Engineering Statics ENGR 2301 Chapter 1 Introduction And Measurement What is Mechanics? • Mechanics is the science which describes and predicts the conditions of rest or motion of bodies under the action of forces. • Categories of Mechanics: - Rigid bodies - Statics - Dynamics - Deformable bodies - Fluids • Mechanics is an applied science - it is not an abstract or pure science but does not have the empiricism found in other engineering sciences. • Mechanics is the foundation of most engineering sciences and is an indispensable prerequisite to their study. 1 - 2 Fundamental Principles • Newton’s First Law: If the resultant force on a particle is zero, the particle will remain at rest or continue to move in a straight line. • Newton’s Second Law: A particle will have an acceleration proportional to a nonzero resultant applied force. • Parallelogram Law F ma • Newton’s Third Law: The forces of action and reaction between two particles have the same magnitude and line of action with opposite sense. • Newton’s Law of Gravitation: Two particles are attracted with equal and opposite forces, Mm GM • Principle of Transmissibility F G W mg, g r 2 R2 1 - 3 Significant Figures Scientific Notation • Leading or trailing zeroes can make it hard to determine number of significant figures: 2500, 0.000036 • Each of these has two significant figures • Scientific notation writes these as a number from 1-10 multiplied by a power of 10, making the number of significant figures much clearer: 2500 = 2.5 × 103 If we write 2.50x103, it has three significant figures 0.000036 = 3.6 x 10-5 Significant Figures Round-off error: The last digit in a calculated number may vary depending on how it is calculated, due to rounding off of insignificant digits Example: $2.21 + 8% tax = $2.3868, rounds to $2.39 $1.35 + 8% tax = $1.458, rounds to $1.46 Sum: $2.39 + $1.46 = $3.85 $2.21 + $1.35 = $3.56 $3.56 + 8% tax = $3.84 Numerical Accuracy • The accuracy of a solution depends on 1) accuracy of the given data, and 2) accuracy of the computations performed. The solution cannot be more accurate than the less accurate of these two. • The use of hand calculators and computers generally makes the accuracy of the computations much greater than the accuracy of the data. Hence, the solution accuracy is usually limited by the data accuracy. • As a general rule for engineering problems, the data are seldom known with an accuracy greater than 0.2%. Therefore, it is usually appropriate to record parameters beginning with “1” with four digits and with three digits in all other cases, i.e., 40.2 lb and 15.58 lb. 1 - 6 Chapter 1: U.S. Customary Units . The base U.S. customary units are the units of length, force and time. These units are the foot (ft), the pound (lb) and the second (s). The second (s) is same as corresponding SI unit. The foot is defined as 0.3048 m. The pound (lb) is defined as the weight of a platinum standard, called the standard pound, which is kept at the National Institute of Standards and Technology, outside Washington, the mass of which is 0.453 592 43 kg. Chapter 1: U.S. Customary Units . Since weight of a body depends on upon the earth gravitational attraction, which varies with location, the U.S. customary units do not form an absolute system of units. The standard pound (lb) needs to be placed at sea level and at a latitude of 45° to properly defined a force of 1 lb. On the other hand, SI system of units, the meter (m), the kilogram (kg), and the second (s) may be used anywhere on the earth. They may even be used on another planet. They will always have same significance. Hence, they are called absolute system of units. Chapter 1: U.S. Customary Units . The standard pound also serves as the unit of mass in commercial transactions in the United States, it can not be so used in engineering computations since it will not be consistent with Newton’s second law, F = ma. So, the unit of mass was derived from basic U.S. system of units. This unit of mass is called the slug. F = ma, therefore, 1 lb = (1 slug) (1 ft/s²). And 1 slug = (1 lb) ÷ (1 ft/s² ) = 1 lb · s²/ft . Since acceleration of gravity g is 32.2 ft/s², slug is a mass 32.2 times larger than the mass of standard pound (lb). Chapter 1: Other U.S. Customary Units . Other U.S. customary units