### Example of Thermodynamics Problems

Thermodynamics is a branch of physical science that treats various phenomena of heat, including the properties of matter, specially the laws of transformation of heat into other forms of energy and vice versa.

Matter – is anything that occupies space and has weight

Properties – characteristic of matter with is quantifiable

2 basic categories of properties of matter

1. Extensive – mass dependent
2. Intensive – mass independent

Extensive Properties

1. mass – Amount of matter in a substance
2. volume – space occupied by matter
3. weight – force exerted by gravity on a given mass

Mass weight relations

English                  Metric                   SI

W            lbf                           kgf                          W

M            slug                        hyl                          kgm

g              Fb/s^2                  m/s^2                   m/s^2

a = 32.2ft/s^2                    9.8 m/s^2            9.81 m/s^2

Second Law of Newton (Law of Motion)

– state that the acceleration of a particular body is directly proportional to the net force acting on it and inversely to its mass.

Example of Thermodynamics Problems with Solution

Problem # 1:

What is the weight of 66 kgm man at standard condition.

W = mg

m = kgm

g = 9.8

Problem # 2:

What is the weight of an object is 50lb. What is its at standard condition.

Problem # 3:

What is the mass in grams and the weight in dynes and gram force of 12 oz salt? Local acceleration is 9.65 m/s^2?

Problem # 4:

Five masses in a region where the acceleration due to gravity is 30.5 ft/s^2 are as follows:  M1 is 500gm, M2 weighs 800gf, M3 weighs 15 poundals, M4 is 0.10 slug of mass. What is the total mass expressed in a pounds (b) slugs (c) grams.

### Engineering Mechanics

Engineering Mechanics is the science which considers the effects of forces on rigid bodies. The subject is divided into two parts.

1. Statics – the effects and distribution of force on rigid bodies which are and remain at rest.
2. Dynamics – consider the motion of rigid bodies caused by the forces acting upon them.

Force System – a force system

– is any arrangement where two or more forces act on a body or on a group of related bodies

Resultant of two concurrent coplanar forces

Resultant of two or more Concurrent coplanar

Resultant of Concurrent Forces in Space

Example:
Given the three concurrent forces which through (1, -3, 4) and the indicated points
F1 = 150N (5, -6, 2)
F2 = 340N (4, 0, -3)
F3 = 280N (-1, 2, 6)

Determine the magnitude of resultant force.

Solution: Resolution of Forces

### Finding the Differential Equation from a General Solution

To find the differential equation when the general solution is given, differentiate the general solution, differentiate the derived solution etc. until the number of derived equation is equal to the number of independent arbitrary constant finally eliminate the constants from the derived equations.

Finding the Differential Equation from a General Solution Examples

Example # 1:

Find the differential equation of X^2 + Y^2 = CX

Example # 2:

Find the Differential Equation of ( X – C1 )^2 + C2y = C3

Example # 3:

Find the differential Equation of all lines through the origin is

y = mx

m = y/x

Example # 4:

Find the differential equation of all circles through (0,0) and (2,0)

Solution:

The standard equation of a circle is (x-h)^2 + (y-k)^2  =  1-2

### Linear First and Second Order Differential Equation

Linear First and Second Order Differential Equation

Linear First Oder Differential Equation

The equation in the form dy/dx + Py = Q where P and Q are functions of x only is called Linear Differential Equations since y and its derivatives are of the first degree.

The solution for dy/dx + Py = Q is obtained by multiplying throughout by an Integrating factor   to become

Example: Solve the equation dy +4xy dx = 2xdx

Solution:

Rearranging:  dy/dx + 4xy = 2x

then P = 4x and Q = 2x

Linear Second Order Differential Equation

Equation in the form a (d^2y/dx^2) + b(dy/dx) + cy = 0 where a, b, and c are constants, is called a linear second order differential equation with constant coefficient

Setting D = d/dx and D^2 = d^2/dx. The following procedures may be followed.

1. write the equation in D – operator form (aD^2 + bD + C) y=0, substitute m for D and solve the auxiliary equation am^2 + bm + c=0 for m

A. If the roots are real and different (b^2 > 4ac) say .

Then the general solution is

B. If the roots are real and equal  twice the general solution is

C. If the roots are imaginary (b^2 – 4ac) Say

the general solution is

Example:  Solve the equation 2(d^2y/dx^2) + 5(dy/dx) – 3y = 0

Solution:

Writing D – operator form: (2D^2  + 5D – 3) y = 0

Substituting m for D gives the auxiliary equation 2m^2 + 5m – 3 = 0 which can be factored as (2m – 1) (m + 3) and the roots are m = ½ and m = -3

Since the roots are real and different the general solution is

then the general solution is

### How to Solve Differential Equation with Example

How to Solve Differential Equation with Example

Differential Equation

– are equation that contain differential coefficients.

