Demonstration School of Suan Sunandha Rajabhat University...

Demonstration School of Suan Sunandha Rajabhat University

Book of Worksheets

Physical Science 1

SCI 30103 Mathayom 5/2

1st Semester Academic Year 2020

Lecturer: Ariyaphol Jiwalak

Name……………………………………….. Class.…….. No.…….

Preface

The physics book that you are reading now is my attempt to refine the content from the standardized textbooks to suit Thai students. However, there are still some mistakes. And I welcome suggestions from students to improve the books for students in the next generation.

I would like students to realize that physics is a subject that provides a basic understanding of various fields of science. Physics can explain the nature and teaches us to think systematically and logically. Understanding physics is very useful for understanding things that occurs around us. I wrote this book, not for anyone to become a physicist. But I wrote for everyone who studies this course to have some basic physics knowledge and have good experience and good memories in physics.

Ariyaphol Jiwalak

14 days self-quarantine during an outbreak of the COVID-19, 2020

Content

Page

Chapter 1: Introduction to physical science 1 1. Mathematical method for physics 2

- Graph 2 - Trigonometry 3 - Vectors 5

2. Quantities and Units 7 - Base quantities and Base units 7 - Unit prefixes 7 - Unit conversion 8 - Scalar quantity and Vector quantity 10

Problems 11

Chapter 2: Linear motion 14

1. Displacement, Distance, Velocity, Speed, and Acceleration 15 - Displacement and Distance 15 - Velocity and Speed 15 - Acceleration 16 - Ticker timer 18

2. Graphs of linear motion 19 - s-t graph 19 - v-t graph 19 - a-t graph 19

3. Free fall 28 Problems 32

Chapter 3: Force and law of motion 37 1. Force 38

- Types of forces 38 - Free-body diagram 40

2. Mass 41

Page

Chapter 3: Force and law of motion (cont.) 3. Newton’s laws of motion 42

- Newton’s first law 42 - Newton’s second law 43 - Newton’s third law 46

4. Newton’s law of universal gravitation 47 - Gravitational force 47

Problems 48

Chapter 4: Projectile Motion 50 Problems 52

Chapter 5: Circular Motion 53 1. Angular quantities 54

- Angular Displacement 54 - Angular Velocity 54

2. Period and Frequency 55 - Period 55 - Frequency 55

3. Uniform circular motion and Non-uniform circular motion 56 - Uniform circular motion 56 - Non-uniform circular motion 56

4. Centipetal Acceleration and Centipetal Force 57 Problems 62

Chapter 6: Simple harmonic motion 64 1. An object attached to a spring 65

- Horizontal SHM 65 - Vertical SHM 66

2. Simple pendulum 67 Problems 69

Page

Chapter 7: Nuclear physics 71

1. Structure of nuclei 72 - Proton-Neutron hypothesis 72

2. Radioactivity 73 - Rays emitted by radioactive elements 73

3. Decay processes 74 - Alpha decay 75 - Beta decay 75 - Gamma ray emission 75

4. Radioactive decay 76 - Half-life 76

5. Nuclear stability 78 - Binding energy 78

6. Nuclear reactions 79 - Balancing nuclear equations 79 - Types of nuclear reactions 80

Problems 82

Physical Science 1 (SCI 30103) Chapter 1: Introduction to Physical Science ___________________________________________________________________________________________

Demonstration School of Suan Sunandha Rajabhat University © 2020 1

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1. Mathematical method for physical science - Graph

Linear Parabola Hyperbola

- Trigonometry Definition of the trigonometric functions Trigonometric tables

- Vectors Addition Subtraction Components of vectors

2. Quantities and Units - Base quantities and Base units - Unit prefixes - Unit conversion - Scalar quantity and Vector quantity

Chapter 1: Introduction to Physical Science



1. MATHEMATICAL METHOD FOR PHYSICAL SCIENCE .

Graph.

Linear Parabola Hyperbola

slope = _______

y-intercept = _______

y = y =

y

x

y

x

y

x



Trigonometry.

• Definitions of the trigonometric functions

• Trigonometric tables

functions θ

0o 30o 37o 45o 53o 60o 90o

sin θ l

cos θ

tan θ

sin θ = _____ csc θ = _____

cos θ = _____ sec θ = _____

tan θ = _____ cot θ = _____

Hypotenuse

Adjacent

Opposite

θ



Example 1.1: You wish to find the height of a tree but cannot measure it directly. You stand 50.0 m from the tree and determine that a line of sight from the ground to the top of the tree makes an angle of 30o with the ground. How tall is the tree?

Example 1.2: A cross-country skier skis 1.00 km north and then 2.00 km east on a horizontal snowfield.

How far and in what direction is she from the starting point?

30o



Vectors.

• Vector addition

Determine R⃗⃗ = A⃗⃗ + B⃗⃗

A⃗⃗ is in the same direction as B⃗⃗

A⃗⃗ is opposite direction to B⃗⃗

A⃗⃗ is perpendicular to B⃗⃗

A⃗⃗ makes any angle with B⃗⃗

A⃗⃗

B⃗⃗

A⃗⃗

B⃗⃗

A⃗⃗

B⃗⃗

A⃗⃗

B⃗⃗



• Vector subtraction

Determine R⃗⃗ = A⃗⃗ - B⃗⃗ = A⃗⃗ + (-B⃗⃗ )

A⃗⃗ is in the same direction as B⃗⃗

A⃗⃗ is opposite direction to B⃗⃗

A⃗⃗ makes any angle with B⃗⃗

• Components of vectors

θ

F⃗

A⃗⃗

B⃗⃗

A⃗⃗

B⃗⃗

A⃗⃗

B⃗⃗



2. QUANTITIES AND UNITS .

Base quantities and Base units.

The International System of Units (SI) is made up of 7 base units.

Unit prefixes.

