Dr. Khaled Lotfy General Physics

Dr. Khaled Lotfy General Physics

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General Physics chapter 1

It is doubtless fact that people always want to know about the mysteries of nature and

the world around them since they are born. So they start thinking and formulating their

views on nature. Lots of natural facts were collected by various experimental

observations. This is Science! The word “Science” originally based on the Latin verb

“Scientia” that means “To Know”. So, Science means “to know nature (and its laws)

by observations! Science needs scientific methods to find its way. The Scientific

method can be given as followings:

- - Systematic observations,

- - Formulation of reasons (called hypothesis –that means “not certain”),

- - Theoretical predictions,

- - Experimental verifications of theoretical predictions –that means “theory is invalid

until it gives same experimental verification”)

So, what is the relationship between Science and Physics? It is well known that the

Physics is a branch of Science. But what is Physics?

The Matter is defined as “any substance that occupies space and has mass in

universe.” and The Energy is defined as “capacity to do WORK -anything that

occupies NO space and has NO mass-”.

Physics:

Is the branch of Science that deals with different forms of Energy, its effect on

Matter and its relations with Matter?

Scientific Notation

If you want to report a really big number, it becomes tedious to write it out. For

example, the human body contains approximately

7,000,000,000,000,000,000,000,000,000 atoms. If you used this number often, you

would surely like to have a more compact notation for it. This is exactly what

Scientific Notation is.


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Scientific notation: Number = mantissa x 10 exponent

(power)

The number of atoms in the human body can thus be written compactly as 7 x 1027

,

where 7 is the mantissa and 27 is the exponent.

Example: 460000 = 4.6 x 105 and 0.0023 = 2.3 x 10

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Another example

(7×1027

)×(7×109 )=(7×7)×10

27+9 =49×10

36 = 4.9×10

37.

Significant Figures

When we specified the number of atoms in the average human body as 7 × 1027

, we

meant to indicate that we know it is at least 6.5 ×1027

but smaller than 7.5 × 1027

.

However, if we had written 7.0×1027

, we would have implied that we know the true

number is somewhere between

6.95× 1027

and 7.05× 1027

. This is statement is more precise than the previous

statement.

Here are some rules about using significant figures followed in each case by an

example:

-The number of significant figures is the number of reliably known digits. For

example, 1.62 has 3 significant figures; 1.6 has 2 significant figures.

- If you give a number as an integer, you specify it with infinite precision. For

example, if someone says that he or she has 3 children, this means exactly 3, no less

and no more.

-Leading zeros do not count as significant digits. The number 1.62 has the same

number of significant digits as 0.00162. There are three significant figures in both

numbers. We start counting significant digits from the left at the first nonzero digit.

- Trailing zeros, on the other hand, do count as significant digits. The number 1.620

has four significant figures. Writing a trailing zero implies greater precision!

-Numbers in significant notation have as many significant figures as their mantissa.

For example, the number 9.11 × 10–31

has three significant figures because that’s what

the mantissa (9.11) has?. The size of the exponent has no influence.

You can only add or subtract when there are significant figures for that place in every

number. For example, 1.23 + 3.4461 = 4.68, and not 4.6761 as you may think.


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Physical Quantity

Physical Quantity: Quantity that can be measured.

The Types of Physical Quantity are Basic or derived

Basic ( fundamental) Quantity Cannot be defined in terms of other physical

quantities.

Length: Distance between two points in space.

Mass : amount of matter in an object.

Time: Duration between two events.

Derived Quantity:

Quantity that derived by combining base quantities (velocity, acceleration)

SI unit system: mks (Metric) system

Meter (m):

“ one ten-millionth of the distance from the North Pole to the

equator.”

“Distance a light in vacuum travels.”

Kilogram (kg):

The mass of a particular platinum-iridium (Pt– Ir) cylinder kept at

the International Bureau of Weights and Standards, France.


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Second (s):

0f mean solar day.

The time interval during which 9,192,631,770 oscillations of the

electromagnetic wave that corresponds to the transition between

two specific states of the cesium-133 atom.


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Types of Physical Quantities

Scalar Quantity: Quantity has magnitude only

For example, distance (x), mass (m), time (t), volume (V),

density (d), work (W), energy (E)…etc. temperature).

Vector Quantity : Quantity has magnitude and direction

For example, displacement (x), velocity (v), acceleration (a), force (F), moment (M),

weight (G)…etc.,

Vectors

Vectors are mathematical descriptions of quantities that have both magnitude and

direction

Cartesian Coordinate System

A Cartesian coordinate system is defined as a set of two or more axes with angles of

90° between each pair.

