PROJECTILE'S TRAJECTORY

Characteristics of a Projectile'sTrajectory

The force acting is only gravity.

Two components of the projectile's motion - horizontal and vertical motion.

Horizontally Launched Projectiles
Consider a cannonball projected horizontally by a cannon from the top of a very high cliff

In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. This is consistent with the law of inertia.

If merely dropped from rest in the presence of gravity, the cannonball would accelerate downward, gaining speed at a rate of 9.8 m/s every second. This is consistent with our conception of free-falling objects accelerating at a rate known as the acceleration of gravity.

 

Cannonball is projected horizontally in the presence of gravity, it would maintain the same horizontal motion as before - a constant horizontal velocity.

The force of gravity will act upon the cannonball to cause the same vertical motion as before - a downward acceleration. The cannonball falls the same amount of distance as it did when it was merely dropped from rest

 

Forces	Horizontal Motion No	Vertical  Motion Yes The force of gravity acts downward
Acceleration	No	Yes "g" is downward at 9.8 m/s/s
Velocity	Constant	Changing (by 9.8 m/s each second)

 

Non-Horizontally Launched Projectiles

 

PROJECTILE

Projectile
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 such as
i. an object dropped from rest
ii. an object that is thrown vertically upward
iii. an object which is thrown upward at an angle to the horizontal.

Projectile would show a single force acting downwards and labeled force of gravity (or simply F_grav).

 

Projectile Motion and Inertia

 

 

 

PERHIMPUNAN HARAM....TINGGALKANLAH YANG BURUK

Presiden Pertubuhan Muafakat Sejahtera Masyarakat Malaysia (Muafakat), Ismail Mina Ahmad menegaskan 

"umat Islam perlu mengelak daripada menyertai perhimpunan yang jelas bertentangan dengan hukum syarak kerana cuma mahu menunaikan impian seseorang melalui rusuhan jalanan......"

Pengerusi Sekretariat Ilmuwan Malaysia (Ilmu), Prof. Madya. Dr. Fadlan Mohd. Othman berkata, 

"...selain solat hajat umat Islam juga digalakkan berdoa supaya Allah menggagalkan segala perancangan jahat untuk menimbulkan keadaan huru-hara melalui perhimpunan haram itu. Pegangan Ahli Sunnah Wal Jamaah sendiri mewajibkan umat Islam untuk menyokong serta patuh kepada pemerintah Islam sedia ada. Kalau pemerintah tidak baik sekalipun, dalam Islam ada etika atau adab yang digariskan oleh Nabi Muhammad SAW sendiri iaitu dengan menasihati bukannya dengan berdemonstrasi. Saya menyeru kepada semua umat Islam tidak menyertai perhimpunan tersebut dan sebaliknya bersama-sama kita mendoakan supaya kesejahteraan serta keamanan dinikmati sekarang tidak tergugat...".

Ikutlah nasihat yang baik, tinggalkanlah perbuatan yang merosakkan diri.

KINEMATICS OF LINEAR MOTION

1. Mechanics
-is the study of the motion of objects.

2. Kinematics
-is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations without regard for the cause.

3. Scalars
-are quantities that are fully described by a magnitude (or numerical value) alone.
-example : distance, speed

4.Vectors
- are quantities that are fully described by both a magnitude and a direction.
-example : displacement, velocity, acceleration

5. Distance
-refers to "how much ground an object has covered" during its motion.
-It is length of path.

6. Displacement
- refers to "how far out of place an object is"; it is the object's overall change in position.
-It is difference between starting and finishing positions with the direction of its motion.

7. Speed 

-refers to "how fast an object is moving".
-The average speed is the rate of change of distance traveled with time.
-Average speed is also the average of all instantaneous speeds; found simply by a distance/time ratio.

  

-Instantaneous speed is the speed at any given instant in time.
-The instantaneous speed is equal to the magnitude of the instantaneous velocity.

8. Velocity

-refers to "the rate at which an object changes its position."
-The average velocity is the rate of change of displacement with time.

  

-The instantaneous velocity is equal to the magnitude of the instantaneous speed.

9. Acceleration

- defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.

-An object travelled with constant acceleration if the velocity is changing by a constant amount each second.

-Accelerating objects are constantly changing their velocity, we can say that the distance traveled / time is not a constant value.

 Example :  A boy walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. He took 12 seconds.

The difference between distance and displacement: 

He has walked a total distance of 12 meters ("covered 12 meters of ground")

There is no displacement for his motion (displacement = 0 m). When finished walking, he is not "out of place"

The difference between speed and velocity
His average speed is distance / time =  12 / 12 =  1.5  m/s.
His average velocity is displacement / time = 0 / 12 = 0 m/s .

VELOCITY VS TIME GRAPHS

Describing Motion with Velocity vs. Time Graphs                                                       

-The slope of the line on a velocity-time graph reveals useful information about the acceleration of the object.