Base quantities SI base units Symbol

Length

Time

Mass

Thermodynamic temperature

Luminous intensity

Electric current

Amount of substance

Power of ten Prefix Abbreviation

109

106

103

10-2

10-3

10-6

10-9



Unit conversions.

Example 2.1:

1125 × 103 newton = _______________ meganewton

7.0 × 10-15 meter = _______________ nanometer

0.0352 kilogram = _______________ gram

16 milligram = _______________ gram

3.6 gigameter = _______________ micrometer

74,000 milligram = _______________ kilogram

1.75 × 102 mm2 = _______________ m2

2 cm3 = _______________ m3

1.000 g/cm3 = _______________ kg/m3

72 km/hr = _______________ m/s

25 m/s = _______________ km/hr

20 round / 4 sec = _______________ round/sec

120 round/minute = ________ round/sec = ________ sec/round

80 sec / 50 round = _______________ sec/round



Example 2.2: One of the world’s largest cut diamond is the First Star of Africa (mounted in the British Royal Sceptre and kept in the Tower of London). Its volume is 30.2 cubic centimeter. What is its volume in cubic meters?

Example 2.3: The world land speed record of 1220 km/h was set on October 15, 1997, by Andy Green

in the jet-engine car Thrust SSC. Express this speed in meters per second. Example 2.4: On an interstate highway in a rural region of Wyoming, a car is traveling at a speed of 38.0

m/s. Is the driver exceeding the speed limit of 120 km/h?



Scalar quantity and Vector quantity.

• Scalar quantity Scalar quantity is ________________________________________________________________________________ For example:

• Vector quantity Vector quantity is ________________________________________________________________________________ For example:



xProblemsx

Problem 1: The number 300,000,000 can be written as

a) 3 × 106.

b) 3 × 107.

c) 3 × 108.

d) 3 × 109.

e) 3 × 10-9. Problem 2: The fundamental SI units for mass, length, and time, respectively, are

a) newton, meter, minute. b) kilogram, meter, second. c) pound, foot, hour. d) pound, foot, second. e) kilogram, centimeter, hour.

Problem 3: A millimeter is

a) 103 m.

b) 102 m.

c) 101 m.

d) 10-3 m.

e) 10-6 m. Problem 4: How many nanometers are in a kilometer?

a) 10-9 b) 109 c) 10-12 d) 1012 e) 1027



Problem 5: The data plotted on a graph of distance on the y-axis vs. time on the x-axis yields a linear graph. The slope of the graph is

a) ∆d

∆t.

b) (∆d)(∆t).

c) ∆t

∆d.

d) (∆d) + (∆t).

e) (∆d) - (∆t).

Problem 6: The cosine of an angle in a right triangle is equal to the a) sine of the angle. b) tangent of the angle. c) hypotenuse of the triangle. d) side adjacent to the angle. e) ratio of the side adjacent to the angle and the hypotenuse of the triangle.

Problem 7: Which of the following quantities is NOT a vector quantity?

a) displacement b) mass c) resultant d) equilibrant e) 10 km at 30° north of east

Problem 8: The resultant of the two displacement vectors 3 m east and 4 m north is

a) 5 m northeast. b) 7 m northeast. c) 1 m southwest. d) 1 m northeast. e) 12 m northeast.



Problem 9: The x-component of the vector shown is most nearly (sin 30o = 0.5, cos 30o = 0.87, tan 30o = 0.58)

a) 10 m. b) 5 m. c) 8.7 m. d) 5.8 m. e) 100 m.

Problem 10: Two displacement vectors, each having a y-component of 10 km, are added together to

form a resultant that forms an angle of 60° from the +x-axis. What is the magnitude of the resultant? (sin 60o = 0.87, cos 60o = 0.5) a) 23 m. b) 40 m. c) 12 m. d) 20 m. e) 30 m.

Physical Science 1 (SCI 30103) Chapter 2: Linear Motion ___________________________________________________________________________________________



1. Displacement, Distance, Velocity, Speed, and Acceleration - Displacement and Distance

Displacement Distance

- Velocity and Speed Velocity Speed

- Acceleration - Ticker timer

2. Graphs of linear motion - s-t graph - v-t graph - a-t graph

3. Free fall

Chapter 2: Linear Motion



1. DISPLACEMENT, DISTANCE, VELOCITY, SPEED, AND ACCELERATION .

Displacement and Distance.

• Displacement (s⃗)

Displacement is defined as the change in position of a particle in some time inverval. The unit of displacement is meter (m).

• Distance (s) Distance is the length of a path followed by a particle. The unit of distance is meter (m).

Velocity and Speed.

• Velocity (v⃗⃗)

Velocity is defined as the displacement s⃗ divided by the time interval t during which the displacement occurs.

v⃗⃗ ≡ s⃗

t

The unit of velocity is meters per second (m/s).

• Speed (v) Speed is defined as the distance s devided by the time interval t required to travel that

distance.

vav ≡ s

∆t

The unit of speed is meters per second (m/s).



Acceleration.

• Acceleration (a⃗) Acceleration is defined as the change in velocity ∆v⃗⃗ divided by the time interval t during which

that change occurs.

a⃗ ≡ ∆v⃗⃗

t

The unit of acceleration is meters per second squared (m/s2).

Note: Scalar quantity Vector quantity Distance, Time, Speed Displacement, Velocity, Acceleration



Example 1.1: A sprinter can run 100 meters in 11 seconds. Find her average speed. Example 1.2: A car moving initially at 10 m/s accelerates up to 30 m/s during the course of 4 seconds.

Find the acceleration of the car. Example 1.3: A car traveling initially at a speed of +12 m/s accelerates at a rate of +4 m/s2 for a time of

5 s. What is the car’s speed at the end of 5 s?



Ticker timer.

The ticker timer makes dots on a paper tape at a frequency of 50 times in a second. Therefore,

each adjacent point is 1/50 seconds apart.

Direction of motion

• Constant velocity

The distance between each dot is constant.

