Scalar and vector quantities

Situation:

Fauziah travelled from Kuala Lumpur to Kangar, a distance of 507 km. After that, she continued her journey to Butterworth, a distance of 138 km. From Butterworth, Fauziah then travelled back to Kuala Lumpur, a distance of 369 km. What is the total distance travelled by Fauziah? What is the final displacement of Fauziah?

1. Distance (scalar quantity) refers to how far an object has traveled regardless of direction.
2. Displacement (vector quantity) refers to how far an object is from where it started. 

Solution:
Total distance traveled = 507 + 138 + 369 = 1 014 km
Final displacement = 0 km (Fauziah back to Kuala Lumpur)

1. A scalar quantity is a quantity that has magnitude, but no direction. 

Examples: distance, time, mass, volume, and speed  

2. A vector quantity is a quantity that has both magnitude and direction. 

Example: Displacement, velocity, acceleration, and force.

Base and derived quantities

 Normal body temperature of a healthy human being is 37 degree Celsius.

A physical quantity is a quantity that can be measured (eg: temperature, time, length, mass, area and speed). Physical quantities can be divided into two types:

1. Base quantities - The base unit of a measurement is not defined in terms of other units but has its own standard definition in the International System of Units (SI) (widely accepted by most countries):

a. SI unit of length: metre ( m) - The metre is the distance traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.

b. SI units of mass: kilogram (kg) - The kilogram is the mass of the international prototype kilogram in the custody of the Bureau International des Poids et Mesures at Sèvres in France.

c. SI unit of time: second (s)- The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

d. SI unit of electric current: ampere (A)- The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross section, and placed 1 metre apart in a vacuum, would produce be tween these conductors a force equal to 2 x 10-7 newton per metre of length.

e. SI unit of temperature: kelvin (K)- The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

2. Derived quantities - Physical quantities that are derived from the base quantities by multiplication or division.

Conversion of units

Conversion of units refers to conversion factors between different units of measurement for the same quantity. The process of conversion depends on the specific situation and the intended purpose.

It happened the same when you want to convert your RM (Malaysian ringgit) to Rupiah (Indonesian rupiah). RM1 is equal to 2813 Rupiah and RM355 is equal to 1 million Rupiah! Wow, it is easy to be a millionaire in Indonesia;p

There are three categories of conversion of units are as the example below:

Example:

Category 1

a. Convert 1 kg to unit gram

1 kilogram = 1000 grams

b. Convert 1 milligram to unit gram

1 milligram = 0.001 grams

c. Convert 30 ms to unit second

30 ms = 30 x 10^-3 s

         = 3.0 x 10^-2 s

d. Convert 84 km to unit metre

84 km = 84 x 10³ m

         = 8.4 x 10⁴ m

Category 2

a. Convert 5 cm² to unit m² 

5 cm² = 5 cm x 1 cm

         = (5 x 10^-2) m x (1 x 10^-2)m

         = 5 x 10^-4 m² 

b. Convert 100 mm³ to unit m³ 

100 mm³ = 100 mm x 1 mm x 1mm

             = (100 x 10^-3) m x (1 x 10^-3) m x (1 x 10^-3) m

             = 1.0 x 10^-7 m³  

Category 3

a. Convert 1000 kg m^-3 to unit g cm^-3 

1000 kg m^-3 = (1000 x 10³)g / (1 x 10⁶cm³)

                      = 1 g cm^-3  

 b. Convert 108 km j^-1 to unit ms^-1

108 km j^-1  = (108 x 10³ )m / (60 x 60) s

                = 3.0 x 10 ms^-1  

 

Online unit converter click here

Prefixes

Prefixes for units are used to represent very small and very large values.

Example:

a. 2 Tm = 2 x 10¹² m

b. 20 Tm = 2 x 10¹³ m

c. 1 Mm = 1 x 10⁶ m

d. 1 nm = 1 x 10^-9 m 

e. 10 nm = 1 x 10^-8 m 

Please note that a thousand kilogram is not a kilokilogram!!

1000 kilogram ≠ 1 kilokilogram
1000 kilogram = 1 megagram

Scientific notation

Scientists have a need to express very large (or very small numbers) in some convenient way. For example, light travels at a speed of 300000000 m/s (three hundred million metres per second),

1 second                    300000000m

1 minute (60s)            18000000000m

1 hour (60min)           1108000000000m

1 day (24h)                25920000000000m

1 year (365 days)        9460800000000000m

9460800000000000m?????? That’s a huge number to write or read!!! And very inconvenient too. 

Therefore, scientific notation is a method to write very large (or small) numbers so they are more neat, simple and easy to read.

General form is,

A x 10ⁿ,                    where    A is integer (1≤ A < 10)

                                                   N (positive or negative integer)

So,

9460800000000000m = 9.4608 x 10¹⁵m

Example,

a. 38700000 m can be written as 3.87 x 10⁷ m

b. 76800 second can be written as 7.68 x 10⁴ second
c. 0.0012 m can be written as 1.2 x 10^-3 m

Introduction to Physics

Ok, now try to look around and outside the window. What can you see?? ....Don't tell me you can't see anything unless you are blind;p

Actually almost everything around you relate to Physics. This is rather a simple explanation for you. When you look at a big tree, you may see leaves fall down. Don't you ever think why the leaves don't fly up??? Why the larger leaves fall first or is it larger leaves will fall first??

In science, we can find the answer by carried out an experiment to verify the answer we seek. It can be done by making observation and careful measurement to gather necessary data. You can't simply jump into a conclusion before you run an experiment. This is how Physics students learn Physics, it is not the same as you learn History. History and Physics are like oil and water.Isn't it??;)

When we talk about taking measurement, we actually talking about things that can be quantified and give it a numerical value(numbers). Don't blame me why you have to face with numbers every time you tried to solve Physics problems. Physics and Maths are like husband and wife, and their children is Add Math;p

This is how it looks like when Add Math growing up. Gorgeous!!

Ok, here are some steps and terminology you need to understand before you run an experiment:

Steps of the Scientific Method

1.      Observation/Research:

 Make observations and gathering all available information about the object or phenomena to be studied. Observations are made using the sense of sight, hearing, touch, taste, and smell.

2.      Identifying a suitable question:

After all the information has been gathered, a suitable question is suggested for a scientific investigation.

3.      Identifying and controlling variable:

• Variables are factors or physical quantities which change in the course of a scientific investigation.

• Identifying the manipulated variables, responding variable, and fixed (or constant) variables.

• Manipulated variable are physical quantities which you control and change (manipulate) for the purpose of investigating the result of an experiment.

• Responding variables are physical quantities which are the result of the changes made to the manipulated variable.

• Fixed or constant variable are physical quantities which are kept constant throughout the experiment.

4.      Formulate a Hypothesis:

The hypothesis is an educated guess about the relationship between the independent and dependent variables.

Predict a possible answer to the problem or question.

Example:

If soil temperatures rise, then plant growth will increase.

The longer is the pendulum the longer is the period of its oscillation.

“If more sugar is added, then the bread will rise higher.”

5.      Experiment:

Develop and follow a procedure. Include a detailed materials list.  

The outcome must be measurable (quantifiable).

6.      Collect and Analyze Results:

Modify the procedure if needed. Confirm the results by retesting. Include tables, graphs, and photographs.

7.      Conclusion:

Include a statement that accepts or rejects the hypothesis. Make recommendations for further study and possible improvements to the procedure.