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Introduction to Physics
Scientific Notation
Why do we use scientific notation?
Scientific notation was developed to easily represent numbers that are either very large or very small
The mass of Earth is approximately
\[5972000000000000000000000\;\; kg \]
The mass of Earth can be written as
\[5.972 ×1000000000000000000000000 \]
The number 1000000000000000000000000 is problematic as it's a multiple of ten
10 ×10×10×10×10×10×10×10 ×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10
Written in scientific notation:
\[10=10^1 / 10×10=10^2 / 10×10×10×10 = 10^4 .......\]
So the problematic number in scientific notation is:
\[10 ×10×10×10×10×10×10×10 ×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10 =10^{24}\]
\[5.972× 10^{24}\]
On the other hand, the charge of an electron is
\[0.00000000000000000016\;\; C\]
The electron charge can be written as:
\[ 1.6 ÷10000000000000000000 \]
\[\frac{1}{10}=10^{-1}/ \frac{1}{100}=10^{-2}/\frac{1}{100000}=10^{-5}/.....\]
So the problematic number in scientific notation is:
\[\frac{1}{10000000000000000000}=10^{-19}\]
Thus, the electron charge in scientific notation is:
\[q=1.6 × 10^{-19}C\]
Test Yourself
Attempt Number
Physical Quantity Value
Write in Scientific Notation
1
Pressure inside ocean depth
\[98700000 pa\]
\[p=......\]
2
Charge of an iron sphere
\[0.0000007 C\]
\[q=......\]
3
Speed of light in vacuum
\[300000000\frac{m}{s}\]
\[𝜗=......\]
4
Atomic radius is approximately
\[0.0000000025 m\]
\[r=......\]
Basic Units in the International System
In this international system, scientists agreed to use basic measurement units from which all other physical quantities' units are derived.
The following table shows the basic units:
Unit Symbol
Basic Unit
Basic Quantity
m
Meter
Length
kg
Kilogram
Mass
S
Second
Time
K
Kelvin
Temperature
Prefixes
These are multiples and submultiples of measurement units.
The following table shows the prefixes:
Conversion Factor
For example, \[k=10^3\]
Therefore
\[\frac{10^3}{k}=\frac{k}{10^3}=1\]
This is called the conversion factor
Solved Example: The distance from Dubai to Riyadh is 6.3 Megameters. What is the distance in meters?
\[6.3 Mm×\frac{10^6 m}{Mm}=6.3×10^6 m\]
Solved Example: Convert 16.4 milligrams to kilograms
\[16.4 mg×\frac{10^{-3}g}{mg}×\frac{kg}{10^3 g}=16.4×10^{-3}×10^{-3}=16.4×10^{-6} kg\]
1
Which of the following equals
\[5 \;\;km \]
\[5 × 10^6\;\;cm\;\;\;\;\;\;-C\]
\[ 5 × 10^4\;\;cm\;\;\;\;\;\;-A\]
\[5 × 10^3\;\;cm\;\;\;\;\;\;-D\]
\[ 5 × 10^5\;\;cm\;\;\;\;\;\;-B\]
Click here to show solution
Choose the correct answer
2
Which of the following equals
\[ 5 \;\;µs\]
\[5 × 10^{-3}\;\;S\;\;\;\;\;\;-C\]
\[5 × 10^{-4}\;\;S\;\;\;\;\;\;-A\]
\[5 × 10^{-5}\;\;S\;\;\;\;\;\;-D\]
\[ 5 × 10^{-6}\;\;S\;\;\;\;\;\;-B\]
Click here to show solution
Choose the correct answer
Play and Learn
Identify Prefix Values
Dimensional Analysis
It's the process of formulating several physical formulas and verifying them using measurement units. If the formulas are correct, then the resulting unit value is correct.
Solved Example:
The period of a pendulum
\[T\]
Is measured in seconds
\[s\]
Verify the validity of the following formula for calculating the period:
\[T=2𝜋 \sqrt\frac{L}{g}\]
\[S= \sqrt\frac{m}{\frac{m}{S^2}}=\sqrt{S^2}=S\]
Therefore, the above relationship is correct.
