Nota Fizik: Understanding Derived and Base QuantitiesUnderstanding Derived and Base Quantities

Physical quantities are quantities that can be measured. e.g. Length, Temperature, Speed, Time.

Quantities or qualities that cannot be measured are not physical quantities. e.g. happiness, sadness etc.

Physical quantities can be divided into Base quantitied and Derived quantities.

(i) Physical quantities are quantities that can be measured or can be calculated.(ii) The base quantities are “building block” quantities from which other quantities are derived from.(iii) The base quantities and their S.I. units are:

Base quantities S.I. units Mass kg Length m Time s Electric current A Thermodynamic temperature K

(iii) Derived quantities are quantities derived (iv) Examples of derived quantities.

Derived quantities S.I. units area m2 density kg m-3 weight N velocity m s-1

Standard Notation: To express very large or very small numbers.Example; A X 10 n (ten to the power of n), n must be an integer and 1 ≤ A <10

Nota Fizik: Understanding Scalar and Vector QuantitiesScalar quantities: Quantities that have magnitude only. ( Speed, mass, distance)

Example:

For example speed has unit of ms^-1. but it has no direction.

Mass is kg but we don't know the direction.

Distance is 2km but no direction.

Vector quantities: Quantities that have magnitude and direction. (Velocity, Weight, Displacement)

Example:

Velocity unit is ms^-1 but we must state the direction that is whether from right to left.

Weight unit is Kg but the direction is towards the gravity pull of the earth.

Displacement is 2km but to the north from the point of reference.Posted by O'Deen at 8:47 AM 

Experimental ErrorsWhen doing experiments there are several errors that we need to consider. For example the error when taking reading from instruments and also the influence from the outer surroundings. This is true for all scientific investigations. Even machines have errors! and they do need to be calibrated consistently!

Error is the difference between the measured value and the real or actual value. (The difference in reading is known as the error)

Two main types of error are systematic error and random error.

Systematic error occurs when there is an error when reading the scale that is being used. It is caused by the surroundings, the instrument itself (scale may not be uniform or even blurred due to wear and tear) and of course the observer error.

Systematic error results in the measurement or reading being consistently over the actual value OR consistently smaller than the actual value.

There are several possible causes of systematic error:

One of the most common error is the Zero Error. Zero Error is caused if the reading shown is Not zero when the true value is actually zero. This is most probably caused by a flaw in the instrument for example when using a ruler that has lost its zero scale due to wear and tear hence causing an error in the measurement of length.

Wrong assumptions may also cause error, for example if you assume that water boils at 100 degree celcius but actually its boiling point is higher if there are impurities in it. (Pure water boils at 100 degree celcius)

There is also a possibility to create error when there is a lag of reaction time. For example in a sports day, when measuring a 100 m running time using a stopwatch. The observer may not press the stop button exactly when the foot of the runner touches the finishing line.

Sometimes, as I have mentioned, instruments that are not properly calibrated could also cause error and this has to be put in consideration when writing a report or when there is an anomaly in reading.

Another type of error that needs to be considered is Random Error.

Random error is caused by the observer who reads the measuring instrument. Just like the systematic error, there can exist positive or negative error. Positive error is when the reading is bigger than the real value and negative error is when the reading is smaller than the real value.

One of the ways to reduce random error is to take several readings for a measurement and then taking the average reading to be analysed.

There are several examples of random error.

Miscounting numbers during observation or change in the surrounding due to temperature, wind, light, exposure to chemicals or impurities may cause error. Sometimes the observer may read the scale wrongly (as in the case of reading a scale in on a beaker or ruler (parallax error). Parallax error occurs when a reading is taken from an unsuitable position relative to the scale.

Ways to reduce error

Magnifying glass to enhance the visual of scale on the instrument.Avoiding parallax error by positioning the instrument (meter rule) properly on the table with the eyes perpendicular to the scale. This also applies when reading other instruments. Parallax error can also be reduced by putting a strip of mirror next to the scale (for example in ammeter), the eye must be positioned so that the image formed on the mirror is fully covered by the indicator hand of the ammeter.

Some instruments can be adjusted to eliminate zero error. For example when using an ammeter, there is an adjuster to set the indicator to zero before making any measurement.

In the case of a ruler, measurement can be carried out starting from the next clear scale for example if scale 0.0cm is blurred, we can start measuring the length from 2.0cm, of course taking the difference of value in consideration when recording the final reading.

Nota Fizik: Understanding MeasurementsIn Physics and any scientific investigations. Measurement of quantities is very crucial. It is in fact the core of data generation. Measurements can be done by various methods and various instruments. Here, only a few examples are explained.

A micro balance is used to measure minute masses. It is sensitive but not very accurate.

Slide callipers are usually used to measure the internal or external diameter of an object.

A micrometre screw gauge is used to measure the diameter of a wire of the thickness of a thin object.

All measurement must consider this:

Accuracy: Ability of the instrument to measure the true value or close to the true value. The smaller the percentage error, the more accurate the instrument is.

Sensitivity of an instrument is the ability of the instrument to detect any small change in a measurement.

Consistency: ability of the instrument to produce consistent measurement.(the values are near to each other). The lower the relative deviation, the more consistent the measurement is.

Ways to increase accuracy:- repeat the measurements and get the mean value.- correcting for zero error.- avoiding parallax error.- use magnifying glass to aid in reading.

For example, when asked about how to increase the sensitivity of a mercury thermometer:-use a bulb with thinner wall.-use a capillary tube of smaller diameter or bore.