-If the acceleration is zero, the slope is zero (i.e., a horizontal line).

-If the acceleration is positive, the slope is positive (i.e., an upward sloping line). 

-If the acceleration is negative, the slope is negative (i.e., a downward sloping line).

                       Positive Velocity                                                  Positive Velocity 

                       ZeroAcceleration                                                 Positive Acceleration

  

                                                    

 

 

POSITION VS. TIME GRAPHS

Describing Motion with Position vs. Time Graphs 

-Motion of objects in 1-dimensional kinematics can be represented by words, diagrams, numbers, equations and  graphs.

-The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph.

-The slope of the line reveals useful information about the velocity of the object.

-As the slope goes, so goes the velocity. 

-If the velocity is constant, then the slope is constant (i.e., a straight line). 

-If the velocity is changing, then the slope is changing (i.e. a curved line). 

-If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right).    

-Consider a car moving with a rightward (+). The position vs. time graphs for constant velocity and changing velocity (acceleration) - are depicted as follows.

       Constant Velocity                                            Positive Velocity                                                   
           Positive Velocity                                             Changing Velocity (acceleration)

                                          

 

            Slow, Rightward(+)                                          Fast, Rightward(+)
            Constant Velocity                                            Constant Velocity

                            

 

       Slow, Leftward(-)                                             Fast, Leftward(-)
          Constant Velocity                                            Constant Velocity

                                

 

      Leftward (-) Velocity                                           Leftward (-) Velocity                                       
         Slow to Fast (accelerate)                                    Fast to Slow (decelerate)

                                    

ITULAH SEBABNYA.....

Hari ini saya terbaca kisah ini dan kongsikan di sini

"Wanita Diragut Secara Terang-Terangan

SEORANG wanita di China hanya mampu terbaring dan terduduk ketika dirinya diragut oleh dua orang lelaki di sebuah perhentian bas.Ternyata, kedua-dua peragut itu berani melakukan tindakan terkutuk itu secara terang-terangan di hadapan orang ramai yang lalu lalang di kawasan awam tersebut. 

Kejadian itu telah berjaya dirakam melalui kamera litar tertutup (CCTV) yang dipasang di kawasan berhampiran. Melalui video itu juga menunjukkan orang awam yang berada di tempat kejadian pun seakan tidak menghiraukan insiden yang berlaku atau pun mereka enggan masuk campur kerana dikhuatiri diri mereka akan diapa-apakan oleh peragut tersebut...."

Sifat-sifat seperti inilah menyebabkan pihak berkuasanya membuat peraturan dan hukuman yang berat kepada penjenayah negaranya. Kalau orang di sini pun ikut perangai begitu, pihak berkuasa di sini perlulah lebih tegas dan berbuat seperti pihak berkuasa di sana.

ERROR IN EXPERIMENTS

Random Errors

-caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions.

-statistical methods may be used to analyze the data. 

-the mean m of a number of measurements of the same quantity is the best estimate of that quantity

-the standard deviation s of the measurements shows the accuracy of the estimate.

-The precision of a measurementis (which is limited by the random errors) is how close a number of measurements of the same quantity agree with each other and can be determined by repeating the measurements.

 

The Gaussian normal distribution. 

m = mean of measurements, s = standard deviation of measurements. 

68% of the measurements lie in the interval m - s < x < m + s; 

95% lie within m - 2s < x < m + 2s;  

99.7% lie within m - 3s < x < m + 3s.

 Examples of random errors are: 

1.electronic noise in the circuit of an electrical instrument

2.irregular changes in the heat loss rate from a solar collector due to changes in the wind.

Systematic Errors

-come from the measuring instruments cause by : 

1.something wrong with the instrument or its data handling system

Systematic Errors that occur with instruments having a linear response: 

i.Offset or zero setting error in which the instrument does not read zero when the quantity to be measured is zero. 

ii.Multiplier or scale factor error in which the instrument consistently reads changes in the quantity to be measured greater or less than the actual changes.

 

Systematic errors in a linear instrument (full line).
Broken line shows response of an ideal instrument without error.

Systematic errors also occur with non-linear instruments when the calobration of the instrument is not known correctly.

2.the instrument is wrongly used by the experimenter
i.errors in measurements of temperature due to poor thermal contact between the thermometer and the substance whose temperature is to be found

ii.errors in measurements of solar radiation because trees or buildings shade the radiometer.

The accuracy of a measurement (which can be reduced by systematic errors) is how close the measurement is to the true value of the quantity being measured. 

Systematic errors are difficult to detect even for experienced research workers.