Significant Figures
These are digits that can be measured using measuring devices and contain real digits and estimated digits.
Example: The length of a pen measured by a ruler (using a device) is a significant figure.
While the number of students in 10th grade is not a significant figure as it wasn't measured by a device.
\[ 13.85\;\; Cm \] Pen length
\[ 13.8 \;\;Cm\] is a real digit that all students would read the same
\[5\] is an estimated digit that varies from student to student
Solved Example: This device is called a galvanometer used to measure current and potential difference. Now it's being used to measure current. What is the current measurement?
(2.3) Reading
Note the number of significant figures: two digits
Rules of Significant Figures
Rule 1: All non-zero digits are significant.
Example
\[ 3.46 \] has three significant figures
Rule 2: Zeros to the left of the number are not significant.
\[0.00034\]
has two significant figures
\[(3 , 4)\]
Rule 3: Zeros to the right of the number are not significant.
\[5800\] has two significant figures
\[(5 , 8)\]
Rule 4: Zeros between numbers are significant.
\[5003\] has four significant figures
\[(5 ,0,0, 3)\]
Rule 5: Zeros after the decimal point are significant.
\[6.00\] has three significant figures
\[(6 , 0,0)\]
Test Yourself
Attempt Number
Measured Value
Number of Significant Figures
1
0.00520
\[......................\]
Click here to show solution
2
2010
\[......................\]
Click here to show solution
3
2,000
\[......................\]
Click here to show solution
4
98790
\[......................\]
Click here to show solution
3
Using the rules of significant figures and scientific notation, the product of the following significant figures is:
\[ 50.4 \ × 310 = …………\]
\[1.5 × 10^{3}\;\;\;\;\;\;-C\]
\[15.6 × 10^{3}\;\;\;\;\;\;-A\]
\[1.6 × 10^{3}\;\;\;\;\;\;-D\]
\[ 15.62 × 10^{3}\;\;\;\;\;\;-B\]
Click here to show solution
Choose the correct answer
4
Using the rules of significant figures and scientific notation, find the result of:
\[ 5.63+15.1+14=..............\]
\[34.7\;\;\;\;\;\;-C\]
\[34\;\;\;\;\;\;-A\]
\[34.73\;\;\;\;\;\;-D\]
\[ 35\;\;\;\;\;\;-B\]
Click here to show solution
Choose the correct answer
Accuracy and Precision
Accuracy: How close a measured value is to the true value.
The closer to the true value, the more accurate the measurement.
Precision: How close measured values are to each other, regardless of their closeness to the true value.
The time needed for an object to fall from 2 meters height is approximately:
\[t=0.64\;\;s\]
The fall time was measured by three students, each performing the measurement three times:
Ahmed's measurements
\[( 0.68 S , 0.51 S, 0.95 S )\]
Majid's measurements
\[( 0.77 S , 0.75 S, 0.76 S )\]
Yusuf's measurements
\[( 0.65 S , 0.64 S, 0.63 S )\]
Ahmed's measurements are neither accurate nor precise.
Majid's measurements are not accurate but are precise.
Yusuf's measurements are both accurate and precise.
Measurement and Margin of Error
Devices are read through the clear graduations on the device.
The margin of error is added, which is the smallest graduation on the device divided by 2, and added to the reading.
Example: What is the device reading below? Determine the margin of error.
The device reading here is 2.7
The smallest graduation on the device here is 1, divided by 2, and this value is added or subtracted from the previous reading, becoming:
(Reading (0.5 ± 2.7)
Graphical Representation of Data
What is the purpose of a graph?
What values do you put on the horizontal and vertical axes?
Does the graph's shape have meanings for you?
Conduct the following experiment: Adjust the pendulum to a specific length and measure the time for ten oscillations, then take the time for one oscillation. Repeat the experiment to measure the period of a pendulum with different lengths.