• Speed up at a steady rate (constant acceleration) The distance between each dot increases.

• Slow down at a steady rate (constant acceleration) The distance between each dot decreases.

Calculation

- Average velocity: vav: CH = sCH

tCH=

sCH

5/50

- Average acceleration: aav: CH = vH−vC

tCH=

vH−vC

5/50

- Instantaneous velocity: vD = sCE

tCE=

sCE

2/50

- Instantaneous acceleration: aD = vE−vC

tCE=

vE−vC

2/50

A

B

C

E

D

F

G

H

I

J

Start

Start

Start



2. GRAPHS OF LINEAR MOTION .

Graphs Displacement-time. Velocity-time Acceleration-time.

s - t v - t a - t

Slope ____________ ____________ ____________

Area under the curve ____________ ____________ ____________

Draw a graph of motion from the following situations.

• The object moves from rest at the origin (s = 0) to the right.

Constant velocity Speed up at a steady rate Slow down at a steady rate (constant acceleration) (constant acceleration)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

a (m/s2)

t (s)

a (m/s2)

t (s)

a (m/s2)

t (s)



• The object moves from rest at the origin (s = 0) to the left.

Constant velocity Speed up at a steady rate Slow down at a steady rate (constant acceleration) (constant acceleration)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

a (m/s2)

t (s)

a (m/s2)

t (s)

a (m/s2)

t (s)



Describe the motion of an object from the following s-t graphs.

Displacement-time Describe the motion

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)



Displacement -time Describe the motion

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)

s (m)

t (s)



Describe the motion of an object from the following v-t graphs.

Velocity-time Describe the motion

v (m/s)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)



Velocity-time Describe the motion

v (m/s)

t (s)

v (m/s)

t (s)



Describe the motion of an object from the following a-t graphs.

Acceleration-time Describe the motion

a (m/s2)

t (s)

a (m/s2)

t (s)

a (m/s2)

t (s)



Example 2.1: A football player catches a ball at his goal line (x = 0) at t = 0, and his motion is then

graphed on the displacement vs. time graph below.

a) During which interval is the player accelerating away from his goal line? b) What is his velocity between points B and C? c) Describe his motion between points C and D? d) What is his velocity (magnitude and direction) during the interval from 4 s to 6 s?



Example 2.2: The graph below represents the velocity vs. time graph for a car.

a) During which intervals is the car at rest? b) During which intervals is the car moving at a constant nonzero velocity? State the

velocity at each of these intervals? c) There are two intervals during which the car is accelerating. Find the acceleration in

each of these intervals. d) Sketch the acceleration vs. time graph that corresponds to the motion of the car from

0 s to 14 s.



3. FREE FALL .

• An object is in free fall if it is falling freely under the influence of gravity.

• Experiment shows that If the effects of the air can be ignored; all objects fall with the same constant downward acceleration, regardless of their size or weight.

• The ‘gravitational acceleration’ or ‘acceleration due to gravity’ at or near the earth’s surface has a magnitude of g⃗⃗ = 9.8 m/s2.

Example 3.1: An object is dropped from rest. Example 3.2: An object is thrown vertically upward

with a speed of 29.4 m/s.

u⃗⃗ = +29.4

u⃗⃗ = 0



Draw a graph of motion from the following situations.

A ball is thrown vertically upward A ball is dropped from rest A ball is thrown vertically upward until it reaches the highest point. until it hits the ground. until it hits the ground.

s (m)

t (s)

s (m)

t (s)

v (m/s)

t (s)

v (m/s)

t (s)

a (m/s2)

t (s)

a (m/s2)

t (s)

s (m)

t (s)

v (m/s)

t (s)

a (m/s2)

t (s)



Example 3.3: A ball is dropped from rest from a high window of a tall building and falls for 3 seconds. Neglecting air resistance:

a) What is the speed of the ball?

b) What is the ball’s acceleration?



Example 3.4: A stone thrown from the top of a building is given an initial velocity of 20.0 m/s straight upward. The stone is launched 50.0 m above the ground, and the stone just misses the edge of the roof on its way down as shown in figure below.

a) Determine the time at which the stone reaches its maximum height.

b) Determine the velocity of the stone when it returns to the height from

which it was thrown. c) Find the velocity and displacement of the stone at t = 5.00 s.

u⃗⃗ = 20 m/s



xProblemsx

Problem 1: Consider the velocity vs. time graph shown.

The area under the graph from 2 s to 6 s is most nearly a) 8. b) 16. c) 24. d) 32. e) 36.

Problem 2: Which of the following statements is true?

a) Displacement is a scalar and distance is a vector. b) Displacement is a vector and distance is a scalar. c) Both displacement and distance are vectors. d) Neither displacement nor distance are vectors. e) Displacement and distance are always equal.

Problem 3: Which of the following is the best description of a velocity?

a) 60 miles per hour b) 30 meters per second

c) 30 km at 45° north of east d) 40 km/hr e) 50 km/hr southwest



Problem 4: A jogger runs 3 km in 0.3 hr, then 7 km in 0.70 hr. What is the average speed of the jogger? a) 10 km/hr b) 3 km/hr c) 1 km/hr d) 0.1 km/hr e) 100 km/hr

Problem 5: A motorcycle starts from rest and accelerates to a speed of 20 m/s in a time of 5 s. What

is the motorcycle's average acceleration? a) 100 m/s2 b) 80 m/s2 c) 40 m/s2 d) 20 m/s2 e) 4 m/s2

Problem 6: A bus starting from a speed of +12 m/s slows to +6 m/s in a time of 3 s. The average

acceleration of the bus is a) 2 m/s2 b) 4 m/s2 c) 3 m/s2 d) -2 m/s2

e) -4 m/s2

Problem 7: A train accelerates from rest at a rate of 4 m/s2 for a time of 10 s. What is the train's speed

at the end of 10 s? a) 14 m/s b) 6 m/s c) 2.5 m/s d) 0.4 m/s e) 40 m/s



Problem 8: A stone is dropped from rest. What is the acceleration of the stone immediately after it is dropped? a) zero b) 5 m/s2 c) 10 m/s2 d) 20 m/s2 e) 30 m/s2

Problems 9-10 refer to the following.