MATH SKILLS IN PHYSICS

Significant Figures
Two kinds of numbers
i. exact numbers: example: There are exactly 20 apples in a box
                                              Most cats have exactly 2 ears and 4 legs. 

ii.inexact numbers: example: any measurement
the width of a piece of  paper, 220 mm     (2 significant figures). 
                        more precise, 216 mm       (3 significant figures). 
                        more precise, 215.6 mm    (4 significant figures). 

PRECISION VERSUS ACCURACY

Accuracy refers to how closely a measured value agrees with the correct value.
Precision refers to how closely individual measurements agree with each other.

The number of significant figures is the number of digits believed to be correct by the person doing the measuring. It includes one estimated digit.  

Rules for Working with Significant Figures:

1. Leading zeros are never significant.
   Imbedded zeros are always significant.
   Trailing zeros are significant only if the decimal point is specified.
   Hint: Change the number to scientific notation. It is easier to see.
2. Addition or Subtraction:
   The last digit retained is set by the first doubtful digit.
3. Multiplication or Division:
   The answer contains no more significant figures than the least accurately known number.

Examples:

Going from left to right, the first non-zero digit is the first significant figure.

Each digit to its right is a significant figure.

To write a number x to n significant figures means to write down the number with n significant figures which is closest to x.

For example,  consider 0.000026857
To 1 significant figure it is 0.00003

To 2 significant figures it is 0.000027

To 3 significant figures it is 0.0000279
To 4 significant figures it is 0.00002686

Consider  4.198.

To 1 significant figure it is 4

To 2 significant figures it is 4.2

To 3 significant figures it is 4.20
(we write 4.20 instead of 4.2 to show that we have 3 significant figures).

To 4 significant figures it is 4.198

Consider 58 651

To 1 significant figure it is 60 000

To 2 significant figure it is 59 000

To 3 significant figure it is 58 700

To 4 significant figure it is 58 650

To 5 significant figure it is 58 651

Attentively, significant figures for whole numbers can be done using scientific notation.

Consider the number 70 000.

To 1 significant figure it is 7 x 10⁴

To 2 significant figures it is 7.0 x 10⁴

To 3 significant figures it is 7.00 x 10⁴

To 4 significant figures it is 7.000 x 10⁴

Example	Number of Significant Figures	Scientific Notation
0.00682	3	6.82 x 10-3
1.072	4	1.072 (x 100)
300	1	3 x 102
300.	3	3.00 x 102
300.0	4	3.000 x 102

 ^{Addition :  4.7832} 

                   ^1.234 

                ^{+ 2.02}

                   ^{8.0372  > Rounding  8.04}

 ^{> The answer must be rounded off to 3 significant figures, since 2.02 only has 3 significant figures.}

^{Subtraction : 1.0236}

                   ^{- 0.97268} 

                     ^{0.05092 > Rounding 0.0509}

>Subtraction is interesting when concerned with significant figures. Even though both numbers involved in the subtraction have 5 significant figures, the answer only has 3 significant figures when rounded correctly. Remember, the answer must only have 1 doubtful digit

Multiplication : 2.8723 x 1.6 = 4.59568 > Rounding 4.6

Division :  45.2   = 7.1093775 > Rounding 7.11

                                 ^{6. 3578}

Notes on Rounding

• When rounding off numbers to a certain number of significant figures, do so to the nearest value. 
• example: Round to 3 significant figures: 2.3467 x 10⁴ 
• (Answer: 2.35 x 10⁴)
• example: Round to 2 significant figures: 1.612 x 10³ 
•  (Answer: 1.6 x 10³)
• What happens if there is a 5? There is an arbitrary rule:
• If the number before the 5 is odd, round up.
• If the number before the 5 is even, let it be.
  The justification for this is that in the course of a series of many calculations, any rounding errors will be averaged out.
• example: Round to 2 significant figures: 2.35 x 10² 
• (Answer: 2.4 x 10²)
• example: Round to 2 significant figures: 2.45 x 10² 
• (Answer: 2.4 x 10²)
• Of course, if we round to 2 significant figures: 2.451 x 10², the answer is definitely 2.5 x 10² since 2.451 x 10² is closer to 2.5 x 10² than 2.4 x 10².

PHENOMENON OF TOTAL INTERNAL FERLECTION

Condition for total internal reflection
1.Light travel from a denser to rarer medium
2.i > C in denser medium for a pair of media in contact

Explaination
Suppose that a laser beam is submerged in a tank of water and pointed upwards towards water-air boundary.

 

The maximum possible angle of refraction is 90-degrees. If the angle of refraction were greater than 90 degrees, then the refracted ray would lie on the incident side of the medium. There is some specific value for the angle of incidence (the critical angle) that yields an angle of refraction of 90-degrees.Any angle of incidence that is greater than the critical angle would not result in refraction. All of the energy (the total energy) carried by the incident wave to the boundary stays within the water and undergoes reflection off the boundary. When this happens, total internal reflection occurs.