Mathematical Pendulum
Pendulum Length (m)
Time for 10 Oscillations (s)
Period (s)
When drawing the graph:
On the horizontal axis, we put the values that were controlled - in this experiment, the pendulum length. These are called independent values.
On the vertical axis, we put the values that changed as a result of changing the independent values - here, the time. These are called dependent values.
The relationship between pendulum length and period is plotted in the graph above.
From the values you obtained, can you accurately determine the period for a pendulum length not in the table you obtained?
\[ ...............................................................\]
From the graph you obtained, can you accurately determine the period for a pendulum length not in the previous table?
\[ ...............................................................\]
From the graph you obtained, can you predict the period for a large pendulum length not in the previous table?
\[ ...............................................................\]
The relationship between volume and mass was studied for a set of different masses of the same type, resulting in the following values:
Draw the graph between mass and volume, taking into account while drawing:
On the horizontal axis, we put the values that were controlled - in this experiment, the cube's mass. These are called independent values.
On the vertical axis, we put the values that changed as a result of changing the independent values - here, the object's volume. These are called dependent values.
In the following experiment, a car moves at constant speed from different positions. Change the values and show the graphs.
The car started from the origin. The relationship between position and time was plotted, resulting in the following graph:
The resulting graph is a straight line passing through the origin, so we say the relationship between position and time is direct.
The equation form of the graph is \[y=m.x\]
m= slope of the graph \[m =\frac{y_2-y_1}{x_2-x_1}\]
Calculate the slope \[m=\frac{x_2-x_1}{t_2-t_1}\] In another experiment, the graph between position and time was plotted, and the car started away from the origin.
The resulting graph is a straight line but doesn't pass through the origin, so we say the relationship between position and time is linear.
The equation form of the graph is \[y=m.x+ b\]
b= point where the graph intersects the vertical axis \[m =\frac{x_2-x_1}{t_2-t_1}\]
If the graph of an experiment is of the form:
The relationship might be inverse.
To verify this, we apply the following relationship:
If verified, we say the relationship is inverse.
\[\frac{y_1}{y_2}=\frac{x_2}{x_1}\]
To verify the above graph, is it considered an inverse relationship?
\[\frac{6}{3}=\frac{100}{50}\]
Therefore, the relationship is inverse.
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Introduction to Physics |
Why do we use scientific notation?
Scientific notation was developed to easily represent numbers that are either very large or very small
The mass of Earth is approximately
\[5972000000000000000000000\;\; kg \]
The mass of Earth can be written as
\[5.972 ×1000000000000000000000000 \]
The number 1000000000000000000000000 is problematic as it's a multiple of ten
10 ×10×10×10×10×10×10×10 ×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10
Written in scientific notation:
\[10=10^1 / 10×10=10^2 / 10×10×10×10 = 10^4 .......\]
So the problematic number in scientific notation is:
\[10 ×10×10×10×10×10×10×10 ×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10×10 =10^{24}\]
\[5.972× 10^{24}\]
On the other hand, the charge of an electron is
\[0.00000000000000000016\;\; C\]
The electron charge can be written as:
\[ 1.6 ÷10000000000000000000 \]
\[\frac{1}{10}=10^{-1}/ \frac{1}{100}=10^{-2}/\frac{1}{100000}=10^{-5}/.....\]
So the problematic number in scientific notation is:
\[\frac{1}{10000000000000000000}=10^{-19}\]
Thus, the electron charge in scientific notation is:
\[q=1.6 × 10^{-19}C\]
Attempt Number Physical Quantity Value Write in Scientific Notation 1 Pressure inside ocean depth
\[98700000 pa\] \[p=......\] 2 Charge of an iron sphere
\[0.0000007 C\] \[q=......\] 3 Speed of light in vacuum
\[300000000\frac{m}{s}\] \[𝜗=......\] 4 Atomic radius is approximately
\[0.0000000025 m\] \[r=......\] In this international system, scientists agreed to use basic measurement units from which all other physical quantities' units are derived.