In the next Figure, for example, the point P has the position (3.3, 3.8), because its x-

coordinate has a value of 3.3 and its y-coordinate has a value of 3.8. Note that each

coordinate is a number and can have a positive or negative value or be zero.


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We can also define a one-dimensional coordinate system, for which any point is

located on a single straight line, conventionally called the x-axis. Any point in this

one-dimensional space is then uniquely defined by specifying one number, the value

of the x-coordinate, which again can be negative, zero, or positive (the next

figure).The point P in Figure 1.14 has the x-coordinate Px = –2.5.

In a three-dimensional space, we have to specify three numbers to uniquely determine

the coordinates of a point. We use the notation P = (Px, Py, Pz)to accomplish this.

Cartesian Representation of Vectors

The next figure shows the displacement vector ⃗⃗ that points from point P = (–2, –3)

to point Q = (3,1). With the notation just introduced, the components of are the

coordinates of point Q minus those of point P, ⃗⃗ = (3–(–2),1–(–3)) = (5, 4).


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The next figure shows another vector from point R = (–3, –1) to point S = (2, 3).The

difference between these coordinates is (2–(–3),3–(–1) = (5, 4) , which is the same as

the vector ⃗⃗ pointing from P to Q.

The operation of addition, subtraction and multiplication of ordinary algebra can be

extended to vectors with some new definitions and a few new rules. There are two

fundamental definitions.


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Two vectors, A and B are equal if they have the same magnitude and direction,

regardless of whether they have the same initial points, as shown in Figure.

A vector having the same magnitude as A but in the opposite direction to A is denoted

by -A , as shown in Figure


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Adding and subtracting vectors

When you add two vectors you can visualize the process as laying them end-

to-end. For example if you wish to add the vectors a and b you can think of it

as vector b beginning at the end of vector a, as can be shown in this fig.

.

You can also add b and a, where the vector a begins at the end of vector b,

as can be shown in this fig.

By combining both these pictures you can see that it does not matter which

way around you add the vectors as the journeys they describe begin and end

at the same place, they simply take different routes. The vector which

described the overall journey represented by the addition of vectors is called

the resultant vector. Here, if you call the resultant vector c, you can

combine the two diagrams above to see that:


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This diagram shows that, mathematically:

a + b = b +a = c

The diagram also shows that if you add the number of steps in the x–direction in a and

b you get the number of steps in the x-direction of the resultant c. This is also true for

the y-direction (and also the z-direction). By expressing a and b as the general vectors:

a = a1i + a2j + a3k and b =b1i + b2j + b3k

you can calculate the number of i ’s (which represent steps in the x-direction) in the

resultant c by adding a1 and b1 , the number of j ’s (which represent steps in the y-

direction) by adding a2 and b2 and the number of k ’s (which represent steps in the

z-direction) by adding a3 and b3 . You can write this mathematically as:


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Subtraction of vectors can be thought of in a similar way.

Remember that a vector which has the same magnitude but opposite

direction to another vector is the negative of that vector.

If you wish to subtract the vector b from vector a you can think of adding the

vector - b to a. To the left is a representation of

a + (-b) = a-b = c

You can also subtract a from b and show that the resultant is -c. To the left is

a representation of

b + (-a) = b - a = - c


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Vector Length and Direction

From this figure

The magnitude of A

The direction of A

We can also obtain the Cartesian components of a vector of given length and

direction:

Ax =A cos θ Ay =A sin θ


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Multiple Choice

1. 5.0 × 105 + 3.0 × 10

6 =

A) 8.0 × 105 B) 8.0 × 10

6 C) 5.3 × 10

5 D) 3.5 ×10

5 E) 3.5 × 10

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2. (5.0 × 104)

× (3.0 ×10–6

) =

A) 1.5 × 10–3

B) 1.5 × 10–1

C) 1.5 × 101 D) 1.5 × 10

3 E) 1.5 ×10

5

3. (7.0 × 106)/(2.0 × 10

–6) =

A) 3.5 × 10–12

B) 3.5 × 10–6

C) 3.5 D) 3.5 × 106 E) 3.5 × 10

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4. The number of significant figures in 0.00150 is:

A) 2 B) 3 C) 4 D) 5 E) 6

5. The number of significant figures in 15.0 is:

A) 1 B) 2 C) 3 D) 4 E) 5

6- The unit of the length in SI is

A) Kilogram B) Gram C) Meter D) Pound E) None

7. The SI base unit for mass is:

A) gram B) pound C) kilogram D) ounce E) kilopound

8. The unit of density might be:

A) pound per foot B) gram per liter C) kilogram per cubic meter D) cubic

kilogram per meter E) cubic meter per kilogram

9. A gram is:

A) 10–6

kg B) 10–3

kg C) 1 kg D) 103 kg E) 10

6 kg

10. A nanosecond is:

A) 109 s B) 10

–9 s C) 10

–10 D) 10

–10 s E) 10

–12

11. The water has a density of 1 gm/cm3, which is:

A)100 kg/m3 B) 0.1 kg/m

3 C) 1000 kg/m

3 D) 0.01 kg/m

3 E) None

12.108 m/hr is equal to:

A) 1 cm/s B) 2 cm/s C) 3 cm/s D) 4 cm/s E) 5 cm/s

13. A square with an edge of exactly 1 cm has an area of:

A) 10–6

m2 B) 10

–4 C) 10

2 m

2 D) 10

-4 m

2 E) 10

6 m

2

14. A cubic box with an edge of exactly 1 cm has a volume of:

A) 10–9

m3 B) 10

–6 m

3 C) 10

–3 m

3 D) 10

3 m

3 E) 10

6 m

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15. 1 m is equivalent to 3.281 ft. A cube with an edge of 1.5 ft has a volume of:

A) 1.2 ×102 m

3 B) 9.6 × 10

–2 m

3 C) 10.5 m

3 D) 9.5 × 10

–2 m

3 E) 0.21 m

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16. A sphere with a radius of 1.7 cm has a volume of:

A) 2.1 ×10–5

m3 B) 9.1 ×10

–4 m

3 C) 3.6 × 10

–3 m

3 D) 0.11 m

3 E) 21 m

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17. A sphere with a radius of 1.7 cm has a surface area of:

A) 2.1 ×10–5

m2 B) 9.1 ×10

–4 m

2 C) 3.6× 10

–3 m

2 D) 0.11 m

2 E) 36 m

2

18. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 m has a

volume of:

A) 0.20 m3 B) 0.14 m

3 C) 9.3 × 10

–3 m

3 D) 2.3 × 10

–3 m

3 E) 7.4 × 10

–4 m

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19. A sphere has a radius of 21 cm and a mass of 1.9 kg. Its density is about:

A) 2.0 × 10–6

kg/m3 B) 2.0 × 10

–2 kg/m

3 C) 1.4 kg/m

3 D) 14 kg/m

3 E) 49 kg/m

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20.Which of the following is a fundamental (base) unit?


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A) J B) kg C) g D) N E) None

21. Mass, length and Time are quantities

A) Derived B) Fundamental (base) C) Both fundamental and derived D) None

22. How many micrometers are there in 1 km

A) 109 B) 10 C) 10

6 D) 1000 E) 10

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Conti- chapter 1

1. The magnitude and direction of, – ⃗⃗ + ⃗⃗ where ⃗⃗ = (20.0,-50.0), ⃗⃗ = (90.0,–20.0).

A) 76.2, 23.2 B) 10, 5 C) 20, 5 D) 30, 5 E) 40, 5

2. The X-component of a position vector has length 60 m and is at an angle of 700

above the x-axis.

A) 5.5 m B) 10.5 m C) 20.5 m D) 30.5 m E) 40.5 m

3. The y-component of a vector having length 20 m at an angle of 30° with x- axis will

be equal to

A) 5 m B) 10 m C) 20 m D) 30 m E) 40 m

4. The magnitude vector that satisfies the equation ̂ – ̂

A) 2.83 B) 3.83 C) 4.83 D) 5.83 E) 6.83

5. The resultant of the two- dimensional vectors (-1.5, 0.7), (-3.2, 0.7) and (7,-3.3) lies

in quadrant is

A) I B) II C) III D) IV E) V

6. Which of the following is a vector quantity?

A) Mass B) Density C) Speed D) Temperature E) None of these

7. Which of the following is a scalar quantity?

A) Mass B) Velocity C) Displacement D) Acceleration E) None of these

8.The vector that has :

A) a magnitude and direction B) direction only C) a magnitude only D) None

9. The angle between = (25 m) ̂ + (45 m) ̂ and the positive x- axis is

A) 29◦ B) 61

◦ C) 151

◦ D) None

Dr. Khaled Lotfy General Physics

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