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INTRODUCTION TO PHYSICS
What is physics? The word physics comes from the Greek word “physis” which means “nature”. Physics is a branch of natural science that deals with the study of matter and how it is related to energy. Natural science deals with the physical and natural world. Matter refers to anything which occupies space and has weight. Energy is the ability of the body to do work. Branches of physics and what they deal with Physics is divided into several branches or themes as indicated in Table below. Each branch deals with different aspects of Physics. THE BRANCHES OF PHYSICS WHAT IT DEALS WITH 1 Mechanics It deals with the behaviour of physical objects or particles under the action of forces. 2 Heat It deals with heat, as a form of energy, its transmission and applications. 3 Light It deals with the nature of light and its properties, how it travels and its applications. 4 Electricity It deals with the production of electricity, its transmission and applications. 5 Magnetism It deals with the properties of magnets, their production, properties and applications. 6 Wave motion It deals with the transfer of energy from one point to another without movement of substances. 7 Modern physics It deals with recent developments in physics and their applications The importance of studying physics Physics is important for good health Machines, such as those used in hospitals to treat cancer and those used to study the brain, broken bones and babies developing in the womb, are made using knowledge gained from the study of physics. Physics makes communication easy Physicists play an important role in the manufacture of computers, radios, televisions and mobile phones. These make communication easy. The physics laboratory Most of the practical works in science, for example, experiments, tests, observations or investigations are conducted in a special place called a laboratory. A laboratory is a building, part of a building or other place specifically designed for scientific work. It contains many pieces of apparatus and materials for practical use. Apparatus is equipment or tools needed for a particular scientific activity or purpose. We use apparatus when we are carrying out an experiment. Experiment is a scientific step-by-step process undertaken to make a discovery, test a proposed law or theory, or demonstrate a known fact.
UNITS AND MEASUREMENTS
Introduction The physical properties of matter can be classified as intensive (do not depend on quantity of matter) and extensive (depend on the quantity of matter). Estimation and measurement The difference between a measurement and an estimation is that a measurement is an exact data while an estimation is a guess as to what something may measure. For example, you can use a ruler to get the exact measurements of a piece of paper. However, if you don't have a ruler, you can make an educated guess as to what the paper's length and width measurements may be. FUNDAMENTAL AND DERIVED UNITS However different countries or even different parts of a country may follow different standards that specify a particular unit for every physical quantity. It is worth mentioning that various international, national and local standards may also follow different units for same physical quantity. Such variety in standardization paved the way for evolution of one internationally acceptable standard of measurement, known as Metric System or International System of Units (SI system). Entire metric system is composed of two different types of units, namely, fundamental units and derived units. Among all such units specified in SI System, there exist only seven independent units and all other units are formed by combining these
seven independent units. These seven independent units are called Fundamental Units (or Base Units ); whereas all other units that are obtained or derived from fundamental units are called Derived Units. Differences between fundamental unit and derived unit Fundamental Unit Derived Unit Fundamental units are all those units which are independent of any other unit (including themselves). Derived units are all those units which are obtained by multiplying and/or dividing one or more fundamental units with or without introducing any other numerical factor. Fundamental units cannot be further reduced to elementary level; in fact, these are elementary units. Derived units can be reduced to its elementary level, which are composed of fundamental units. Fundamental units cannot be expressed in terms of derived units. Derived units can be expressed in terms of fundamental units. Only seven fundamental units exist in Metric System or SI system. There exist a large number of derived units in Metric System. Examples of seven fundamental units, their abbreviation and corresponding physical properties are as follows: Length (Meter, m) Mass (Kilogram, kg) Time (Second, s) Temperature (Kelvin, K) Amount of substance (Mole, mole) Electric current (Ampere, A) Luminous intensity (Candela, cd) Examples of few derived units along with corresponding physical properties are: Velocity (m/s) Acceleration (m^2 /s) Momentum (kg-m/s) Force (N) Density (kg/m^3 ) Heat (J) Energy (J) Power (W), etc. Fundamental quantities are the basic quantities that are independent of other quantities. It is the basic units upon which other units depend. Derived quantities and unities are those obtained by simple combination of fundamental quantities and units.