Example:

– classified according to the highest derivative that occurs in Them the differential equation dy/dx = 12x is a first order differential equation d^2y/dx^2 + 4dy/dx – 3y = 0 is a second order differential equation. A solution to a differential equation that contains one or more arbitrary constant of integration is called general solution. When additional information is Given so that these constants may be calculated the particular solution of differential equation is obtained.

Variable Separable

A differential equations can be of type dy/dx = f(x)solved by direct integration by writing it in the form dy = f(x) dx

Example:

Solve the differential equation dy/dx = 2x + Sin 3x

Solution: dy = (2x + Sin 3x) dx

y = x2 – 1/3 Cos 3x + c  general solution

Differential equation of type dy/dx = f(y) can be solved by direct integrating by writing it in the form.

dx = dy/f(x)

Example:

Solve the equation (y^2 – 1) dy/dx = 3y Given that y = 1 when x = 13/6

Differential Equation of type

dy/dx = f(x)  g(y) can be solve by Direct Integration by writing it in the form dy/g(y) = f(x)dx

Differential Equation of type dq/dt = KQ the general solution of an equation of the form dq/dt = KQ is Q = Ce^kt . where C is constant

Example:

solve the equation dy/dx = 3y

here we have  Q = y   dQ = dy                     then

t = x       k = 3                          y = Ce^3x

Example:

Obtain the differential equation of the family of straight lines with slope and y intercept equal

Solution:

The standard equation of the line in slope – intercept form is y = mx + b.

Since the slope and y intercept are equal m = b = c then y = cx + c

isolating constant and differentiate

### Teaching and Learning of Japanese and Mandarin Chinese

Acquiring a second language is hard enough; learning a foreign tongue is even harder. This difficulty is particularly more pronounced in learning East Asian languages such as Japanese and Mandarin Chinese whose grammatical structure, orthography, and phonology seem too exotic for English users.

Thankfully, there is Bikol which, in my own classroom experience, provides the following learning aids:
a) prior knowledge upon which the students can build new learning;
b) cognitive landmark that may guide the students in navigating that complicated maze called foreign language acquisition and transitioning them from the familiar to the unknown; and
c) basis for analogy or comparison that may enhance comprehension.

FOREIGN VS. NATIVE SOUNDS & SYMBOLS

Teaching Japanese Phonetics
It is a well known fact that Japanese cannot produce the /l/ sound. This is not a racial predisposition. Perhaps, the Japanese are not able to develop the ability to perceive, hence, articulate the /l/ sound because such sound in nonexistent in their native language. By nature, such ability would find no usefulness.

And then there is this mistaken notion that the Japanese language is replete with the /r/ sound. Actually “r” is a mere symbol used to represent a sound that is midway between /r/ and /l/. This sound, although described as “midway between /r/ and /l/,” is actually closer to /d/.

The following texts that describe the Japanese /r/ and give suggestions on how it should be properly articulated were verbatimly lifted from authoritative sources and given to the students for them to understand.

“r—a sound peculiar to Japanese pronounced with the tip of the tongue moving midway in the mouth but not rolled. If the tongue is given slightly more tension, this sound easily becomes “d.” It is like neither “r” nor “l” in English but is sort of between the two, like the Spanish “r” in “pero.”

“/r/ is probably the most difficult sound for English-speaking students. This is neither /r/, /l/, nor /d/ in English, but may be most close to /d/. In Japanese it is necessary to distinguish /r/ and /d/.In both cases the tongue touches somewhere and comes off quickly and decisively. The difference between these /r/ and /d/ is that of the position of contact.

/r/ against the alveolar ridge with the very tip of the tongue
/d/ against the teeth with somewhere more front of the tongue”

“I put my foot in my mouth again today. When I introduced Miss Winters to my Japanese friends I meant to say Edo bungaku o kenkyuu shite imasu (She’s studying the literature of the Ed period). But my “d” sounded like an “r.” So what I actually said was “She’s studying pornographic literature” [Ero bungaku o kenkyuu shite imasu].”

“I then remembered what Sensee told me about the pronunciation of the “d” sound; I should have pressed the tip of the tongue against the upper teeth ridge.”

Teaching Japanese Orthography

Filipino students find the Japanese hiragana (cursive script) and katakana (angular script) too intimidating. They find such writing systems completely foreign. But using baybayin as springboard may somehow ease the intimidation and melt the resistance against learning them.