frequently used are: mile (mi) = 5280 ft. inch (in) = 1/12 ft kilopound (kip) = force of 1000 lb ton = mass of 2000 lb. Note: In engineering computation, this must be converted into slugs. Conversion into basic units of feet, pounds, seconds and slug is often necessary in engineering computation. This is a very involved process in U.S. system of units than in SI system of units. E.G., to convert velocity of 30mi/h into ft/s, following steps are required: v = (30 mi/hr) (5280 ft/1 mi)(1h/3600s) = 44 ft/s Chapter 1: System of Units . International System Of Units (SI Units): The universal system used around the world except U.S.A. and a couple of other small countries. SI stands for System Universal, a French word translated in English. Four fundamental units, called Kinetic Units are units of length, time, mass and force. Three of these units (Length, Time and Mass) are defined arbitrarily and are referred to as basic units. The fourth one, the force, is defined by equation F = ma and hence called derived unit. Chapter 1: SI Units – Length and mass . Base unit of Length: The Meter: Originally defined as one ten-millionth A of the distance from the equator to either pole, is now defined as 1 650 earth 763.73 wavelengths of the orange-red light corresponding to a certain C transition in an atom of krypton-86. equator B This was changed once again in 1983 to: “The meter is the length of path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second. Base unit of mass: The Kilogram originally defined as equal to mass of the 0.001 m³ of water is now defined as mass of a platinum-iridium standard kept at the International Bureau of Weights and Measures at Serves, near Paris, France. Chapter 1: SI Units -- Time . Base unit of Time: The Second: Originally defined as 1/86 400 of the mean solar day, is now defined as the duration of 9 192 631 770 cycles of the radiation corresponding to the transition between two levels of the fundamental state of the cesium-133 atom. Chapter 1: SI Units -- Force . Base unit of Force: The Newton(N): The unit of force is a derived unit. It is defined as the force which gives an acceleration of 1 m/s² to a mass of 1 kg. As we know from Newton’s second fundamental law, F = ma . So, 1 N = (1 kg ) (1 m/s² ) = 1 kg · m/s² Chapter 1: SI Units –Weight . Weight of a body: It is the force of gravity exerted on body. Like any other force, should be expressed in Newtons, not in kg. W = mg . I.E., W = ( 1 kg)( 9.81 m/s² ) . I.E. W = 9.81 N . While standard kg also serves as the unit of Weight in commercial transactions, it can not be so used in engineering computations. Chapter 1: SI Units – commonly used units . The most frequently used units are kilometer(km), millimeter(mm), megagram(Mg) which is known as metric ton, gram(g) and kilonewton(kN). 1 km = 1000 m 1mm = 0.001 m 1 Mg = 1000 kg 1 g = 0.001 kg 1 kN = 1000 N 3.82 km = 3820 m 47.2 mm = 0.0472 m 3.82 km = 3.82 x 10³ m m ³־mm = 47.2 x 10 47.2 Chapter 1: SI Units – Derived units . There are many other units derived from the basic kinetic units (Length, Mass, Time and Force). The most common derived units are units of Area and Volume. The unit of Area is square meter (m²) which represents the area of a square of side 1 m. The unit of Volume is the cubic meter (m³), equal to the volume of a cube of side 1 m. The Volume of liquid is measured in cubic decimeter (dm³) is commonly referred as a liter (L). Chapter 1: SI Units – Multiplication factors-Length . Multiple and sub-multiple of the units of Length: m ¹־dm = 0.1 m = 10 1 m ²־cm = 0.01 m = 10 1 m ³־mm = 0.001 m = 10 1 1 km = 1 000 m = 10³ m . Multiple and sub-multiple of the units of Area: m² ²־m)² = 10 ¹־dm² = (1 dm)² = (10 1 m)² = 10 -4m2 ²־cm² = (1 cm)² = (10 1 m)² = 10 -6m 2 ³־mm² = (1 mm)² = (10 1 . Multiple and sub-multiple of the units of Volume: m³·³־m)³ = 10 ¹־dm³ = (1 dm)³ = (10 1 m)³ = 10 -6m 3 ²־cm³ = (1 cm)³ = (10 1 m)³ = 10 -9m 3 ³־mm³ = (1 mm)³ = (10 1 Chapter 1: SI Units – Multiplication factors conventions- . In order to avoid exceedingly small or large numerical values, many sub-units are defined and used. When more than four digits are used on either side of the decimal point -- as in 427 200 m or 0.002 16 m – spaces, never commas, should be used to separate the digits into groups of three.