ECOR 1045 Statics Lecture 1 PDF

ECOR 1045 – Statics Course Instructor: Dr. Thomas Walker Department of Civil and Environmental Engineering Lecture 1: Introduction Chapter 1 (Hibbeler, Statics and Dynamics 15th edition)  What is Statics?...

ECOR 1045 – Statics Course Instructor: Dr. Thomas Walker Department of Civil and Environmental Engineering Lecture 1: Introduction Chapter 1 (Hibbeler, Statics and Dynamics 15th edition)  What is Statics? ▪ A branch of mechanics ▪ Study of bodies when acted upon by forces ▪ Either the bodies or the forces can be large ECOR 1045 – Lecture 1: Introduction 2  Branches of Mechanics Mechanics Deformable Rigid Body Body Fluid Statics Dynamics Compressible Incompressible ECOR 1045 – Lecture 1: Introduction 3  Fundamental Units ▪ Four fundamental physical quantities (dimensions) | Length Used to locate a body in space or to measure the size of a body (m, ft) | Mass Used to measure the quantity of matter in a body (kg, slug) | Time Used to measure the succession of events (s, min, h) | Force Used to measure a “push” or “pull” directed on a body (N, lb) ECOR 1045 – Lecture 1: Introduction 4  System of Units ▪ Two systems of units | SI: Système International d’Unités | Imperial Units: US Customary System ▪ Both systems have three base units and one derived unit ECOR 1045 – Lecture 1: Introduction 5  Base and Derived Units ECOR 1045 – Lecture 1: Introduction 6  Unit Conversion ECOR 1045 – Lecture 1: Introduction 7  Dimensional Homogeneity ▪ The terms of all equations must be dimensionally homogeneous | Dimensions of LHS= Dimensions of RHS ▪ Consider the kinematic equation: | 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 𝑚 𝑚 𝑚 | 𝑠 = 𝑠 + 𝑠2 ∙𝑠 𝑚 𝑚 𝑚 | 𝑠 = 𝑠 + 𝑠 ▪ Always display units on final answers ECOR 1045 – Lecture 1: Introduction 8  Models and Idealizations ▪ Models and idealizations are often used to solve problems | Particle Has mass but negligible size | Rigid Body Can be considered a collection of particles that remain fixed to one another under load | Concentrated Force A force applied over a relatively small area on the rigid body ECOR 1045 – Lecture 1: Introduction 9  Newton’s Laws of Motion ▪ Engineering mechanics is formulated based on Newton’s Laws of Motion | The laws were postulated based on experimental observation | The laws apply to the motion of a particle with respect to a non- accelerating reference frame ECOR 1045 – Lecture 1: Introduction 10  Newton’s Laws of Motion ▪ 1st Law of Motion | A particle at rest or in motion will remain at rest or in motion unless acted upon by an unbalanced external force. ECOR 1045 – Lecture 1: Introduction 11  Newton’s Laws of Motion ▪ 2nd Law of Motion | A particle of mass (m) acted upon by an unbalanced system of forces (F) experiences an acceleration (a) in the same direction as the force and with a magnitude proportional to the force. 𝑭 = 𝑚𝒂 ECOR 1045 – Lecture 1: Introduction 12  Newton’s Laws of Motion ▪ 3rd Law of Motion | For every action there is an equal and opposite reaction. ECOR 1045 – Lecture 1: Introduction 13  Newton’s Law of Gravitational Attraction ▪ Gravity is a mutual force of attraction between two bodies 𝑚1 𝑚2 𝐹=𝐺 𝑟2 | F = force of gravity between two particles | m1, m2 = mass of each particle m1 | r = distance between the two particles r F | G = universal constant of gravitation 3 F −12 𝑚 𝐺 = 66.73 × 10 𝑘𝑔∙𝑠 2 m2 ECOR 1045 – Lecture 1: Introduction 14  Weight of a Body ▪ Consider an object of mass m on the surface of the Earth ▪ The force exerted between the body and the Earth (the body’s weight W) is given as: 𝑀𝑒 𝑚 𝑊 = 𝑚𝑔 = 𝐺 𝑅𝑒 2 | where Me and Re are the mass and radius of the Earth, respectively ECOR 1045 – Lecture 1: Introduction 15  Precision of Numerical Calculations ▪ Precision depends on: | Precision of data provided | Precision of computations ▪ The result of a computation cannot be more precise than the least precise datum ECOR 1045 – Lecture 1: Introduction 16  Significant Figures ▪ The number of significant figures conveys the precision of a number ▪ How many significant figures are in each number? | 4903 | 23,500 | 0.00356 ▪ Use engineering notation (not scientific notation) | 4.903 x 103 | 23.5 x 103 or 23.50 x 103 | 3.56 x 10-3 ECOR 1045 – Lecture 1: Introduction 17  Conventions for Calculations ▪ Only round off your final answer ▪ Calculations should show at least 4 significant figures; final answer should be rounded to 3 | Marks deducted for not using 3 significant figures ▪ Limitations on measurement precision and geometry mean it is rarely possible to obtain more than 3 significant figures of precision ▪ Keep units in calculations and final answers | Marks deducted for not using appropriate units ECOR 1045 – Lecture 1: Introduction 18  Sample Problem ▪ A car is travelling at 55.0 mph, determine its speed in: | A) km/h | B) m/s A) 𝑚𝑖 𝑚𝑖 𝑓𝑡 𝑚 𝑘𝑚 55.0 = 55.0 × 5280 × 0.3048 = 88.51 ℎ ℎ 𝑚𝑖 𝑓𝑡 ℎ Answer: 88.5 km/h B) 𝑚𝑖 𝑚𝑖 𝑓𝑡 1ℎ 1 𝑚𝑖𝑛 𝑚 55.0 = 55.0 × 5280 × × = 24.59 ℎ ℎ 𝑚𝑖 60 𝑚𝑖𝑛 60 𝑠𝑒𝑐 𝑠 Answer: 24.6 m/s ECOR 1045 – Lecture 1: Introduction 19  Unit Rules ▪ Units have standard abbreviations, and are never plural | m=5 kg (not kgs) ▪ Separate units with a dot | meter*second= 𝑚 ∙ 𝑠 (not ms, which is a millisecond) ▪ Most units are lowercase | E.g. m, kg, s | Exceptions: N (Newton), Pa (Pascal), M (mega-) and G (giga-) ▪ Exponential powers apply to units | cm x cm = cm2 ▪ Compound prefixes should not be used | 0.001 kg = 1g (not 1 mkg) ▪ See textbook for other rules 20  Important Reminders ▪ Develop a sense for the numbers ▪ Use engineering language and terminology ▪ Keep appropriate units in all calculations ▪ Use 4 significant digits in calculations and round off to 3 for final answer ▪ Use engineering notation ▪ Marks will be deducted for not following these basic rules ECOR 1045 – Lecture 1: Introduction 21