“Ra” is formed simply by adding a diacritic to “da.” Such process may also be used as springboard in teaching the transformation of basic kana characters into sonant and semisonant characters.

TEACHING JAPANESE & MANDARIN CHINESE GRAMMAR USING BIKOL THROUGH ANALOGY

I-adjectives, considered as true adjectives, are native to the Japanese language. They are so called because they end in character い(„i‟).
Example: oishii (delicious)
atsui (hot)
atatakai (warm)
When used as noun modifiers, i-adjectives behave like English adjectives, that is, they precede the nouns that they modify. For example:
oishii tabemono (delicious food)
atsui kōhii (hot coffee)
atatakai tenki (warm weather)
Na-adjectives are those that originated from Chinese and other foreign languages.
Example: shizuka (peaceful)
nigiyaka (lively)
shinsetsu (kind)
They are called na-adjectives because they need particle “na” when modifying nouns. For instance:
shizuka na machi (peaceful town)
nigiyaka na pātii (lively party)
shinsetsu na sensei (kind teacher)
Most students could not grasp the sense of the English translation because they could not account for the missing “na.” But translating the Japanese phrases into Bikol does the trick.
shizuka na machi (matoninong na banwa)
nigiyaka na pātii (maribok na party)
shinsetsu na sensei (maboot na maestra)
By employing Japanese-Bikol analogy, the Bikol translation enhances comprehension.

Mandarin Chinese Basic Sentence Pattern
The first sentence learned by a student of Mandarin Chinese is usually “Nǐ (you) hăo (fine).” It‟s literal translation is “you are fine,” but its equivalent expression in English is “Hi.”
“Nǐ hăo” may be expanded to “Nǐ hăo ma?” whose literal translation is “you are fine?” but is equivalent in English to “How are you?”
The formulaic response is “Wŏ (I) hăo” (I am fine) or “Wŏ hĕn (very) hăo” (I am very fine).
“Wŏ hăo” is the basic—being the simplest—sentence pattern in Mandarin Chinese. Ironically, it is its simplicity that makes it hard to comprehend. English users are told that a sentence may not be complete without a verb. But “Wŏ hăo” is a complete, albeit verbless sentence.
In Mandarin Chinese, when the complement is an adjective, a linking verb is not necessary, as in:
Wŏ hăo. (I am fine.)
Hànyŭ (Mandarin Chinese) nán (difficult). Mandarin Chinese is difficult.
But the complement is a noun, the linking verb “shì” is needed, as in:
Wŏ shì (am) Fēilǜbīnrén (Filipino). (I am [a] Filipino.)
Tā (she) shì lăoshī (teacher). (She is a teacher.)

### How to Solve Projectile Motion Problems

Projectile Motion is a form of motion where a particle (called a projectile) is thrown obliquely near the earth’s surface, and it moves along a curved path under the action of gravity. The path followed by a projectile motion is called its trajectory. Projectile motion only occurs when there is one force applied at the beginning of the trajectory after which these is no interference apart from gravity.

These are the formulas to solve Projectile Problems.

Example of Projectile Motion Problems with Solution:

1. A stone is projected from the ground with a velocity of 15 m/s at an angle of 30 degree with the horizontal ground. How high in meter will it rise? Use g = 9.817 m/s/s.

Figure:

2. Former Bob and his horse Flash jump a 100m wide canyon. The flight through the air takes 5s. Find the initial velocity (That is, find the magnitude and the angle of the initial velocity)

1st You need to solve the vertical using the formula V = Vo  +  gt. Substitute the gravity and the time.

2nd Solve the horizontal, use the formula x = Vox times the time.

Use Pythagorean Theorem formula to solve initial Velocity and the Angle.

Answer: 31.3 m/s for the Initial Velocity , and 50.8 degree for the Angle.

3. A rock is thrown horizontally off a 100m cliff. It lands 95m away. At what speed was it thrown?

4. A ball is thrown from a tower 30m high above the ground with a velocity of 300 m/s directed at 20 degree from the horizontal. How long will the ball hit the ground?

5. A Projectile is shot from edge of a cliff 125m above ground level with an Initial speed of 65 m/s at an angle of 37 degree above the horizontal. Determine the magnitude and the direction of the velocity at the maximum height.

Answer: The Projectile’s velocity at its max height is completely horizontal, and this is the same as the initial horizontal velocity.

