## Sunday, 18 December 2005

### Fisika SMA

Pengalaman Belajar Fisika di SMAN BI 1 Banjar

## Experiment: Vector Addition by the Numerical Method

SUBJECT: Mathematics
DESCRIPTION: A set of problems dealing with vector addition.
CONTRIBUTED BY: Carol Hodanbosi
EDITED BY: Jonathan G. Fairman - August 1996

#### Purpose:

A vector is a quantity that has both magnitude, or size, and direction. Forces can be represented by vectors, since they have both a size and direction of action. Below is an example of a mass supported by two cables. If the mass is not moving, all the forces acting on the mass are considered to be balanced. You will investigate each of the forces acting on the mass and compare their relationships.

Fw represents the weight of the object. It is found by mulitplying its mass by gravity. That is, Fw = m * g, where g equals 9.8 m/s2. This force is directed downward.

#### Exercises:

1. If the object represented by F has a mass of 4.8 kilograms, find its weight.

2. What direction is the weight of the object acting? Draw this vector through the center of mass of F .

3. The lines CB and CA are vector quantities that are supporting and acting opposite the object F . Draw a line through point C parallel to the base support. Measure the angle between CB and the line just drawn.
Since vectors CB and CA are not acting parallel or perpendicular to the base of the stand, it is helpful to find the components of each of these vectors. Components are vectors that combine vectorally to form the resultant vector, in this case CB or CA . For example, to find the components of CA or CB one first needs to find the angle that vector forms with the horizontal line, angle ACD or angle BCE , see diagram below.

To find components of vector CB , form a right triangle with CB as the hypotenuse. Since CB is a vector, or a ray, one will be selecting a fixed portion of CB . Recall the trigonometric functions of the sine (side opposite/ hypotenuse) and the cosine (side adjacent / hypotenuse). The sine of angle BCE would equal side BE/CB , while the sine of angle ACD = AD/ AC .
Let's assume that the angle ACD and angle BCE are both 35° and that the weight represented by vector CF is 100 newtons. Since the weight is static, and not moving, we can assume all the forces are balanced. The vector represented by CE (to the right) must be balanced by the vector CD (to the left).The downward force of the weight represented by CF must be balanced by the two upward forces DA and EB . Since the two right triangles have two congruent angles (35°) and two congruent sides, (FD and CE ) the two triangle are congruent (Leg, Acute angle).
Because DA + EB = CF then DA = EB = 50 newtons.

By substitution, Sin angle BCE = BE/CB

Sin 35° = 50/CB
CB = 50 /Sin 35°
CB = 87.17 newtons
One can also find the measure of CE or CD using the tangent function.
tan BCE = BE/EC
tan 35° = 50 /EC
EC = 50 /tan 35°
EC = 71. 4 newtons

Now use the following diagram to solve the problems below.
A load of 500 kg is suspended at the end of a horizontal boom supported by a cable. The cable makes a 42° angle with the boom and is attached to a wall by a supporting pin. You can assume the boom's mass is negligible.
4. Find the downward force vector (the weight of the mass).

5. Represent the components of the cable (one is inward toward the wall, the other is upward, opposite the mass).

6. Find the tension in the cable.

7. Find the outward force of the boom.

Sumber:

NASA

## Friday, 18 November 2005

### Fisika SMA

Pengalaman Belajar Fisika di SMAN BI 1 Banjar

Belajar di Sekolah Bertaraf Internasional

To better understand the science of propulsion it is necessary to use some mathematical ideas from vector analysis. Most people are introduced to vectors in high school or college, but for the elementary and middle school students, or the mathematically-challenged:

DON'T PANIC!.

There are many complex parts to vector analysis and we aren't going there. We are going to limit ourselves to the very basics. Vectors allow us to look at complex, multi-dimensional problems as a simpler group of one-dimensional problems. We will be concerned mostly with definitions The words are a bit strange, but the ideas are very powerful as you will see.

Math and science were invented by humans to describe and understand the world around us. We live in a (at least) four-dimensional world governed by the passing of time and three space dimensions; up and down, left and right, and back and forth. We observe that there are some quantities and processes in our world that depend on the direction in which they occur, and there are some quantities that do not depend on direction.

For example, the volume of an object, the three-dimensional space that an object occupies, does not depend on direction. If we have a 5 cubic foot block of iron and we move it up and down and then left and right, we still have a 5 cubic foot block of iron.