- Measurement: The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.
- Unit: The unit of a physical quantity is an arbitrarily chosen standard which is widely accepted by the society and in terms of which other quantities of similar nature may be measured.
- Dimensions: The dimensions of a physical quantity are the powers to which the fundamental units of mass, length and time must be raised to represent the given physical quantity.
- Dimensional Formula: The dimensional formula of a physical quantity is an expression telling us how and which of the fundamental quantities enter into the unit of that quantity. It is customary to express the fundamental quantities by a capital letter, e.g., length (L), mass (AT), time (T), electric current (I), temperature (K) and luminous intensity (C). We write appropriate powers of these capital letters within square brackets to get the dimensional formula of any given physical quantity.
- Error: The measured value of the physical quantity is usually different from its true value. The result of every measurement by any measuring instrument is an approximate number, which contains some uncertainty. This uncertainty is called error. Every calculated quantity, which is based on measured values, also has an error.
- Dimensions of physical quantities: The dimensions of a physical quantity indicate how it is made up in terms of the SI base quantities. In other words, the physical quantity is said to have been expressed in terms of dimensions of the three fundamental units: L ength (L), M ass (M), and T ime (T) Examples of derived quantities and units
HOW TO READ VERNIER CALIPER MEASUREMENT
In order to read the measurement readings from vernier caliper properly, you need to remember two things before we start. For example, if a vernier caliper output a measurement reading of 2.13 cm , this means that: The main scale contributes the main number(s) and one decimal place to the reading (E.g. 2.1 cm, whereby 2 is the main number and 0.1 is the one decimal place number) The vernier scale contributes the second decimal place to the reading (E.g. 0.03 cm) To obtain the main scale reading: Look at the image above, 2.1 cm is to the immediate left of the zero on the vernier scale. Hence, the main scale reading is 2.1 cm To obtain the vernier scale reading: Look at the image above and look closely for an alignment of the scale lines of the main scale and vernier scale. In the image above, the aligned line corresponds to 3. Hence, the vernier scale reading is 0.03 cm. In order to obtain the final measurement reading , we will add the main scale reading and vernier scale reading together. This will give 2.1 cm + 0.03 cm = 2.13 cm. Use the following formula : Obtained reading = Main scale reading + Vernier scale reading Let’s go through another example to ensure that you understand the above steps: Main scale reading: 10.0 cm (Immediate left of zero). Vernier scale reading: 0.02 cm (Alignment of scale lines)
Measurement reading: 10.02 cm
Exercise: What are the readings of the vernier calipers below?
HOW TO READ MICROMETER SCREW GAUGE MEASUREMENT
The above image shows a typical micrometer screw gauge and how to read it. Steps: To obtain the first part of the measurement: Look at the image above, you will see a number 5 to the immediate left of the thimble. This means 5.0 mm. Notice that there is an extra line below the datum line, this represents an additional 0.5 mm. So, the first part of the measurement is 5.0 + 0.5 = 5.5 mm. To obtain the second part of the measurement: Look at the image above, the number 28 on the rotating vernier scale coincides with the datum line on the sleeve. Hence, 0.28 mm is the second part of the measurement. You just have to add the first part and second part of the measurement to obtain the micrometer reading: 5.5 +
0.28 = 5.78 mm.
To ensure that you understand the steps above, here’s one more example:
First part of the measurement: 2.5 mm. Second part of the measurement: 0.38 mm. Final measurement: 2.88mm
Exercise: What are the readings of the vernier calipers below?