A ball is thrown straight upward with an initial velocity of +15 m/s. Problem 9: What is the ball's acceleration just after it is thrown?

a) zero b) 10 m/s2 upward c) 10 m/s2 downward

d) 15 m/s2 upward

e) 15 m/s2 downward

Problem 10: How much time does it take for the ball to rise to its maximum height?

a) 25 s b) 15 s c) 10 s d) 5 s e) 1.5 s



Problem 11: Each of the choices below shows a pair of graphs. Which choice shows the pair of graphs that are equivalent to each other? a) X

b) X

c) X

d) X

e) X



Problem 12-13 refer to the graph below. Consider the velocity vs. time graph.

Problem 12: During which interval is the object at rest?

a) AB b) BC c) CD d) DE e) EF

Problem 13: During which interval is the speed of the object increasing?

a) AB b) BC c) CD d) DE e) EF

Physical Science 1 (SCI 30103) Chapter 3: Force and Law of Motion ___________________________________________________________________________________________



In the last chapter, we discussed kinematics, the study of how motion occurs. In this chapter, we review dynamics, the study of the causes of motion.

1. Force

- Types of forces Contact forces Non-contact forces

- Free-body diagram 2. Mass 3. Newton’s laws of motion

- Newton’s first law - Newton’s second law - Newton’s third law

4. Newton’s law of universal gravitation - Gravitational force

Chapter 3: Force and Law of Motion



1. FORCE (F⃗⃗ ) .

• A force is ___________________________________________________________________________.

• A force can cause an object to change its velocity: - change __________ of velocity: faster of slower. - change __________ of velocity: change direction of movement.

• A force is a __________ quality. Therefore, it has both __________ and __________.

• The unit for the force is __________.

• Examples of forces:

Types of forces.

Contact forces Non-contact forces

https://en.wikipedia.org/wiki/Velocity



Superposition of forces Example 1.1: Figure below shows the horizontal force each wrestler applies to the object, as viewed

from above. The forces have magnitudes F1 = 250 N, F2 = 50 N, and F3 = 125 N. Find the x- and y-components of the net force on the object, and find its magnitude and direction.

53°

F⃗ 1

F⃗ 2

F⃗ 3

x

y



Free-Body Diagram (FBD).

• A FBD shows the chosen body by itself, “free” of its surrounding, with vectors drawn to show the magnitudes and directions of all the forces that act on the object.

• Be careful to include all the forces acting on the body, but be equally careful NOT to include any forces that the body exerts on any other body.

• You must be able to answer this question for each force: What other body is applying this force?

• When a problem involves more than one body, you have to draw a separate FBD for each body. Draw a Free-body diagram in each of the following situations. Situation 1:

Situation 2: Situation 3:

Situation 4:

Situation 5:

F

T



Situation 6: A coin is tossed straight up into the air. After it is released it moves upward, reaches its highest point and falls back down again. - The coin is moving upward after it is released.

- The coin is at its highest point.

- The coin is moving downward.

___________________________________________________________________________________________

2. MASS (m) .

• __________ is the resistance of an object to changing its state of motion or state of rest.

• We measure inertia by measuring the __________ of an object, or the amount of material it contains.

• A mass is a __________ quality. Therefore, it has only __________.

• The SI unit for mass is the __________.



3. NEWTON’S LAWS OF MOTION .

Newton’s first law of motion: law of inertia.

“An object in a state of constant velocity (including zero velocity) will continue in that state unless acted upon by a net force.” Example 3.1: You are driving a Maserati GranTurismo S on a straight testing track at a constant speed of

250 km/h. You pass a 1971 Volkswagen Beetle doing a constant 75 km/h. On which car is the net force greater?



Newton’s second law of motion: equation of motion.

“A net force acting on a mass causes that mass to accelerate in the direction of the net force. The acceleration is proportional to the force, and inversely proportional to the mass of the object being accelerated.”

ΣF⃗ = ma

where ΣF⃗ = net force (N) m = mass (kg) a = acceleration (m/s2)

- The newton (N) is defined as a kg m/s2

- ΣF⃗ and a are vectors pointing in the same direction. Weight

• The weight of an object is defined as the amount of gravitaional force acting on its mass.

W⃗⃗⃗ = mg⃗

• The unit for the weight is the __________.

Example 3.2: Find the weight in newtons of a girl having a mass of 40 kg. Example 3.3: A one-euro coin was dropped from rest from the Leaning Tower of Pisa. If the coin falls

freely, so that the effects of the air are negligible, how does the net force on the coin vary as it falls?



Example 3.4: A worker applies a constant horizontal force with magnitude 20 N to a box with mass 40 kg resting on a level floor with negligible friction. What is the acceleration of the box?

Example 3.5: Two ropes pull on a 50 kg cart as shown below. What is the acceleration of the cart?



Example 3.6: Two forces act on a 40 kg sled resting on ice as shown from the top view below. What is the magnitude and direction of the acceleration of sled?

Example 3.7: A hockey puck having a mass of 0.30 kg slides on the frictionless, horizontal surface of an

ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck

shown in figure below. The force F 1 has a magnitude of 5.0 N, and is directed at θ1 = 30°

below the x axis. The force F 2 has a magnitude of 8.0 N and its direction is θ2 = 60° above the x axis. Determine both the magnitude and the direction of the puck’s acceleration.

30o



Newton’s third law of motion: law of action and reaction.

“for every action force, there is and equal and opposite reaction force”

F⃗ 1 exerts on 2 = - F⃗ 2 exerts on 1

(action = reaction) Example 3.8: An apple sits at rest on a table, in equilibrium.

a) What forces act on the apple? b) What is the reaction force to each of the forces acting on the apple? c) What are the action–reaction pairs?