The following table shows the basic units:
Unit Symbol Basic Unit Basic Quantity m Meter Length kg Kilogram Mass S Second Time K Kelvin Temperature These are multiples and submultiples of measurement units.
The following table shows the prefixes:
Conversion Factor
For example, \[k=10^3\]
Therefore
\[\frac{10^3}{k}=\frac{k}{10^3}=1\]
This is called the conversion factor
Solved Example: The distance from Dubai to Riyadh is 6.3 Megameters. What is the distance in meters?
\[6.3 Mm×\frac{10^6 m}{Mm}=6.3×10^6 m\]
Solved Example: Convert 16.4 milligrams to kilograms
\[16.4 mg×\frac{10^{-3}g}{mg}×\frac{kg}{10^3 g}=16.4×10^{-3}×10^{-3}=16.4×10^{-6} kg\]
Which of the following equals
\[5 \;\;km \] \[5 × 10^6\;\;cm\;\;\;\;\;\;-C\]
\[ 5 × 10^4\;\;cm\;\;\;\;\;\;-A\]
\[5 × 10^3\;\;cm\;\;\;\;\;\;-D\]
\[ 5 × 10^5\;\;cm\;\;\;\;\;\;-B\]
Choose the correct answer Which of the following equals
\[ 5 \;\;µs\]
\[5 × 10^{-3}\;\;S\;\;\;\;\;\;-C\]
\[5 × 10^{-4}\;\;S\;\;\;\;\;\;-A\]
\[5 × 10^{-5}\;\;S\;\;\;\;\;\;-D\]
\[ 5 × 10^{-6}\;\;S\;\;\;\;\;\;-B\]
Choose the correct answer It's the process of formulating several physical formulas and verifying them using measurement units. If the formulas are correct, then the resulting unit value is correct.
Solved Example:
The period of a pendulum
\[T\]
Is measured in seconds
\[s\]
Verify the validity of the following formula for calculating the period:
\[T=2𝜋 \sqrt\frac{L}{g}\]
\[S= \sqrt\frac{m}{\frac{m}{S^2}}=\sqrt{S^2}=S\]
Therefore, the above relationship is correct.
These are digits that can be measured using measuring devices and contain real digits and estimated digits.
Example: The length of a pen measured by a ruler (using a device) is a significant figure.
While the number of students in 10th grade is not a significant figure as it wasn't measured by a device.
\[ 13.85\;\; Cm \] Pen length
\[ 13.8 \;\;Cm\] is a real digit that all students would read the same
\[5\] is an estimated digit that varies from student to student
Solved Example: This device is called a galvanometer used to measure current and potential difference. Now it's being used to measure current. What is the current measurement?
(2.3) Reading
Note the number of significant figures: two digits
Rule 1: All non-zero digits are significant.
Rule 2: Zeros to the left of the number are not significant.
\[0.00034\]
has two significant figures
\[(3 , 4)\]
Rule 3: Zeros to the right of the number are not significant.
\[5800\] has two significant figures
\[(5 , 8)\]
Rule 4: Zeros between numbers are significant.
\[5003\] has four significant figures
\[(5 ,0,0, 3)\]
Rule 5: Zeros after the decimal point are significant.
\[6.00\] has three significant figures
\[(6 , 0,0)\]
Attempt Number Measured Value Number of Significant Figures 1 0.00520 \[......................\]
2 2010
\[......................\]
3 2,000 \[......................\]
4 98790 \[......................\]
Using the rules of significant figures and scientific notation, the product of the following significant figures is:
\[ 50.4 \ × 310 = …………\]
\[1.5 × 10^{3}\;\;\;\;\;\;-C\]
\[15.6 × 10^{3}\;\;\;\;\;\;-A\]
\[1.6 × 10^{3}\;\;\;\;\;\;-D\]
\[ 15.62 × 10^{3}\;\;\;\;\;\;-B\]
Choose the correct answer Using the rules of significant figures and scientific notation, find the result of:
\[ 5.63+15.1+14=..............\]
\[34.7\;\;\;\;\;\;-C\]
\[34\;\;\;\;\;\;-A\]
\[34.73\;\;\;\;\;\;-D\]
\[ 35\;\;\;\;\;\;-B\]
Choose the correct answer Accuracy: How close a measured value is to the true value.