INTRODUCTION TO MOTION When we talk about motion or rest it is with reference to some point known as the origin. So, now with respect to the change in the position we have two quantities which can be used to describe that change in position. They are distance and displacement. So now the question is, what is the difference between the two? Talking about distance, it is defined as the total path length covered during the motion. It can be represented only by magnitude. On the other hand, displacement is the shortest distance between the initial and final position. It requires both magnitude and direction for complete representation. What is Motion? We can define motion as the change of position of an object with respect to time. A book falling off a table, water flowing from the tap, rattling windows, etc all exhibit motion. Even the air that we breathe exhibits motion! Everything in the universe moves. We live in a universe that is in continual motion. The fundamental particle of a matter that is the atom is in constant motion too. Every physical process in the universe is composed of motion of some sort. The motion can either be swift or slow, but motion exists. It is important that we give due attention to the study of motion because of its importance in the physical world. Motion is mainly described in terms of the following terms: Distance Displacement Speed, s =
distance
time
Time Types Of Motion We might have noticed that different objects move differently. Some objects move in a curved path, some in a straight path and a few others in a different way. According to the nature of the movement, motion is classified into three types as follows: Linear Motion Rotary Motion Oscillatory Motion Linear Motion In linear motion, the particles move from one point to another in either a straight line or a curved path. The linear motion depending on the path of motion is further divided as follows Rectilinear Motion – The path of the motion is a straight line. Curvilinear Motion – The path of the motion is curved. A few examples of linear motion are the motion of the train, football, the motion of a car on the road, etc. Rotatory Motion Rotatory motion is the motion that occurs when a body rotates on its own axis. A few examples of the rotatory motion are as follows: The motion of the earth about its own axis around the sun is an example of rotary motion. While driving a car, the motion of wheels and the steering wheel about its own axis is an example of rotatory motion. Oscillatory Motion
(−2.5kg ∗ 20ms) = (F)(0.2s) (−50kg ⋅ ms) = (F)(0.2s) −50/0.2 = F −250N=F
An 800 kg car strikes a 1200 kg car from behind. The bumpers lock and they move forward together. If their new
final velocity is equal to 15 ms, what was the initial velocity of the first car?
Susan pushes a car 1100 kg with 50 N of force. How long does she need to push it to get it to a velocity of 6 ms if it
starts at rest and there is no friction?
A 2.2kg hammer moving with a velocity of 10 ms strikes a nail, after which the hammer has a velocity of 0 ms. If
the hammer strikes the nail with 180 N of force, how long were the two in contact?
What is Acceleration? Acceleration is defined as the rate of change of velocity with respect to time. The SI unit of acceleration is m/s^2. Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time. Acceleration formula is given as: acceleration= (final velocity) − (initial velocity) ÷ time acceleration =
Final Velocity − Initial Velocity
Time
acceleration, a =
V − u
t
Where, a is the acceleration in ms- vf is the final velocity in ms- u is the initial velocity in ms- t is the time interval in s Δv is the small change in the velocity in m.s- DISTANCE VS DISPLACEMENT Distance travelled by an object is the length of path taken. Distance is how far something travels. SI unit of speed is metre (m). It is a Scalar quantity. Speed Can never be negative and distance travelled will never decrease Displacement is the shortest distance from the initial to the final position of an object. Displacement is how far something travels in a given direction. SI unit of displacement is metre (m). It is a Vector quantity. It Can be negative Distinguishing Between Distance and Displacement If you have problems grasping the difference in concept of displacement and distance travelled, please study the example below. Consider the diagram above: Difference between distance and displacement: If an object started travelling from B to C and ends at D, distance travelled is BC + CD. Displacement is BD. Displacement can be ZERO: If the object started travelling from B to C to D and ends at B, distance travelled is BC + CD + DB. Displacement is ZERO. (The object ends at the same place it started) Displacement can be NEGATIVE: If the object travels from B to A, the displacement is negative. By CONVENTION, the direction towards the right and top are positive. A way to remember: Go right = positive, go left = negative. Speed vs Velocity To understand the difference between speed and velocity, you will need to grasp the difference between distance and displacement,
Speed is the distance moved per unit time. Speed is How fast something is moving.