Nota Fizik: Analysing scientific investigationSo you are here probably because you want to get a deeper meaning an concept of scientific investigation.

You should have probably been familiar with the steps involved in scientific investigation i.e. Identifying problem, making hypothesis, generating data etc...

However, what I would like to emphasis in this post is the different types of variable.

You should know that "A variable is a quantity that varies in value". It represents "something" that are involved in a measurement in scientific investigation. Thus, a proper scientific investigation always involve variables and its measurement. A quantity that can be measured is called a physical quantity.

Three types of variables are:

Manipulated variable is a variable that is set or fixed before and experiment is carried out. it is usually plotted on x- axis.

Responding variable is a variable that changes according to and dependent to manipulated variable. it is usually plotted on y-axis.

Fixed variable is fixed and unchanged throughout the experiment.

Now lets see how to make inference and hypothesis?

How to make inference and hypothesis?

Inference: state the relationship between two VISIBLE QUANTITIES in a diagram or picture.

Hypothesis: state the relation ship between two MEASURABLE VARIABLES that can be investigated in a lab.

How to tabulate data?

-the name or the symbols of the variables must be labelled with respective units.-all measurements must be consistent with the sensitivity of the instruments used.-all the calculated values must be correct.-all the values must be consistent to the same number of decimal places.

A graph is considered well-plotted if it contains the following:

- a title to show the two variables and investigation.- two axes labelled with correct variables and units- scales must be chosen carefully and graph must occupy more than 50% of the graph paper.- all the points are correctly drawn.- the best line is drawn.

Linear Motion Calculation ExamplesA bicycle moved from point A and then moved 50 m to the north in 60 seconds. The bicycle then moved 120 m to the east in 40 seconds. Finally, it stopped. Calculate the

1. Total distance moved by the bicycle2. Displacement3. Velocity4. Average speed5. Speed of the bicycle when it is moving to the north

Solution:

1. Total distance = 50m + 170m                          = 170m

2. Displacement

Remember displacement is the shortest distance between two points.

Imagine A as the beginning of a triangle.  Then connect it with a line of 50m upwards then it turns left 120m (go east). so the distance is the hypotenuse.

Using Pythagoras' theorem = Squared root (120^2 + 50^2)                                         = 130m

3. Velocity = Displacement / time

= 130 m / 100 s= 1.3 m s^-1

4. Average speed of the bicycle = total distance / total time

= 170m/ 100s= 1.7 m s^-1

5. Speed = distance / time

Distance = 50m, time = 60s

= 50m / 60s

= 0.83 ms^-1

Be careful during calculation as most of the time Physics requires a good skill in maths!!

Distance, Displacement, Velocity, Speed and AccelerationDistance and Displacement

Distance is the total path length traveled from one location to another. It is a scalar quantity.

Displacement is the distance between two locations measured along the shortest path connecting them, in specified location. It is a vector quantity. The SI unit of distance and displacement is metre (m).

Speed and Velocity

Speed is the distance traveled per unit time or the rate of change of distance.

Speed = total distance traveled / time taken

Velocity is the speed in a given direction or the rate of change of displacement.

Average velocity = displacement/ time taken

Acceleration and Deceleration

Acceleration is the rate of change of velocity.

Acceleration = change of velocity / time taken

Change of velocity = final velocity (v) – initial velocity (u)

Acceleration = (final velocity – initial velocity) / time taken  = (v – u) / t

Things to remember:

1. Constant velocity means the object is not accelerating. Acceleration is zero.2. Constant acceleration means the object is increasing its velocity.

Label of the Parts

(This image is licienced under GDFL. The source file can be obtained from wikipedia.org)

Range and AccuracyThe range of a micrometer is 0-25mm.The accuracy of a micrometer is up to 0.01mm.

How to Use a Micrometer?

1. Turn the thimble until the object is gripped gently between the anvil and spindle.

2. Turn the ratchet knob until a "click" sound is heard. This is to prevent exerting too much pressure on the object measured.

3. Take the reading.

Derived Quantities

A derived quantity is a Physics quantity that is not a base quantity. It is the quantities which derived from the base quantities through multiplying and/or dividing them.Example

(Speed is derived from dividing distance by time.)

Derived UnitThe derived unit is a combination of base units through multiplying and/or dividing them.

Example 1Find the derived unit of density.Answer

Unit ConversionArea and Volume

Example 2Convert the unit of length, area and volume below to the units given.a) 7.2 m = ____________cmb) 0.32 m2 = ____________cm2c) 0.0012 m3 = ____________cm3d) 5.6 cm =

____________me) 350 cm2 = ____________m2f) 45000 cm3 = ____________m3Answer

a) 7.2 m = 7.2 x 102 cm

b) 0.32 m2 = 0.32 x 104 cm2 = 3.2 x 103 cm2

c) 0.0012 m3 = 0.0012 x 106 cm3 = 1.2 x 103 cm3

d) 5.6 cm = 5.6 x 10-2 me) 350 cm2 = 350 x 10-4 m2 = 3.5 x 10-2 m2

f) 45000 cm3 = 45000 x 10-6 m3 = 4.5 x 10-2 m3

SpeedExample 3Complete the following unit conversion a) 12 kmh-1 = __________ ms-1 b) 12 ms-1 = __________ kmh-1

Answer

a)

12kmh−1=12km1h=12000m60×60s=3.33ms−1

b)

12ms−1=12m1s=121000km13600h=43.2kmh−1