Action force Reaction force



4. NEWTON’S LAW OF UNIVESAL GRAVITATION .

Gravitational force (F⃗ G).

Newton’s law of universal gravitation states that “Every mass in the universe attracts every other mass in the universe. The gravitational force

between two masses is proportional to the product of the masses and inversely proportional to the square of the distance between their centers.”

FG ∝

m1m2

r2

FG = Gm1m2

r2

where FG = gravitational force (N) m1 and m2 = masses (kg) r = distance between their centers (m)

G = gravitational constant (6.67 × 10-11 N m2/kg2 or m3/kg s2)

Example 4.1: Find the gravitational force that the earth exerts on the body of mass 2.00 kg.

where the mass of the earth is 5.98 × 1024 kg

the radius of the earth is 6.38 × 103 km

r m2 m1



xProblemsx

Problem 1: The amount of force needed to keep a 0.1 kg hockey puck moving at a constant speed of 5 m/s on frictionless ice is a) zero. b) 0.1 N. c) 0.5 N. d) 5 N. e) 50 N.

Problem 2: A force of 20 N is needed to overcome a frictional force of 5 N and accelerate a 3 kg mass

across a floor. What is the acceleration of the mass? a) 4 m/s2 b) 5 m/s2 c) 7 m/s2 d) 20 m/s2 e) 60 m/s2

Problem 3: A force of 50 N directed at an angle of 45o from the horizontal pulls a 70 kg sled across a

frictionless pond. The acceleration of the sled is most nearly

a) 0.5 m/s2 b) 0.7 m/s2 c) 5 m/s2 d) 35 m/s2 e) 50 m/s2



Problem 4: A ball falls freely toward the Earth. If the action force is the Earth pulling down on the ball, the reaction force is a) the ball is pulling up on the earth. b) air resistance acting on the ball. c) the ball striking the Earth when it lands. d) the inertia of the ball. e) there is no reaction force in this case.

Problem 5: Which of the following diagrams of two planets would represent the largest gravitational

force between the masses?

a) A

b) B

c) C

d) D

e) E

Physical Science 1 (SCI 30103) Chapter 4: Projectile Motion ___________________________________________________________________________________________


7สียงแล

• Projectile motion results when an object is thrown either at an angle relative to the ground or

horizontally through the air.

• The object is moving horizontally and vertically at the same time.

• The horizontal velocity of a projectile is __________, but the vertical velocity is __________ by gravity.

• The trajectory of the projectile has a __________ shape.

• At any point along the trajectory, the velocity vector is the vector sum of the horizontal and vertical

velocity vectors; that is,

v⃗ = v⃗ x + v⃗ y

By the Pythagorean theorem

v = √vx2 + vy

2

and vx = v cos θ

vy = v sin θ

θ = tan-1 (vy

vx)

Chapter 4: Projectile Motion

v⃗ = vx

v⃗

vy

vx

vy

vx

vx

vy

vx u⃗

ux

uy

θ

θ

v⃗

v⃗

vy = 0



Example 1: A skier moves along a ski-jump ramp. What is her acceleration at each of the points G, H, and I in figure below after she flies off the ramp? Neglect air resistance.



xProblemsx

Problem 1: Which of the following is NOT true of a projectile launched from the ground at an angle (neglecting air resistance)? a) The horizontal velocity is constant. b) The vertical acceleration is upward during the first half of the flight, and downward

during the second half of the flight. c) The horizontal acceleration is zero. d) The vertical acceleration is 10 m/s2. e) The time of flight can be found by horizontal distance divided by horizontal velocity.

Problem 2: A projectile is launched from level ground with a velocity of 40 m/s at an angle of 30o

from the ground. What will be the vertical component of the projectile’s velocity just

before it strikes the ground?

a) 10 m/s b) 20 m/s c) 30 m/s d) 35 m/s e) 40 m/s

Physical Science 1 (SCI 30103) Chapter 5: Circular Motion ___________________________________________________________________________________________


7สียงแล

1. Angular quantities - Angular Displacement - Angular Velocity

2. Period and Frequency - Period - Frequency

3. Uniform circular motion and Non-uniform circular motion - Uniform circular motion - Non-uniform circular motion

4. Centipetal Acceleration and Centipetal Force - Centipetal Acceleration - Centipetal Force

Chapter 5: Circular Motion



1. ANGULAR QUANTITIES .

Angular Displacement (θ).

The angular displacement is a change of angular position. The unit of angular displacement is the radian (rad).

Angular Velocity (ω⃗⃗ ).

The angular velocity is the ratio of the angular displacement θ to the time interval t.

ω⃗ ≡ θ

t

The unit of angular velocity is the radian per second (rad/s).

θ

C x

y

r s

Note: 2π radian = 360 degree

2 × 3.14 radian = 360 degree

∴ 1 radian ≈ 57.3 degree



2. PERIOD AND FREQUENCY .

Period (T).

Period is the time for one revolution. The unit of period is the seconds (s)

Frequency (f).

Frequency is the number of revolutions per unit time. The unit of frequency is the revolutions per second (s-1) or Hertz (Hz)

Relationship between period and frequency

f = 1

T



3. UNIFORM CIRCULAR MOTION AND NON-UNIFORM CIRCULAR MOTION .

Uniform circular motion.

An object moving in a circle at a constant speed.

Non-uniform circular motion.

An object moving in a circle at a varying speed. For example, a roller coaster.