On the other hand, the location, of an object does depend on direction. If we move the 5 cubic foot block 5 miles to the north, the resulting location is very different than if we moved it 5 miles to the east. Mathematicians and scientists call a quantity which depends on direction a vector quantity.

A quantity which does not depend on direction is called a scalar quantity.

Sumber:

http://www.grc.nasa.gov/WWW/K-12/airplane/vectors.html

## Tuesday, 18 October 2005

### Fisika SMA

Pengalaman Belajar fisika di SMAN BI 1 Banjar

(Sekolah Bertaraf Internasional)

SIGNIFICANT DIGITS

The number of significant digits in an answer to a calculation will depend on the number of significant digits in the given data, as discussed in the rules below.

Approximate calculations (order-of-magnitude estimates) always result in answers with only one or two significant digits.

When are Digits Significant?

Non-zero digits are always significant. Thus, 22 has two significant digits, and 22.3 has three significant digits.

With zeroes, the situation is more complicated: Zeroes placed before other digits are not significant; 0.046 has two significant digits.

Zeroes placed between other digits are always significant; 4009 kg has four significant digits. Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.

Zeroes at the end of a number are significant only if they are behind a decimal point as in (c).

Otherwise, it is impossible to tell if they are significant. For example, in the number 8200, it is not clear if the zeroes are significant or not. The number of significant digits in 8200 is at least two, but could be three or four. To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point:

8.200 ´ 103 has four significant digits8.20 ´ 103 has three significant digits
8.2 ´ 103 has two significant digits
Significant Digits in Multiplication, Division, Trig. functions, etc.

In a calculation involving multiplication, division, trigonometric functions, etc., the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied, divided etc.

Thus in evaluating sin(kx), where k = 0.097 m-1 (two significant digits) and x = 4.73 m (three significant digits), the answer should have two significant digits.

Note that whole numbers have essentially an unlimited number of significant digits. As an example, if a hair dryer uses 1.2 kW of power, then 2 identical hairdryers use 2.4 kW:

1.2 kW {2 sig. dig.} ´ 2 {unlimited sig. dig.} = 2.4 kW {2 sig. dig.}

Significant Digits in Addition and Subtraction

When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

Example:

5.67 J (two decimal places)
1.1 J (one decimal place)
0.9378 J (four decimal place)
7.7 J (one decimal place)

Keep One Extra Digit in Intermediate Answers

When doing multi-step calculations, keep at least one more significant digit in intermediate results than needed in your final answer.

For instance, if a final answer requires two significant digits, then carry at least three significant digits in calculations. If you round-off all your intermediate answers to only two digits, you are discarding the information contained in the third digit, and as a result the second digit in your final answer might be incorrect.

(This phenomenon is known as "round-off error.")

The Two Greatest Sins Regarding Significant Digits
1. Writing more digits in an answer (intermediate or final) than justified by the number of digits in the data.
2. Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.

## Identifying significant digits

The rules for identifying significant digits when writing or interpreting numbers are as follows:
• All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4 and 5).
• Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 has five significant figures: 1, 0, 1, 1 and 2.
• Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.
• Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures. This convention clarifies the precision of such numbers; for example, if a result accurate to four decimal places is given as 12.23 then it might be understood that only two decimal places of accuracy are available. Stating the result as 12.2300 makes clear that it is accurate to four decimal places.
• The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
• A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, $13 \bar{0} 0$ has three significant figures (and hence indicates that the number is accurate to the nearest ten).
• The last significant figure of a number may be underlined; for example, "20000" has two significant figures.
• A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant.
However, these conventions are not universally used, and it is often necessary to determine from context whether such trailing zeros are intended to be significant. If all else fails, the level of rounding can be specified explicitly.

The abbreviation s.f. is sometimes used, for example "20 000 to 2 s.f." or "20 000 (2 sf)". Alternatively, the uncertainty can be stated separately and explicitly, as in 20 000 ± 1%, so that significant-figures rules do not apply.
Scientific notation
Generally, the same rules apply to numbers expressed in scientific notation. However, in the normalized form of that notation, placeholder leading and trailing digits do not occur, so all digits are significant. For example, 0.00012 (two significant figures) becomes 1.2×10−4, and 0.000122300 (six significant figures) becomes 1.22300×10−4. In particular, the potential ambiguity about the significance of trailing zeros is eliminated. For example, 1300 to four significant figures is written as 1.300×103, while 1300 to two significant figures is written as 1.3×103.

