating or chilling,

normally to extreme temperatures, to achieve a desired result such as hardening or

softening of a material. Heat treatment techniques includeannealing, case

hardening, precipitation strengthening, tempering and quenching. It is noteworthy that

while the term heat treatment applies only to processes where the heating and cooling

are done for the specific purpose of altering properties intentionally, heating and cooling

often occur incidentally during other manufacturing processes such as hot forming or

welding. The specific composition of an alloy system will usually have a great effect on

the results of heat treating. If the percentage of each constituent is just right, the alloy will

form a single, continuous microstructure upon cooling. Such a mixture is said to

be eutectoid. However, If the percentage of the solutes varies from the eutectoid mixture,

two or more different microstructures will usually form simultaneously. A hypoeutectoid

solution contains less of the solute than the eutectoid mix, while a hypereutectoid solution

contains more.[7]