- Centipetal Force Fc → Centipetal Acceleration ac → change __________ of velocity

- Centipetal Force Ft → Centipetal Acceleration at → change __________ of velocity

v⃗ 1

v⃗ 2

m

m

v⃗ 1

v⃗ 2

Fc

ม

ac

ม

v⃗

m m

m



4. CENTIPETAL ACCELERATION AND CENTIPETAL FORCE .

Identify the centipetal force in each of the following situations. Situation 1:

Situation 2:

Situation 3:

m M

r

v⃗

v⃗

m l

v⃗

m k

https://www.google.co.th/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwj50vTcmprXAhVIgbwKHWHICwEQjRwIBw&url=https://www.sciencebuddies.org/science-fair-projects/references/linear-nonlinear-springs-tutorial&psig=AOvVaw1mWdhGC1UUXz0M0cKsJjes&ust=1509516824530921



Situation 4:

Situation 5:

θ

m

l

θ

v⃗

m

m

m

m

l




r v⃗

m

r

v⃗ m

https://www.google.co.th/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjy3t_i6_DZAhWBUbwKHWO1Cg0QjRx6BAgAEAU&url=http://clipartix.com/cars-clipart/&psig=AOvVaw2UcMAyjHrY5S02Jo-JMP-u&ust=1521289609432221

https://www.google.co.th/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjy3t_i6_DZAhWBUbwKHWO1Cg0QjRx6BAgAEAU&url=http://clipartix.com/cars-clipart/&psig=AOvVaw2UcMAyjHrY5S02Jo-JMP-u&ust=1521289609432221



θ

r

m

Situation 8:


r m

μs

v⃗

v⃗

r m μ

s

https://www.google.co.th/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjo0vGzlfDZAhVCFJQKHe-vCHwQjRx6BAgAEAU&url=http://www.duraflexracing.com/top-view-of-cars/cars/&psig=AOvVaw12BDyiqNkdhSBNhApIyhJs&ust=1521266229097296



Situation 11:

Situation 12:

Situation 13:

θ

μs

r m

m

θ

r

https://www.google.co.th/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjgr-fNpfDZAhUHUbwKHUBxCAMQjRx6BAgAEAU&url=http://carpng.com/airplane-front-view-7489/&psig=AOvVaw3rvlIkTHPkT0lhjaWMlIF8&ust=1521270823357447

https://www.google.co.th/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwi-6Zylo-_cAhUbU30KHTOWAy0QjRx6BAgBEAU&url=https://www.shutterstock.com/th/image-vector/vector-red-car-front-view-213431794&psig=AOvVaw0o9H9W6HZuTAaet5HOhUS4&ust=1534429958220299



xProblemsx

Problem 1-2 refer to the following diagram.

Problem 1: A ball on the end of a string is swung in a horizontal circle, rotating clockwise as shown.

When the ball is at point A, the direction of the velocity, centipetal force, and centipetal acceleration vectors, respectively, are a) x b) x c) x d) x e) x

Problem 2: If the string were suddenly cut when the ball is at point A in the figure above, the

subsequent motion of the ball would be a) to move to the right. b) to move to the left. c) to move to the top of the page. d) to move to the bottom of the page. e) to move up and to the left.



Problem 3-4 refer to the following diagram. A 30 kg child sits on the edge of a carnival ride at a radius of 2 m. The ride makes 2

revolutions in 4 s.

Problem 3: The period of revolution for this ride is

a) 1

2 rev/s.

b) 1

2 s.

c) 2 rev/s. d) 2 s. e) 4 s.

Problem 4: The speed of the child is most nearly

a) 4 m/s. b) 6 m/s. c) 24 m/s. d) 120 m/s. e) 360 m/s.

Physical Science 1 (SCI 30103) Chapter 6: Simple Harmonic Motion ___________________________________________________________________________________________


7สียงแล

1. An object attached to a spring

- Horizontal SHM - Vertical SHM

2. Simple pendulum

Chapter 6: Simple Harmonic Motion (SHM)



1. AN OBJECT ATTACHED TO A SPRING .

Horizontal SHM.

s⃗ − max 0 max

v⃗⃗ 0 max 0

a⃗⃗ max 0 − max

F⃗⃗⃗ max 0 − max

k

equilibrium position

natural length

F⃗⃗ext

m

m

s⃗

m






equilibrium position

natural length k

Vertical SHM.

Example 1.1: Consider the mass suspended on a spring. The mass vibrates between levels A and C, and

level B is halfway between A and C. Assume there is no loss of energy due to friction as the mass oscillates, and the potential energy at point B is zero.

a) At which point(s) is the speed of the mass the greatest? b) At which point(s) is the potential energy the greatest? c) If the potential energy at point A is 20 joules, what is the kinetic energy at point B?

m

F⃗⃗ext

s1 s2

m






2. SIMPLE PENDULUM .

• Period and Frequency Period T = 2π√l

g

Frequency f = 1

2π√

g

l

m

θ l



Example 2.1: Find the period and frequency of a simple pendulum 1.000 m long at a location where g = 9.800 m/s2.

Example 2.2: A pendulum swings back and forth between points A and C as shown below. B is the

midpoint between points A and C.

Which of the following statements are true? a) The potential energy at A is equal to the kinetic energy at C. b) The kinetic energy at B is equal to the total energy of the pendulum. c) The pendulum has both kinetic energy and potential energy at point A. d) The potential energy is maximum at points A and C. e) The kinetic energy is maximum at point B.



xProblemsx

Problem 1: According to Hooke’s law for a mass vibrating on an ideal spring, doubling the stretch distance will a) double the velocity of the mass. b) double the force that the spring exerts on the mass. c) quadruple the force the spring exerts on the mass. d) double the period. e) double the frequency.

Problem 2: For an ideal spring, the slope of a force vs displacement graph is equal to

a) the work done by the spring. b) the amplitude. c) the period. d) the frequency. e) the spring constant.

Problem 3: A pendulum swings with an amplitude θ as shown

If the amplitude is increased and the pendulum is released from greater angle, a) the period will decrease. b) the period will increase. c) the period will not change. d) the frequency will increase. e) the frequency will decrease.



Problem 4: A mass on an ideal spring vibrates between points A and E as shown.