### Engineering notation

See main article on Engineering notation

## Rounding

To round to n significant figures:
• Start with the leftmost non-zero digit (e.g. the "1" in 1200, or the "2" in 0.0256).
• Keep n digits. Replace the rest with zeros.
• Round up by one if appropriate. For example, if rounding 0.039 to 1 significant figure, the result would be 0.04. There are several different rules for handling borderline cases — seerounding for more details.
• Officially[2] if the first not significant figure is a 5 not followed by any other digits or followed only by zeros, the last significant figure should be rounded down or up to the nearest even number. So to round 1.25 to 2 significant figures should be 1.2 and 1.35 should be 1.4. If the first non-significant digit is a 5 followed by other non-zero digits, the last significant digit should be rounded up. For example, 1.2459 as the result of a calculation or measurement that only allows for 3 significant figures should be written 1.25.

## Arithmetic

For multiplication and division, the result should have as many significant figures as the measured number with the smallest number of significant figures.
For addition and subtraction, the result should have as many decimal places as the measured number with the smallest number of decimal places.

## Importance

### Superfluous precision

If a sprinter is measured to have completed a 100-metre race in 11.71 seconds, what is the sprinter's average speed? By dividing the distance by the time using a calculator, we get a speed of 8.53970965 m/s.
The most straightforward way to indicate the precision of this result (or any result) is to state the uncertainty separately and explicitly, for example in the above case as 8.5397±0.0037 m/s or equivalently 8.5397(37) m/s.

This is particularly appropriate when the uncertainty itself is important and precisely known (here, 100 m is presumed to be precise, and the time is 11.71±0.005 s, or an uncertainty of nearly 430 ppm).

In this case, it is safe and indeed advantageous to provide more digits than would be called for by the significant-figures rules.
If the degree of precision in the answer is not important, it is again safe to express trailing digits that are not known exactly, for example 8.5397 m/s.
If, however, we are forced to apply significant-figures rules, expressing the result as 8.53970965 m/s would seem to imply that the speed is known to the nearest 10 nm/s or thereabouts, which would improperly overstate the precision of the measurement.

Reporting the result using three significant figures (8.54 m/s) might be interpreted as implying that the speed is somewhere between 8.535 and 8.545 m/s.

This is actually very close to the true precision, the actual speed being somewhere between 8.5360 and 8.5434 m/s.

Reporting the result using two significant figures (8.5 m/s) would introduce considerable roundoff error and degrade the precision of the result.
(Note: in actual practice, 100 m is not this precise!

For example, a pair of 0.05-metre-wide (2-inch) lines at the start and end would introduce a separate uncertainty of ±0.05 m (2 in) or 500 ppm to the above calculation.

Now the total uncertainty has risen to 500 + 430 = 930 ppm, since both sources must be added together.

Applied to the speed, that now becomes 8.5397±0.0080 or 8.5397(80) m/s, the actual speed being somewhere between 8.5317 and 8.5477 m/s.)

Sumber:

Wikipedia

## Sunday, 18 September 2005

### Fisika SMA

Catatan di Sekolah Bertaraf Internasional

Pengalaman di SMAN BI 1 Banjar

Jangka Sorong dan Mikrometer

"A caliper (British spelling also calliper) is a device used to measure the distance between two symmetrically opposing sides. A caliper can be as simple as a compass with inward or outward-facing points. The tips of the caliper are adjusted to fit across the points to be measured, the caliper is then removed and the distance read by measuring between the tips with a measuring tool, such as a ruler.
They are used in many fields such as metalworkingmechanical engineeringgunsmithinghandloadingwoodworkingwoodturning and inmedicine. (Wikipedia)"

## Parts

The parts of a micrometer caliper, labeled. (Notice also that there is a handy decimal-fraction equivalents chart printed right on the frame of this inch-reading micrometer.)
A micrometer is composed of:
Frame
The C-shaped body that holds the anvil and barrel in constant relation to each other. It is thick because it needs to minimize flexion, expansion, and contraction, which would distort the measurement. The frame is heavy and consequently has a high thermal mass, to prevent substantial heating up by the holding hand/fingers. It is often covered by insulating plastic plates which further reduce heat transference. Explanation: if you hold the frame long enough so that it heats up by 10°C, then the increase in length of any 10 cm linear piece of steel is of magnitude 1/100 mm. For micrometers this is their typical accuracy range. Micrometers typically have a temperature specified, at which the measurement is correct.
Anvil
The shiny part that the spindle moves toward, and that the sample rests against.
Sleeve / barrel / stock
The stationary round part with the linear scale on it. Sometimes vernier markings.
Lock nut / lock-ring / thimble lock
The knurled part (or lever) that one can tighten to hold the spindle stationary, such as when momentarily holding a measurement.
Screw
(not seen) The heart of the micrometer, as explained under "Operating principles". It is inside the barrel. (No wonder that the usual name for the device in German is Messschraube, literally "measuring screw".)
Spindle
The shiny cylindrical part that the thimble causes to move toward the anvil.
Thimble
The part that one's thumb turns. Graduated markings.
Ratchet stop
(not shown in illustration) Device on end of handle that limits applied pressure by slipping at a calibrated torque.

