University of Ontario Institute of Technology

• MECE 2230U

• Newton’s 1st law F = ma Gravitational force G = 66.73(10-12) m3 /kg • s2 Weight W = mg g = GMe/r2 = 9.81 m/s2 = 32.2 ft/s2 Ɵ Me = Mass of the Earth Vector Components Fx = F * cos Ɵ = F * a c Fy = F * sin Ɵ = F * b c Direction of Ɵ resultant vector: tan-1 * Σ Fy Σ Fx Unit Vector Cartesian (3D) vector Az = A * cosØ A’ = A * sinØ A’ = Ax + Ay A = Ax + Ay + Az Ø = angle between z axis and vector Coordinate direction: α (A-x) β (A-y) γ (A-z) To find the cartesian form of a vector, divide it into F = F’ + Fz then solve The use of sin and cos changes for Ø. For x and y it’s whatever satisfies projection of F’ to F For z axes it’s whatever satisfies F to the z axes The use of sin and cos changes for Ɵ depending on the projection of F’ Position Vector We find the cartesian vector using the formula, then use the Pythagorean formula to find the magnitude of the position vector To find the direction, we use the unit vector formula to find the directions. Force directed along a line Dot Product A • B = A * B * cos Ɵ = AxBx