Engineering Mechanics: Summary Sheets on Vector Addition, Force Systems, and Equilibrium, Quizzes of Engineering

Download Engineering Mechanics: Summary Sheets on Vector Addition, Force Systems, and Equilibrium and more Quizzes Engineering in PDF only on Docsity! Engineering Mechanics, Summary Sheets 1 General Principles Newton’s law of gravitational attraction : universal constant of gravitation (G = 66.73 x 10-12 m3/kg-s2) Weight g: gravitational acceleration (g = 9.81 m/s2) 2 Force Vector Cosine law Sine law 2.4 Addition of a system of coplanar forcers Scalar notation Cartesian vector notation Coplanar force resultant 2.5 Cartesian vectors F = G m1m2 r2 G W = G mMe r2 = mg C = A2 + B2 ! 2AB cos c A sin a = B sin b = C sin c Fx = F cos ! Fy = F sin ! !F = Fx "i + Fy "j FRx = " Fx FRy = " Fy FR = F2Rx + F2Ry ! = tan!1 FRy FRx !A = !Ax + !Ay + !Az Cartesian vector representation Magnitude of a Cartesian vector: Direction of a Cartesian vector , , 2.6 Addition of Cartesian vectors 2.7 Position vectors 2.8 Force vector directed along a line 2.9 Dot product Laws of operation !A = Ax "i + Ay "j + Az !k A = A2x + A2y + A2z cos " = Ax A cos # = Ay A cos $ = Az A !uA = !AA = Ax A "i + Ay A "j + Az A !k !uA = cos " "i + cos # "j + cos $ !k cos2 " + cos2 # + cos2 $ = 1 !A = A !uA = A cos " "i + A cos # "j + A cos $ !k = Ax "i + Ay "j + Az !k !FR = " !F = " Fx "i + " Fy "j + " Fz !k "r = x "i + y "j + z !k "r = !rB !rA = (xB ! xA) "i + (yB ! yA) "j + (zB ! zA) !k !F = F !u = F "r r !A # !B = AB cos ! !A # !B = !B # !A a( !A # !B ) = (a !A ) # !B = !A # (a !B ) !A # ( !B + !D ) = ( !A # !B ) + ( !A # !D ) !A # !B = AxBx + AyBy + AzBz ! = cos!1 !A # !B AB