1. Introduction to Statics Su-Jin Kim Gyeongsang National University Fall 2017

OCW Statics Lecture by Yiheng Wang: https://www.youtube.com/playlist?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh

OCW What is statics? https://youtu.be/fO2Cdx89O_o?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh SI Units https://youtu.be/vL95jQf_IQk?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Newton's fundamental laws, Law of gravitation https://youtu.be/4D4eADq6VCE?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Scalars and Vectors, Vector addition and subtraction https://youtu.be/NLq6m_Y3WoU?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh Cartesian vectors https://youtu.be/1L8NzLjNAWI?list=PLLbvVfERDon1pceRKOjAxiqFTEvghmZKh

Index What is statics? SI Units Newton's fundamental laws Law of gravitation Scalars and Vectors Vector addition and subtraction Rectangular components Problem solving in Statics

What is statics? Physics ⊃ Mechanics ⊃ Statics, Dynamics, Fluid mechanics Mechanics : Physical science that deals with the response of bodies to the action of forces Statics : Equilibrium of bodies under action of forces Σ F = 0 Σ M = 0 Dynamics : Concerns with the motion of bodies Σ F = ma Σ M = I α Fluid mechanics: Deals with liquid or gases

SI Units [Base Units] Length m Time s Mass kg [Derived Units] Force N F (N) = m (kg) x a (m/s2) Velocity m/s Idealization: Particle, Rigid body, Concentrated force

Newton's fundamental laws Law2. Acceleration motion : F=m a Law1. Law of inertia : ΣF=0 equilibrium  at rest or continue to move Law3. Action and reaction : are equal magnitude, opposite direction, collinear Law2  Dynamics Law1 & 3  Statics

Law of gravitation Law of gravitation : F = G m1m2 / r2 G = 6.673x10-11 m3/kgs2 Earth : m = 5.976x1024 kg, r = 6371 km Weight : gravitational attraction of the earth : W = mg (g = 9.81 m/s2 ) m1 m2 r F m W

Ex) Gravitation Earth-Moon m1= 5.97x1024 kg, m2=7.35x1022 kg r = 384x106 m F = G m1m2 / r2 = 6.673x10-11 m3/kgs2 x 5.97x1024 kg X 7.35x1022 kg / (384x106 m)2 = 1.98 x 1020 N m1 m2 r F

Scalars and Vectors Scalar: length l, mass m, time t, speed v, volume, density, energy (magnitude only) Vector: displacement r, force F, velocity v, acceleration a, moment M (magnitude + direction) length r , displacement r speed v , velocity v

Vector addition and subtraction Magnitude : V = |V| Parallelogram law : R = A + B Triangular rule : R = A + B Subtraction : R = A - B A B R Parallelogram Triangle

Cartesian(Rectangular) vectors Cartesian unit vectors: i, j, k Cartesian components : V = V (Vx, Vy, Vz) = Vx i + Vy j + Vz k Direction: cos a = Vx / |V| Addition: add each components i j k V Vx i Vz k Vy j z x y

Problem solving in Statics Free Body Diagram : Isolate object to a rigid body(or particle) + External forces Equilibrium equation

Ex 1-1 Weight of a people? m = 70 kg W ? N Ans : W = m g = 70 kg x 9.81 m/s2 = 686 N

Ex 1-2 Add Vector A and B A 8 A+B 45° 30° 12 B A = Ax i + Ay j = 8cos45˚ i + 8sin45˚ j B = Bx i + By j =12cos30˚ i -12sin30˚ j A+B = (8cos45˚ +12cos30˚) i + (8sin45˚-12sin30˚) j A+B = 16.05 i - 0.35 j Magnitude: |A+B|=16.05 Direction angle: θ=tan-1 (-0.35/16.05) = -1.25˚

Ex 1-2 Answer of students

Ex 1-3 Vector |A|=6 |B|=4 60˚ |A+B|=? a=?