SI unit is metre per second (ms−1) Scalar quantity Equation: Speed =
d
t
, where d is distance travelled and t is time taken Average speed, s =
total distance travelled
total time taken
, Speed is measured by a speedometer
Velocity (v) of an object is the rate of change of displacement with respect to time. Velocity is How fast something
is moving in a given direction
SI unit is metre per second (ms−1) Vector quantity The magnitude of velocity is speed v=
s
t
, where s is displacement and t is time taken Average velocity, v =
total disp lacement travelled
total time taken
, As velocity is a vector quantity, you
have to specify its magnitude and direction to completely describe it. Acceleration Acceleration of an object is the rate of change of velocity with respect to time. SI unit is metre per second square or metre per second per second (ms−2). Acceleration is the rate at which the velocity changes during a given amount of time. Acceleration is Vector quantity a =
v − u
t
where v is final velocity, u is initial velocity and t is time taken. If the velocity of an object increases , the object is undergoing acceleration. Hence, if the velocity of an object decreases , it is undergoing deceleration. If the velocity of the object is constant , the acceleration is zero. An object is said to be undergoing uniform acceleration when there is a constant change in velocity per unit time. Examples 1: A bus starts from rest and achieves a velocity of 20ms−1 in 10seconds while moving to the right. Calculate its average acceleration.
Average acceleration: a =
v − u
t =^
10 =^ 2ms
− Example 2: A car travelling westwards at 30ms−1^ suddenly comes to a halt in 5s. Find its average acceleration.
a =
v − u
t =^
5 =^
=−6ms−2^ towards the west the negative sign indicates retardation Example 3: A body of mass 2kg is at rest. What should be the magnitude of force which will make the body move with a speed of 30 m/s at the end of 1s? Answer: Mass of the body = 2kg, Initial velocity, u = 0, Final velocity, v = 30 m/s, Time, t = 1s Acceleration, a = (v-u)/t = 30 m/s^2 Force = ma = 30 x 2 = 60N Example 4: A body of mass 5kg is moving with a velocity of 10 m/s. A force is applied to it so that in 25 seconds, it attains a velocity of 35 m/s. Calculate the value of the force applied. Answer: Mass of the body = 5kg, Initial velocity, u = 10 m/s, Final velocity, v = 35 m/s, Time, t = 25s
Acceleration, a = (v-u)/t = 1 m/s^2
Force = ma = 5N Example 5: A boy jogs around his neighbourhood for 1.5 hours as shown in the following diagram:
When the object is stationary, it is a straight horizontal line at 0. When the object is undergoing uniform motion, it is a straight horizontal line at vms−1, where v is the velocity of the object. For straight line with positive gradient , it means that the object is accelerating. For straight line with negative gradient , it means that the object is decelerating. For curves, it means that the acceleration of the object is changing. The area under the graph is the change in the displacement of the object. VELOCITY-TIME GRAPHS Describing Velocity-Time Graphs: When describing the motion of an object try to be as detailed as possible. For instance... During Part A of the journey the objects velocity increases by 8m/s in 4s. It is accelerating at a rate of 2ms- During Part B of the journey the object travels at a constant speed of 8ms-1^ for 3s During Part C of the journey the objects velocity decreases by 8m/s in 3s. It is decelerating at a rate of -2.7ms- Calculating Acceleration from a Velocity-Time Graph The average acceleration can be calculated for any part of a journey by taking the change in velocity and dividing by the change in time for that part of the journey.
Calculating the Distance Travelled from a Velocity-Time Graph The total distance travelled by an object can be determined by calculating the area underneath the velocity time graph. Start by dividing the graph into sections that consist of simple triangles and rectangles as shown above in green, red and purple. Calculate the area of each shape as shown below. You can then simply add the areas together and the total area represents the total distance travelled. E.g., the graph above has a total area of: (
× 10 × 20 ) + ( 20 × 20 ) + (
× 40 × 20 ) = 900.