Vf = Vix

= 65Cos 37

= 51.9 m/s (forward/horizontal)

Laptops can be sent back to the manufacturer if the purchaser finds the screen of the laptop scratched or with a minor blemish, or if it is an unwanted present to him or if the packaging of the laptop is dented etc. Such laptops are inspected, tested again for quality and repackaged by the manufacturer and sold for a very less price. Such laptops are called as refurbished laptops.

Factory refurbished laptops:

The laptops in the factory undergo rechecking for any manufacturing defect by passing through various stages of examination. Then, when no fault is found, the hard disk of the laptop is reformatted and again the operating system is loaded. It is again made to work for less than 4-5 hours time to check for any defect and the parts are replaced if they are found to be defective. The refurbished laptop is then updated with a new serial number to mark it as a factory refurbished laptop. Such factory refurbished laptops are of high quality available to the consumer at a lesser retail price. Such refurbished laptops can be got from almost all the renowned brands. However the process carried out for the restoration of laptops may differ from company to company. The main aim is to make the laptop run again efficiently as it used to be previously.

Custom refurbished laptops:

These are repaired laptops which are reassembled to match the customer’s preference. It gives an opportunity to get a complete laptop solution at a very affordable price to the customer. The utilities offered by the customer refurbished laptops are got at a cost of a used laptop. It also avoids the necessity to upgrade immediately, which is not the case with the standard laptop. It allows the customers to have preferences in terms of selecting the features like the screen size, processor speed requirements, multimedia, memory capacity, hard drive size, optical drive, graphics, accessories, Bluetooth etc.
When purchased in bulk, custom refurbished laptops are the best option as it combines both functionality and price advantage together. Additional benefits can be availed through promotional offers and discounts from the manufacturers.

The refurbished laptops are of high quality as they are checked for high standards of performance at each level of examination done. The consumer can get a branded, quality laptop of a latest model at a very less price compared to the retail price. More over discounts are offered to military personnel, senior citizens and students who can maximize their savings by purchasing a refurbished laptop.

The refurbished laptops can be selected from renowned brands available in the market at a lesser cost. Such refurbished laptops are also got with 1 year warranty which can be extended up to 3 years. The warranty period supports replacement of parts and maintenance required by the laptop. Hence purchasing such laptops are very reliable. The refurbished model laptops enable the customers get more features at a lower cost. When the purchaser is bent on buying the latest, trendiest laptop, but cannot afford to buy a new one he can go for a refurbished laptop to get satisfied.

### How to Make Your Computer Run Faster

10 Simple Tips on How to Make your Computer Run Faster

Many people are interested in making the most of their hardware. So here are 10 Simple Tips on How to Make your Computer Run Faster without having to purchase additional hardware.

One of the factors that slow the performance of the computer is disk fragmentation. When files are fragmented, the computer must search the hard disk when the file is opened to piece it back together. To speed up the response time, you should monthly run Disk Defragmenter, a Windows utility that defrags and consolidates fragmented files for quicker computer response.

* Follow Start > All Programs > Accessories > System Tools > Disk Defragmenter
* Click the drives you want to defrag and click Analyze
* Click Defragment
2. Detect and Repair Disk Errors

Over time, your hard disk develops bad sectors. Bad sectors slow down hard disk performance and sometimes make data writing difficult or even impossible. To detect and repair disk errors, Windows has a built-in tool called the Error Checking utility. It’ll search the hard disk for bad sectors and system errors and repair them for faster performance.

* Follow Start > My Computer
* In My Computer right-click the hard disk you want to scan and click Properties
* Click the Tools tab
* Click Check Now
* Select the Scan for and attempt recovery of bad sectors check box
* Click Start
3. Disable Indexing Services

Indexing Services is a little application that uses a lot of CPU. By indexing and updating lists of all the files on the computer, it helps you to do a search for something faster as it scans the index list. But if you know where your files are, you can disable this system service. It won’t do any harm to you machine, whether you search often or not very often.

* Go to Start
* Click Settings
* Click Control Panel
* Click the Add/Remove Window Components
* Uncheck the Indexing services
* Click Next
4. Optimize Display Settings

Windows XP is a looker. But it costs you system resources that are used to display all the visual items and effects. Windows looks fine if you disable most of the settings and leave the following:

* Show shadows under mouse pointer
* Show translucent selection rectangle
* Use drop shadows for icons labels on the desktop
* Use visual styles on windows and buttons
6. Disable Performance Counters

Windows XP has a performance monitor utility which monitors several areas of your PC’s performance. These utilities take up system resources so disabling is a good idea.

* Then select each counter in turn in the ‘Extensible performance counters’ window and clear the ‘performance counters enabled’ checkbox at the bottom button below

You can optimize your pagefile. Setting a fixed size to your pagefile saves the operating system from the need to resize the pagefile.

