1.0 BASIC CONCEPTS ON STATICS

What are the seven fundamental quantities of measurement?

Here are the seven fundamental quantities. I also included their definitions and SI units.

length - meter (m) - the measurement or extent of something from end to end.

mass - kilogram (kg) - a coherent body of matter with no definite shape.

time - second (s) - the indefinite continued progress of existence and events.

electric current - ampere (A) - flow of electric charge.

thermodynamic temperature - kelvin (K) - A measure proportional to the thermal energy of a given body at equilibrium.

amount of substance - mole (mol) - the number of specified group of entities present in a substance.

luminous intensity - candela (cd) - an expression of the amount of light power emanating from a point source within a solid angle of one steradian.. (The steradian (symbol: sr) is the SI unit of solid angle)

Define concept of:

Mechanics (Greek Μηχανική) is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The discipline has its roots in several ancient civilizations (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and especially Newton, laid the foundation for what is now known as classical mechanics.

The system of study of mechanics is shown in the table below:

Classical mechanics

Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass), space can be explored via measurement and experiment.

Time quantifies or measures the interval between events, or the duration of events.

Mass is the quantity of inertia possessed by an object

Force The capacity to do work or cause physical change; energy, strength, or active power

Particles A very small piece or part; a tiny portion or speck.

Rigid Body An idealized extended solid whose size and shape are definitely fixed and remain unaltered when forces are applied.

Scalar & Vector

Scalar A physical quantity that can be described completely in terms of its magnitude (e.g. length, mass, speed, time, and volume).

vector: quantity possessing both magnitude and direction, represented by line segment of specific length and direction

Free Vector:(mechanics) A vector whose direction in space is prescribed but whose point of application and line of application are not prescribed.

Vector 

A free vector is a vector whose value is not changed by an arbitrary, parallel displacement. An example of a free vector is the velocity of motion of a material point.

A vector is called sliding if its value is not changed by any parallel displacement along its line of action. An example of a sliding vector is a force acting on an absolutely rigid body (two forces that are equal and located on the same straight line produce identical actions on an absolutely rigid body).

A bound vector has its point of application fixed. For example, a force applied to a certain point of an elastic body is a bound vector. The properties of free vectors are studied in vector algebra. The general concept of a vector as an element of a so-called vector space is defined axiomatically.

Newton's First Law

In a previous chapter of study, the variety of ways by which motion can be described (words, graphs, diagrams, numbers, etc.) was discussed. In this unit (Newton's Laws of Motion), the ways in which motion can be explained will be discussed. Isaac Newton (a 17th century scientist) put forth a variety of laws that explain why objects move (or don't move) as they do. These three laws have become known as Newton's three laws of motion. The focus of Lesson 1 is Newton's first law of motion - sometimes referred to as the law of inertia.

Newton's first law of motion is often stated as An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

 

There are two parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects. The two parts are summarized in the following diagram.

 The behavior of all objects can be described by saying that objects tend to "keep on doing what they're doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this same state of rest. If in motion with an eastward velocity of 5 m/s, they will continue in this same state of motion (5 m/s, East). If in motion with a leftward velocity of 2 m/s, they will continue in this same state of motion (2 m/s, left). The state of motion of an object is maintained as long as the object is not acted upon by an unbalanced force. All objects resist changes in their state of motion - they tend to "keep on doing what they're doing."

 Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when:

the container was at rest and you attempted to move it the container was in motion and you attempted to stop it the container was moving in one direction and you attempted to change its

direction.

The water spills whenever the state of motion of the container is changed. The water resisted this change in its own state of motion. The water tended to "keep on doing what it was doing." The container was moved from rest to a high speed at the starting line; the water remained at rest and spilled onto the table. The container was stopped near the finish line; the water kept moving and spilled over container's leading edge. The container was forced to move in a different direction to make it around a curve; the water kept moving in the same direction and spilled over its edge. The behavior of the water during the lap around the track can be explained by Newton's first law of motion.

 

Everyday Applications of Newton's First Law

There are many applications of Newton's first law of motion. Consider some of your experiences in an automobile. Have you ever observed the behavior of coffee in a coffee cup filled to the rim while starting a car from rest or while bringing a car to rest from a state of motion? Coffee "keeps on doing what it is doing." When you accelerate a car from rest, the road provides an unbalanced force on the spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While the car accelerates forward, the coffee remains in the same position; subsequently, the car accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when braking from a state of motion the coffee continues forward with the same speed and in the same direction, ultimately hitting the windshield or the dash. Coffee in motion stays in motion.

Have you ever experienced inertia (resisting changes in your state of motion) in an automobile while it is braking to a stop? The force of the road on the locked wheels provides the unbalanced force to change the car's state of motion, yet there is no unbalanced force to change your own state of motion. Thus, you continue in motion, sliding along the seat in forward motion. A person in motion stays in motion with the same speed and in the same direction ... unless acted upon by the unbalanced force of a seat belt. Yes! Seat belts are used to provide safety for passengers whose motion is governed by Newton's laws. The seat belt provides the unbalanced force that brings you from a state of motion to a state of rest. Perhaps you could speculate what would occur when no seat belt is used. Sometimes referred to as the law of inertia

Newton's Second Law

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

 

Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:

a = Fnet / m

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

Fnet = m * a

In this entire discussion, the emphasis has been on the net force. The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force. The NET FORCE. It is important to remember this distinction.. The net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined.  

Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, the following unit equivalency can be written.

The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.

Newton's Third Law

A force is a push or a pull upon an object that results from its interaction with another object. Forces result from interactions! As discussed in Lesson 2, some forces result from contact interactions (normal, frictional, tensional, and applied forces are examples of contact forces) and other forces are the result of action-at-a-distance interactions (gravitational, electrical, and magnetic forces). According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward

force on your body. There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces and are the subject of Newton's third law of motion. Formally stated, Newton's third law is:

For every action, there is an equal and opposite reaction.

The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on

the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite action-reaction force pairs.

A variety of action-reaction force pairs are evident in nature. Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. But a push on the water will only serve to accelerate the water. Since forces result from mutual interactions, the water must also be pushing the fish forwards, propelling the fish through the water. The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is

opposite the direction of the force on the fish (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction force. Action-reaction force pairs make it possible for fish to swim.

Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. Since forces result from mutual interactions, the air must also be pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards). For every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force pairs make it possible for birds to fly.

Consider the motion of a car on the way to school. A car is equipped with wheels that spin in a clockwise direction. As the wheels spin clockwise, they grip the road and push the road backwards. Since forces result from mutual interactions, the road must also be pushing the wheels forward. The size of the force on the road equals the size of the force on the wheels (or car); the direction of the force on the road (backwards) is opposite the direction of the force on the wheels (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force pairs make it possible for cars to move along a roadway surface.

 

 

 

Introduction

SI base units

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent, as given in Table 1.

Table 1.  SI base unitsSI base unit

Base quantity Name Symbol

length meter m

mass kilogram       kg

time second s

electric current ampere A

thermodynamic temperature       kelvin K

amount of substance mole mol

luminous intensity candela cd

Definitions of the SI base units

 Unit of length   meter The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

 Unit of mass  kilogram   The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

 Unit of time  second The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

 Unit of electric current  

ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.

 Unit ofthermodynamic  temperature

kelvin The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

 Unit of mole 1. The mole is the amount of substance of a system which

amount ofsubstance

contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

 Unit ofluminousintensity

candela The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

SI derived units

Defined in terms of the seven base quantities via a system of quantity equations..

SI derived unit

Derived quantity Name Symbol

area square meter m2

volume cubic meter m3

speed, velocity meter per second m/s

acceleration meter per second squared   m/s2

wave number reciprocal meter m-1

mass density kilogram per cubic meter kg/m3

specific volume cubic meter per kilogram m3/kg

current density ampere per square meter A/m2

magnetic field strength   ampere per meter A/m

amount-of-substance concentration mole per cubic meter mol/m3

luminance candela per square meter cd/m2

mass fractionkilogram per kilogram, which may be represented by the number 1

kg/kg = 1

Derived quantity Name Symbol   Expression  in terms of  

Expressionin terms of

other SI units

SI base units

plane angle radian (a) rad   - m·m-1 = 1 (b)

solid angle steradian (a) sr (c)   - m2·m-2 = 1 (b)

frequency hertz Hz   - s-1

force newton N   - m·kg·s-2

pressure, stress pascal Pa N/m2 m-1·kg·s-2

energy, work, quantity of heat  

joule J N·m m2·kg·s-2

power, radiant flux watt W J/s m2·kg·s-3

electric charge, quantity of electricity

coulomb C   - s·A

electric potential difference,electromotive force

volt V W/A m2·kg·s-3·A-1

capacitance farad F C/V m-2·kg-1·s4·A2

electric resistance ohm V/A m2·kg·s-3·A-2

electric conductance

siemens S A/V m-2·kg-1·s3·A2

magnetic flux weber Wb V·s m2·kg·s-2·A-1

magnetic flux density

tesla T Wb/m2 kg·s-2·A-1

inductance henry H Wb/A m2·kg·s-2·A-2

Celsius temperature

degree Celsius

°C   - K

luminous flux lumen lm cd·sr (c) m2·m-2·cd = cdilluminance lux lx lm/m2 m2·m-4·cd = m-2·cdactivity (of a radionuclide)

becquerel Bq   - s-1

absorbed dose, specific energy (imparted), kerma

gray Gy J/kg m2·s-2

dose equivalent (d) sievert Sv J/kg m2·s-2

catalytic activity katal kat s-1·mol

Table 3.  SI derived units with special names and symbols

(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

SI prefixes

The 20 SI prefixes used to form decimal multiples and submultiples of SI units are given in Table 5.

Table 5.  SI prefixes

Factor Name  Symbol

1024 yotta Y

1021 zetta Z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

101 deka da

  Factor Name  Symbol

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro µ

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names of Table 5 are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.

Example 1:10-6 kg = 1 mg (one milligram), but not 10-6 kg = 1 µkg (one microkilogram)

Example 2:Consider the earlier example of the height of the Washington Monument. We may write hW = 169 000 mm = 16 900 cm = 169 m = 0.169 km using the millimeter (SI prefix milli, symbol m), centimeter (SI prefix centi, symbol c), or kilometer (SI prefix kilo, symbol k).