Application : Mirage

A traveler has lost his way in the desert. Enduring thirst and hunger, he suddenly saw an oasis, so the overjoyed man quickly ran towards it. To his great disappointment, it was just an illusion produced by a mirage. Its formation is a result of the refraction and the total internal reflection of light in the air. 

The Formation of Mirage

 In regions of air with temperature decreases with altitude, light will travel in a curved path due to refraction.

Refraction occurs when a light beam travels from glass to the air. The angle of incidence i is smaller than the angle of refraction r.

Total internal reflection occurs when the incident angle i is larger than the critical angle c.

The path of light when a mirage happens. 

 

PERKONGSIAN MUHASABAH DIRI

Tentang larangan buruk sangka
Saya ingin berkongsi mengenainya yang dipetik dari http://addienblog.blogspot.com/2012/03/larangan-buruk-sangka-dan-mencari-cari.html

Di antara larangannya ialah
1. Allah Ta’ala berfirman.

يَا أَيُّهَا الَّذِينَ آمَنُوا اجْتَنِبُوا كَثِيرًا مِّنَ الظَّنِّ إِنَّ بَعْضَ الظَّنِّ إِثْمٌ ۖ وَلَا تَجَسَّسُوا

“Hai orang-orang yang beriman, jauhilah kebanyakan berprasangka, karena sesungguhnya sebagian tindakan berprasangka adalah dosa dan janganlah kamu mencari-cari kesalahan orang lain” (Al-Hujurat : 12)

2. Rasulullah Shallallahu ‘alaihi wa sallam bersabda.

إِيَّا كُمْ وَالظَّنَّ فَإِنَّ الظَّنَّ أَكْذَبُ الْحَدِيْثِ وَلاَ تَحَسَّسُوا وَلاَ تَجَسَّسُوا وَلاَ تَحَاسَدُوا وَلاَتَدَابَرُوا وَلاَتَبَاغَضُوا وَكُوْنُواعِبَادَاللَّهِ إحْوَانًا

“Berhati-hatilah kalian dari tindakan berprasangka buruk, kerana prasangka buruk adalah sedusta-dusta ucapan. Janganlah kalian saling mencari keburukan orang lain, saling inti-mengintip, saling mendengki, saling membelakangi, dan saling membenci. Jadilah kalian hamba-hamba Allah yang bersaudara” (Riwayat  Al-Bukhari no. 6064 dan Muslim no. 2563 )

3.Ibnu Kathir menyebutkan perkataan Umar di atas ketika menafsirkan sebuah ayat dalam surah Al-Hujurat.Bakar bin Abdullah Al-Muzani yang berkata :  

“Hati-hatilah kalian terhadap perkataan yang sekalipun benar kalian tidak diberi pahala, namun apabila kalian salah kalian berdosa. Perkataan tersebut adalah berprasangka buruk terhadap saudaramu”.  (Tahdzib At-Tahdzib) 

4.Disebutkan bahwa Abu Qilabah Abdullah bin Yazid Al-Jurmi berkata : 

 “Apabila ada berita tentang tindakan saudaramu yang tidak kamu sukai, maka berusaha keraslah mancarikan alasan untuknya. Apabila kamu tidak mendapatkan alasan untuknya, maka katakanlah kepada dirimu sendiri, “Saya kira saudaraku itu mempunyai alasan yang tepat sehingga melakukan perbuatan tersebut”.  [kitab Al-Hilyah karya Abu Nu’aim (II/285) ] 

5.Abu Hatim bin Hibban Al-Busti bekata:

Orang yang berakal wajib mencari keselamatan untuk dirinya dengan meninggalkan perbuatan tajassus dan senantiasa sibuk memikirkan keburukan dirinya sendiri. Sesungguhnya orang yang sibuk memikirkan keburukan dirinya sendiri dan melupakan keburukan orang lain, maka hatinya akan tenteram dan tidak akan merasa gelisah. Setiap kali dia melihat keburukan yang ada pada dirinya, maka dia akan merasa hina tatkala melihat keburukan yang serupa ada pada saudaranya. Sementara orang yang senantiasa sibuk memperhatikan keburukan orang lain dan melupakan keburukannya sendiri, maka hatinya akan buta, badannya akan merasa letih dan akan sulit baginya meninggalkan keburukan dirinya”.[Raudhah Al-‘Uqala (hal.131)]

Beliau juga berkata,:

“Tajassus adalah cabang dari kemunafikan, sebagaimana sebaliknya prasangka yang baik merupakan cabang dari keimanan. Orang yang berakal akan berprasangka baik kepada saudaranya, dan tidak mau membuatnya sedih dan berduka. Sedangkan orang yang bodoh akan selalu berprasangka buruk kepada saudaranya dan tidak segan-segan berbuat jahat dan membuatnya menderita”.[Raudhah Al-‘Uqala (hal.133)]