At which point is the acceleration of the mass the greatest? a) A b) B c) C d) D e) The acceleration is the same at all points.

Problem 5: A mass vibrates on an ideal springs as shown.

The total energy of the spring is 100 J. What is the kinetic energy of the mass at point B? a) 25 J b) 50 J c) 75 J d) 100 J e) 200 J

Physical Science 1 (SCI 30103) Chapter 7: Nuclear Physics ___________________________________________________________________________________________


7สียงแล

1. Structure of nuclei - Proton-Neutron hypothesis

2. Radioactivity - Rays emitted by radioactive elements

Alpha ray Beta ray Gamma ray

3. Decay processes - Alpha decay - Beta decay - Gamma ray emission

4. Radioactive decay - Half-life

5. Nuclear stability - Binding energy

6. Nuclear reactions - Balancing nuclear equations - Types of nuclear reactions

Fission and Chain reactions Fusion

Chapter 7: Nuclear Physics



1. STRUCTURE OF NUCLEI .

Proton-Neutron hypothesis.

“The nucleus consists of protons (which has a positive electric charge) and neutrons (which are electrically neutral). These particles, which are components of nucleus, are called ‘nucleon’.”

The symbol of the element

XZA

where A = mass number

(The sum of the number of protons and the number of neutrons (p+ + n)) Z = atomic number

(The number of protons in the nucleus (p+))

such as proton H11

deuteron H12

tritron H13

neutron n01

electron e-10

Isotopes, Isotones, and Isobars

- Isotopes: same number of protons but a different numbers of neutrons - Isotones: same number of neutrons but a different numbers of protons - Isobars: same mass number

Example 1.1: Determine the number of protons, neutrons, and electrons in a neutral atom of iron Fe2656 .



2. RADIOACTIVITY .

Radioactive element Radioactive elements are elements that can emit rays by themselves.

Radioactivity Radioactivity is a process that the unstable nuclides decay to form other nuclides by emitting

particles and electromagnetic radiation.

Rays emitted by radioactive elements.

• Alpha ray (α, He24 ) is a helium nucleus.

• Beta ray (β, e-10 ) is a high-energy electron.

• Gamma ray (γ) is a high-frequency electromagnetic wave.

Note: Ray is a small group of particles which moves continuously at a high speed as a beam

Mass, Energy: α > β > γ

Velocity, Penetrating power: γ > β > α



3. DECAY PROCESSES .

The stable nuclei are represented by the black dots, which lie in a narrow range called the line of stability. Notice that the light stable nuclei contain an equal number of protons and neutrons. Also notice that in heavy stable nuclei, the number of neutrons exceeds the number of protons, the line of stability deviates upward from the line representing N = Z. This deviation can be understood by recognizing that as the number of protons increases, the strength of the Coulomb force increases, which tends to break the nucleus apart. As a result, more neutrons are needed to keep the nucleus stable because neutrons experience only the attractive gravitational force.



Proton-rich unstable nuclei.

• Alpha decay

For example , Ra88226 → Rn + He2

486

222

Stop to think Compare the ratio of neutron to protons between Ra88226 and Rn86

222 .

• Beta-plus or Positron ( e+10 ) decay

H11 → n0

1 + e+10 + ν

Neutron-rich unstable nuclei.

• Beta-minus decay

n01 → H 1

1 + e -10 + ν̅

For example , I53131 → Xe54

131 + e-10

Nucleus in an excited state.

• Gamma ray emission

For example , Rn* → Rn 86222 + γ

86

222



4. RADIOACTIVE DECAY .

No change in physical or chemical environment, such as chemical reactions or heating or increasing pressure, greatly affects the radioactive decays. “The rate of change of the number of radioactive nuclei in a sample or the ‘decay rate’ is proportional to the number of radioactive nuclei present”. Half-life (T1

2

).

The half-life is the time required for the number of radioactive nuclei to decrease to one-half the original number.

In general, after n half-lives, the number of undecayed radioactive nuclei remaining is

N = N0

2n

where n = t

T1

2

N

t

T12

T12

T12

T12

T12

N0

32

N0

16

N0

8

N0

4

N0

2

N0



Example 4.1: Cobalt Co2760 has a half-life of 5 years. If we start with a 100-gram sample of cobalt, how

much cobalt remains after 20 years?

Example 4.2: The isotope carbon-14, C614 , is radioactive and has a half-life of 5,730 years. If you start

with a sample of 1,000 carbon-14 nuclei, how many nuclei will still be undecayed in 25,000 years?



5. NUCLEAR STABITITY .

You might expect that the very large repulsive Coulomb forces between the closepacked protons in a nucleus should cause the nucleus to fly apart. Because that does not happen, there must be a counteracting attractive force. The nuclear force is an attractive force that acts between all nuclear particles. The protons attract each other by means of the nuclear force, and, at the same time, they repel each other through the Coulomb force. The nuclear force also acts between pairs of neutrons and between neutrons and protons. The nuclear force dominates the Coulomb repulsive force within the nucleus, so stable nuclei can exist.

Binding energy (B.E.).

The binding energy is the energy that must be added to a nucleus to break it apart into its components or the magnitude of the energy by which the nucleons are bound together.

The binding energy of any nucleus can be calculated by using the conservation of energy and the Einstein mass–energy equivalence relationship (E = mc2)



6. NUCLEAR REACTIONS .

Nuclear reactions is a process in which a nucleus changes its composition or energy level which may occur spontaneously (such as the decay of unstable nuclei) or by bombarding nucleus with energetic particles. Balancing nuclear equations.

As a general rule in any nuclear reaction, - the sum of the mass numbers must be the same on both sides of the equation - the sum of the atomic numbers must be the same on both sides of the equation.

Example 6.1: The element tritium H13 is combined with another element to form helium He2

4 and a

neutron, along with the release of energy. The equation for this fusion reaction is

H13 + XZ

A → He24 + n0

1

What is the unknown element X?