Therefore, the total distance travelled was 900m. Average acceleration The average acceleration over a period of time is defined as the total change in velocity in the given interval divided by the total time taken for the change. For a given interval of time, it is denoted as ā. Mathematically, Where v 2 and v 1 are the instantaneous velocities at time t 2 and t 1 and ā is the average acceleration. Velocity-Time Graph Question A car starts from rest and accelerates uniformly until it reaches a velocity of 30ms-1^ after 5s. It travels with uniform velocity for 15s and then brought to rest in 10s with a uniform retardation. Determine: (a) the acceleration of the car (b) the retardation (c) the distance covered after 5s (e) the total distance covered. 10 30 70 30 V(ms-1) T(s) 5 s
s
s v t 30
(a) V = u + at V = u – at 5 = 30 – 5t t = 5s (b) v^2 = u^2 + 2as 52 = 302 – 2 x 5 x s S = 87.5m
- A brick of mass 0.8 kg accidentally dropped from a high scaffolding. It reaches the ground with a kinetic energy of 240 J. How high is the scaffolding? (Take acceleration due to gravity, g, to be 10ms−2.) Solution mgh = ½ mv^2 0.8 x 10 x h = 240 h = 240/8 = 30m
FORCE
Force is defined as the push or pull exerted on an object which produces acceleration in an object. Newton is the SI unit of force. Following are the three changes that can be observed on a body when force is applied: Change in the direction of motion of the body Change in the speed of the body Change in the shape of the body Force can be either balanced or unbalanced. Force is said to be balanced when they cancel out each other such that the resultant force is zero. When the force acting on a body moves the body in the direction of force which is greater than the other, it is known as unbalanced force. What is force? Force is strength or energy applied towards any object for physical action or any movement. A force is a push or pull resulting due to the interaction between two objects. Force is external and results only when there is interaction between objects. Different types of forces and their examples: Force can be classified into two broad categories
1. Contact forces These are those types of forces when two objects interact with each other; they have a physical contact with each other. Types of contact forces are: Frictional force; Tension force; Normal Force; Air Resistance Force, Applied Force, Spring Force. I. Frictional force: As an object moves across a surface it causes friction. II. Tension force: A force that is transmitted through a string, rope, cable or wire when it is pulled tightly by the object on the opposite end is a tension force. III. Normal force: This is the force exerted upon an object that is in contact with another stable object. IV. Air Resistance force: This is a frictional force applied on objects when they are in air. Example- An airplane or a parachute. V. Applied force: A force with which an object has been pushed or pulled. VI. Spring force: It is the force which results when a spring is stretched or compressed. 2. Action at a distance force: These types of forces happen when two interactive objects are not in physical contact with each other; yet they are able to push or pull. Types of Action at a distance force are: Gravitational force, Electrical force and Magnetic forces. I. Gravitational force: This is the force by which the Earth or moon or other massively huge objects attract another object towards them. II. Electrical force: It is one of the fundamental forces of the Universe. It is a force that exists between all charged particles. III. Magnetic force: This is a push or pull exerted by a magnet. The force of attraction between an object and a magnet is called magnetism. Effects of balanced and unbalanced forces on motion
When balanced forces are exerted on a stationary object, it does not move. If balanced forces are exerted on a moving object, its speed will remain unchanged. When unbalanced forces are exerted on a moving object, it will either move more quickly (accelerates) or less quickly (decelerates) depending on the magnitudes of the resultant force. Balanced and Unbalanced Forces When two forces act on an object the net effect will depend on the size and direction of each of the forces. When we place a book on the table, the weight of the book acts down due to gravity, and an equal force acts upwards. The upward force is due to a push by the table. The forces are equal in size and act in opposite directions. These forces are said to be balanced. The shape or position of the book does not change. The forces acting on the moving container are unbalanced. When a crane raises a container, it must exert an upward force greater than the weight of the container. The forces act in opposite directions but they are not equal in size. These forces are said to be unbalanced. Unbalanced forces cause changes in the shape, position or speed of an object. Suppose there is a tug-of-war and there are two teams pulling each other as shown below. What do you say about the teams? Which team will move? In which direction will it move? You can try this activity using a rope. The effect of the above forces is called resultant force.
- If the forces are acting in the same direction, the resultant is obtained by adding the forces.