* Right click on My Computer and select Properties
* Under Performance choose the Settings button
* Select the Advanced tab again and under Virtual Memory select Change

* Highlight the drive containing your page file and make the initial Size of the file the same as the Maximum Size of the file.
8. Remove Fonts for Speed

Fonts, especially TrueType fonts, use quite a bit of system resources. For optimal performance, trim your fonts down to just those that you need to use on a daily basis and fonts that applications may require.

* Open Control Panel
* Open Fonts folder
* Move fonts you don’t need to a temporary directory (e.g. C:\FONTBKUP?) just in case you need or want to bring a few of them back. The more fonts you uninstall, the more system resources you will gain.

9. Use a Flash Memory to Boost Performance

To improve performance, you need to install additional RAM memory. It’ll let you boot your OS much quicker and run many applications and access data quicker. There is no easiest and more technically elegant way to do it than use eBoostr (http://www.eboostr.com).

eBoostr is a little program that lets you improve a performance of any computer, powered by Windows XP in much the same way as Vista’s ReadyBoost. With eBoostr, if you have a flash drive, such as a USB flash thumb drive or an SD card, you can use it to make your computer run better. Simply plug in a flash drive through a USB socket and Windows XP will use eBoostr to utilize the flash memory to improve performance.

The product shows the best results for frequently used applications and data, which becomes a great feature for people who are using office programs, graphics applications or developer tools. It’ll surely attract a special attention of laptop owners as laptop upgrade is usually more complicated and laptop hard drives are by definition slower than those of desktops.

10. Perform a Boot Defragment

There’s a simple way to speed up XP startup: make your system do a boot defragment, which will put all the boot files next to one another on your hard disk. When boot files are in close proximity to one another, your system will start faster.

On most systems, boot defragment should be enabled by default, but it might not be on yours, or it might have been changed inadvertently. To make sure that boot defragment is enabled:
* Run the Registry Editor
* Go to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Dfrg\BootOptimizeFunction
* Set the Enable string value to Y if it is not already set to Y.
* Exit the Registry
* Reboot

### 6 Tips to Save on Your Printer Ink Cartridges

Buying a printer is a one time cost, but since printer ink cartridges need to be bought on a regular basis, the cost of operating the printer and maintaining it in proper condition can add up. Each ‘print’ command, however small, makes your printer use ink, but with some easy tips, you can actually save a lot of ink and use a cartridge for a longer period than usual.

1) Print only what is necessary

Let’s begin with economising. Most often, we end up making unnecessary printouts and in the process waste precious ink. For instance, you might need to print only a small portion of a web page instead of the whole page. Instead of simply printing the whole page, complete with its heavy graphics etc, be specific on what you want to have in hard copy and print only that portion.

Text always consumes less ink compared to graphics or images. If textual information is all that you need then you can make sure that you don’t print the graphics and images. If it is a web page you need to save in a printed form, check for its print version. If there is no print version, you can copy and paste the text in a word document and take a printout of that.

Also try to do a bit of planning and double check what you are printing before hitting the print button.

2) Go for a quick print preview

Most branded printers such as HP, Canon, Dell, Epson or any other printer come with a printer driver which has a very useful print preview function. With this function, you can have a prior preview of the copy you want to take a print out of.

This function is especially handy when you are directly taking the print out from the Internet. At times, what you see on a site is totally different as compared to the printed version. A quick preview can help to get the printout of the material that you specifically want.

3) Make sure the power is turned off

Just as you never switch off your computer without properly shutting it down, the same rule applies to your printer too. If you don’t shut down the printer properly, the print heads will remain directly exposed to air causing the ink to dry in the nozzles which, in turn, could affect the quality of printing adversely. Make it a habit to check the position of the print heads before cutting off the power.

4) Use good software

There are various ink saving software options available online. These software applications are designed to reduce the consumption of your printer ink. With these applications, you can get good quality printout copies with less ink consumption even during high resolution printing.

5) Use printer ink cartridges smartly

If you don’t do printing regularly, run a small printing test at least once a week, to avoid the ink cartridges from drying up. This little precaution will help you to increase the life of the cartridge.

6) Never expose your printer to extreme temperatures

Too much variation in room temperature is bad for printer ink cartridges. You must avoid keeping your printer in too hot or too cold a temperature as the cartridges can dry up. For lasting printer performance, make sure the room has a normal and stable temperature.

With these small but important tips, your printer ink cartridges will get a longer life. It is easy to buy good quality printer ink cartridges at excellent prices from online shops.