Sumber dari: Wikipedia

## Saturday, 20 August 2005

### Besaran dan Satuan

Catatan Belajar di Sekolah Bertaraf Internasional

Pengertian Besaran Besaran adalah sesuatu yang dapat diukur dan dinyatakan dengan angka.

Dalam fisika pengukuran merupakan sesuatu yang sangat vital.

Suatu pengamatan terhadap besaran fisis harus melalui pengukuran.

Pengukuran-pengukuran yang sangat teliti diperlukan dalam fisika, agar gejala-gejala peristiwa yang akan terjadi dapat diprediksi dengan kuat.

Pengukuran dapat dilakukan dengan dua cara:

1. Secara Langsung: Yaitu ketika hasil pembacaan skala pada alat ukur, langsung menyatakan nilai besaran yang diukur, tanpa menggunakan rumus untuk menghitung nilai yang diinginkan.

2. Secara tidak langsung: Yaitu dalam pengukuran memerlukan penghitungan tambahan untuk mendapatkan nilai besaran yang diukur.

Untuk mendapatkan hasil pengukuran yang akurat, faktor yang harus diperhatikan antara lain :
1. Alat ukur yang dipakai
2. Aturan angka penting
3. Posisi mata pengukuran (paralax)

Kesalahan (error) adalah penyimpangan nilai yang diukur dari nilai benar x0.

Kesalahan dapat digolongkan menjadi tiga golongan:

1. Keteledoran

Umumnya disebabkan oleh keterbatasan pada pengamat, diantaranya kurang terampil menggunakan instrumen, terutama untuk instrumen canggih yang melibatkan banyak komponen yang harus diatur atau kekeliruan dalam melakukan pembacaan skala yang kecil.

2. Kesalahan sistmatik Adalah kesalahan yang dapat dituangkan dalam bentuk bilangan (kuantitatif),
contoh : kesalahan pengukuran panjang dengan mistas 1 mm, jangka sorong, 0,1 mm dan mikrometer skrup 0,01 mm

3. Kesalahan acak

Merupakan kesalahan yang dapat dituangkan dalam bentuk bialangan (kualitatif),
Contoh :
a. Kesalahan pengamat dalam membaca hasil pengukuran panjang
b. Pengabaian pengaruh gesekan udara pada percobaan ayunan sederhana
c. Pengabaian massa tali dan gesekan antar tali dengan katrol pada percobaan hukum II Newton.

Ketika mengukur suatu besaran fisis dengan menggunakan instrumen, tidaklah mungkin akan mendapatkan nilai benar X0, melainkan selalu terdapat ketidakpastian.

Ketidakpastian ini disebabkan oleh beberapa hal misalnya batas ketelitian dari masing-masing alat dan kemampuan dalam membawa hasil yang ditunjukkan alat ukur.

Beberapa istilah dalam pengukuran:

1. Ketelitian (accuracy) adalah suatu ukuran yang menyatakan tingkat pendekatan dari nilai yang diukur terhadap nilai benar X0

2. Kepekaan adalah ukuran minimal yang masih dapat dideteksi (dikenal) oleh instrumen, misal galvanometer memiliki kepekaan yang lebih besar daripada Amperemeter / Voltmeter

3. Ketepatan (precision) adalah suatu ukuran kemampuan untuk mendapatkan hasil pengukuran yang sama.

4. Presisi berkaitan dengan perlakuan dalam proses pengukuran, penyimpangan hasil ukuran dan jumlah angka desimal yang dicantumkan dalam hasil pengukuran.

5. Akurasi yaitu seberapa dekat hasil suatu pengukuran dengan nilai yang sesungguhnya. Ketelitian alat ukur panjang

Ucapan Terima Kasih Kepada Para Guru dan Kawan-Kawan di SMAN 1 Banjar

## Thursday, 18 August 2005

### Bissmilahirrohmanirrohim

Assalamualaikum. warohamtullohi wabarokatuh

Nama saya: Arip Nurahman
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