- If the forces are acting in opposite direction, the resultant force is obtained by subtraction
- If the forces are acting on a body at right angles, then the resultant is obtained using Pythagoras theorem. Do you remember Pythagoras theorem? Intermolecular forces Have you ever noticed that while washing glass utensils water remains attached to the utensils or small insects can walk on water because their weight is not enough to penetrate the surface? These and other phenomena result from the forces within substances. These forces are called intermolecular forces and have effects and applications. Intermolecular forces are forces that exist between molecules. The molecules may be of the same substance or of different substances. Inter molecular forces are cohesion force and adhesion force. (c) Cohesive force Cohesion is the force of attraction between the molecules of the same kind. Cohesive forces cause a tendency in liquids to resist separation of its particles. (d) Adhesion is the force of attraction between molecules of different substances. Adhesion causes the liquid to cling to the surface on which it rests.
FRICTION
When we throw a ball on the floor, it starts moving with some velocity. But ideally, no force should be acting in the direction of motion, and according to Newton’s first law, the ball should keep on rolling, but this does not happen. Instead, the ball stops after moving a certain distance, so a force must be acting on it. We call this force “friction.” What is Friction? Friction is defined as the resistance offered by the surfaces that are in contact when they move past each other. Friction provides traction that is needed to walk without slipping. Friction is helpful in most cases. However, they also offer a great measure of opposition to the motion. In addition, about 20 per cent of the engine power of automobiles is consumed in overcoming frictional forces in the moving parts. In the next section, let us go through some of these factors. Factors Affecting Friction Friction is a force that is dependent on external factors. Following are the two factors on which friction depends:
1. On the nature of the two surfaces that are in contact Friction is dependent on the smoothness or roughness of the two surfaces that are in contact with each other. When the surface is smooth, the friction between the two reduces as there is no much interlocking of irregularities taking place. While the surface is rough, friction increases. 2. On the force that is acting on these surfaces
Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. That is the net force was the result (or resultant) of adding up all the force vectors. During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. Observe the following summations of two force vectors: These rules for summing vectors were applied to free-body diagrams in order to determine the net force (i.e., the vector sum of all the individual forces). Sample applications are shown in the diagram below. There are a variety of methods for determining the magnitude and direction of the result of adding two or more vectors. The two methods that will be discussed in this lesson and used throughout the entire unit are: the Pythagorean theorem and trigonometric methods The Pythagorean Theorem The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other. The method is not applicable for adding more than two vectors or for adding vectors that are not at 90-degrees to each other. The Pythagorean theorem is a mathematical equation that relates the length of the sides of a right triangle to the length of the hypotenuse of a right triangle. To see how the method works, consider the following problem: Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement. This problem asks to determine the result of adding two displacement vectors that are at right angles to each other. The result (or resultant) of walking 11 km north and 11 km east is a vector directed northeast as shown in the diagram to the right. Since the northward displacement and the eastward displacement are at right angles to each other, the Pythagorean theorem can be used to determine the resultant (i.e., the hypotenuse of the right triangle). The result of adding 11 km, north plus 11 km, east is a vector with a magnitude of 15.6 km. Later, the method of determining the direction of the vector will be discussed.
Let's test your understanding with the following two practice problems. In each case, use the Pythagorean theorem to determine the magnitude of the vector sum. When finished, click the button to view the answer. Using Trigonometry to Determine a Vector's Direction The direction of a resultant vector can often be determined by use of trigonometric functions. Most students recall the meaning of the useful mnemonic SOH CAH TOA from their course in trigonometry. SOH CAH TOA is a mnemonic that helps one remember the meaning of the three common trigonometric functions - sine, cosine, and tangent functions. The Calculated Angle is Not Always the Direction The measure of an angle as determined through use of SOH CAH TOA is not always the direction of the vector. The following vector addition diagram is an example of such a situation. Observe that the angle within the triangle is determined to be 26.6 degrees using SOH CAH TOA. This angle is the southward angle of rotation that the vector R makes with respect to West. Yet the direction of the vector as expressed with the CCW (counter clockwise from East) convention is 206.6 degrees. Test your understanding of the use of SOH CAH TOA to determine the vector direction by trying the following two practice problems. In each case, use SOH CAH TOA to determine the direction of the resultant. When finished, click the button to view the answer.