The closer to the true value, the more accurate the measurement.
Precision: How close measured values are to each other, regardless of their closeness to the true value.
The time needed for an object to fall from 2 meters height is approximately:
\[t=0.64\;\;s\]
The fall time was measured by three students, each performing the measurement three times:
Ahmed's measurements
\[( 0.68 S , 0.51 S, 0.95 S )\]
Majid's measurements
\[( 0.77 S , 0.75 S, 0.76 S )\]
Yusuf's measurements
\[( 0.65 S , 0.64 S, 0.63 S )\]
Ahmed's measurements are neither accurate nor precise.
Majid's measurements are not accurate but are precise.
Yusuf's measurements are both accurate and precise.
Devices are read through the clear graduations on the device.
The margin of error is added, which is the smallest graduation on the device divided by 2, and added to the reading.
Example: What is the device reading below? Determine the margin of error.
The device reading here is 2.7
The smallest graduation on the device here is 1, divided by 2, and this value is added or subtracted from the previous reading, becoming:
(Reading (0.5 ± 2.7)
What is the purpose of a graph?
What values do you put on the horizontal and vertical axes?
Does the graph's shape have meanings for you?
Conduct the following experiment: Adjust the pendulum to a specific length and measure the time for ten oscillations, then take the time for one oscillation. Repeat the experiment to measure the period of a pendulum with different lengths.
Test Yourself
Basic Units in the International System
Prefixes
Click here to show solution
Click here to show solution
Play and Learn
Identify Prefix Values
Dimensional Analysis
Significant Figures
Example
\[ 3.46 \] has three significant figures
Test Yourself
Click here to show solution
Click here to show solution
Click here to show solution
Click here to show solution
Click here to show solution
Click here to show solution
Measurement and Margin of Error
Graphical Representation of Data
Pendulum Length (m)
Time for 10 Oscillations (s)
Period (s)
On the horizontal axis, we put the values that were controlled - in this experiment, the pendulum length. These are called independent values.
On the vertical axis, we put the values that changed as a result of changing the independent values - here, the time. These are called dependent values.
The relationship between pendulum length and period is plotted in the graph above.
From the values you obtained, can you accurately determine the period for a pendulum length not in the table you obtained?
\[ ...............................................................\]
From the graph you obtained, can you accurately determine the period for a pendulum length not in the previous table?
\[ ...............................................................\]
From the graph you obtained, can you predict the period for a large pendulum length not in the previous table?
\[ ...............................................................\]
The relationship between volume and mass was studied for a set of different masses of the same type, resulting in the following values:
On the horizontal axis, we put the values that were controlled - in this experiment, the cube's mass. These are called independent values.
On the vertical axis, we put the values that changed as a result of changing the independent values - here, the object's volume. These are called dependent values.
In the following experiment, a car moves at constant speed from different positions. Change the values and show the graphs.
The car started from the origin. The relationship between position and time was plotted, resulting in the following graph:
The resulting graph is a straight line passing through the origin, so we say the relationship between position and time is direct.
The equation form of the graph is \[y=m.x\]
m= slope of the graph \[m =\frac{y_2-y_1}{x_2-x_1}\]
Calculate the slope \[m=\frac{x_2-x_1}{t_2-t_1}\] In another experiment, the graph between position and time was plotted, and the car started away from the origin.
The resulting graph is a straight line but doesn't pass through the origin, so we say the relationship between position and time is linear.
The equation form of the graph is \[y=m.x+ b\]
b= point where the graph intersects the vertical axis \[m =\frac{x_2-x_1}{t_2-t_1}\]
If the graph of an experiment is of the form:
To verify the above graph, is it considered an inverse relationship?
\[\frac{6}{3}=\frac{100}{50}\]
Therefore, the relationship is inverse.
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