Example 6.2: A fission reaction occurs when uranium He92235 absorbs a slow neutron and then splits into

xenon and strontium, releasing three neutrons and some energy. The equation for this

fission reaction is

U92235 + n0

1 → Xe54140 + SrZ

A + 3 n01 + energy

What are Z and A for strontium?



Types of nuclear reactions.

• Fission Nuclear fission occurs when a heavy nucleus splits into two smaller nuclei. The fission process

often releases a very large amount of energy. The binding energy per nucleon after the reaction is greater than before.

For example, nuclear fission in the nuclear reactors

Nuclear equation: U 92235 + n → Ba56

141

0

1 + Kr + 3 n0

136

92 + 200 MeV

Chain reactions

Chain reaction refers to a process in which neutrons released in fission produce an additional fission in further nucleus.



• Fusion Nuclear fusion occurs when two small nuclei combine to form a heavier nucleus. Fusion

reactions release energy for the same reaction as fission reactions. The binding energy per nucleon after the reaction is greater than before.

For example, nuclear fusion in the sun

Nuclear equations: H11 + H1

1 → H + e+10 + ν

1

2

H12 + H1

1 → He + γ2

3

He23 + He2

3 → He + 2 H11

2

4

Combined equation: 4 H11 → He + 2 e + 2+1

0ν + 2γ + 2

2

46 MeV



xProblemsx

Problem 1: The neutral element magnesium Mg1224 has

a) 12 protons, 12 electrons, and 24 neutrons. b) 12 protons, 12 electrons, and 12 neutrons. c) 24 protons, 24 electrons, and 12 neutrons. d) 24 protons, 12 electrons, and 12 neutrons. e) 12 protons, 24 electrons, and 24 neutrons.

Problem 2: All isotopes of uranium have

a) the same atomic number and the same mass number. b) different atomic numbers but the same mass number. c) different atomic numbers and different mass numbers. d) the same atomic number but different mass numbers. e) no electrons.

Problem 3: Six protons and six neutrons are brought together to form a carbon nucleus, but the mass

of the carbon nucleus is less than the sum of the masses of the individual particles that make up the nucleus. This missing mass, called the mass defect, has been a) converted into the binding energy of the nucleus. b) given off in a radioactive decay process. c) converted into electrons. d) converted into energy to hold the electrons in orbit. e) emitted as light.

Problem 4: The isotope of thorium Th90234 undergoes alpha decay according to the equation

Th90234 → XZ

A + He24

The element X is

a) U92238

b) Ra88230

c) Pu94236

d) Ra88238

e) U92232



Problem 5: The isotope of cobalt Co2760 undergoes beta decay according to the equation

Co2760 → XZ

A + e-10

The element X is

a) Fe2660

b) Mn2556

c) Ni2860

d) Cu2960

e) Co2761

Problem 6: The half-life of a certain element is 4 years. What fraction of a sample of that isotope will remain after 12 years?

a) 1

2

b) 1

3

c) 1

4

d) 1

8

e) 1

12

Problem 7: Consider the following nuclear equation:

U 92235 + n → Ba56

13901 + Kr + 3 n0

13694

This equation describes the process of a) radioactivity b) fission c) fusion d) electron energy level transition e) reduction and oxidation

References

1. Young, H. D., Freedman, R. A. (2016). Sears and Zemansky’s University Physics with Modern Physics. (14th ed). Pearson.

2. Serway, R. A., Jewett, Jr., J. W. (2018). Physics for Scientists and Engineers with Modern Physics. (10th ed). Cengage learning.

3. Physics I, โดย ขวัญ อารยะธนิตกุล, นฤมล เอมะรัตต์, รัชภาคย์ จิตต์อารี และ เชิญโชค ศรขวัญ, 9th edition, ภาควิชาฟิสิกส์ คณะวิทยาศาสตร์ มหาวิทยาลัยมหิดล, พ.ศ. 2558.

4. Physics II, โดย ขวัญ อารยะธนิตกุล, นฤมล เอมะรัตต์, รัชภาคย์ จิตต์อารี และ เชิญโชค ศรขวัญ, 9th edition, ภาควิชาฟิสิกส์ คณะวิทยาศาสตร์ มหาวิทยาลัยมหิดล, พ.ศ. 2558.

5. สถาบันส่งเสริมการสอนวิทยาศาสตร์และเทคโนโลยี. (2562). หนังสือเรียนรายวิชาพื ้นฐานวิทยาศาสตร์ วิทยาศาสตร์กายภาพ เล่ม 2. (พิมพ์ครั้งที่ 1). กรุงเทพฯ: โรงพิมพ์ สกสค. ลาดพร้าว.

Biography

Name Date of Birth Place of Birth

Ariyaphol Jiwalak 4 July 1992 Chanthaburi, Thailand

Educational Background Mahidol University, 2011-2014 Bachelor of Science (Physics)

Mahidol University, 2015-2018 Master of Science (Physics, International Program) Royal Government of Thailand Scholarship

Development and Promotion of Science and Technology Talent Project (DPST) by the Institute for the Promotion of Teaching Science and Technology (IPST)

Home Address 5/371 Prachachuen Road, Bangsue Sub-district, Bangsue District, Bangkok, 10800

Tel. 089-7525223 E-mail: [email protected] Publication / Presentation Jiwalak A., Emarat N. and Arayathanitkul K., Students' physics laboratory skill in

measurement and uncertainty. Siam Physics Congress, 20-22 May 2015, Krabi, Thailand.

Jiwalak A., Emarat N. and Arayathanitkul K., An activity sheet for teaching double-slit interference. Siam Physics Congress, 21-23 May 2018, Phitsanulok, Thailand.

The Demonstration School of Suan Sunandha Rajabhat University

1 U-Thong nok Road, Dusit, Bangkok 10300 Thailand

www.sd.ssru.ac.th

www.facebook.com/sd.ssru

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