Part A - Moment due to a force specified by magnitude and endpoints Learning Goal: To use the vector cross product to calculate the moment produced by a force, or forces, about a specified point on a member. The moment of a force F about the moment axis passing through O and perpendicular to the plane containing O and F can be expressed using the vector cross product, Mo = rx F. In a properly constructed Cartesian coordinate system, the vector cross product can be calculated using a matrix determinant: As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 1) The force has magnitude F = 140 N and is directed as shown. The dimensions are x = 0.450 m, x2 = 1.80 m, y = 2.60 m, and 21 = 1.30 m. What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. View Available Hint(s) i j k M=rx F = | Tx ry rz Fr Fy Notice that the order of the elements of the matrix determinant is important; switching rows 2 and 3 of the determinant would change the sign of the moment from positive to negative (or vice versa.) Figure vec Mo=[ 469.56,500, - 750.8 i,j, k] N. m Submit Previous Answers Incorrect; Try Again F B 1 of 3 Part B - Moment due to a force specified as a Cartesian vector As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 2) The force is given by F = 120 Ni - 135 N j + 70 N k. The dimensions are x = 1.35 m, y = 1.90 m, and = 1.05 m. What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. View Available Hint(s) Mo =[ vec i,j,k] N. m Part B - Moment due to a force specified as a Cartesian vector Learning Goal: To use the vector cross product to calculate the moment produced by a force, or forces, about a specified point on a member. The moment of a force F about the moment axis passing through O and perpendicular to the plane containing O and F can be expressed using the vector cross product, Mo = r F. In a properly constructed Cartesian coordinate system, the vector cross product can be calculated using a matrix determinant: As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B. (Figure 2) The force is given by F = 120 Ni - 135 N j + 70 N k. The dimensions are x = 1.35 m, y = 1.90 m, and = 1.05 m. What is the moment about the origin due to the applied force F? Express the individual components of the Cartesian vector to three significant figures, separated by commas. View Available Hint(s) i j k M=rx F = rx Ty rz Fx Fy Fz Notice that the order of the elements of the matrix determinant is important; switching rows 2 and 3 of the determinant would change the sign of the moment from positive to negative (or vice versa.) Mo =[ Figure < 2 of 3 y1 B Submit V vec Part C - Moment due to two forces i,j, k] N. m Review 142.0, = 85.0, and y == 52.4. The dimensions are x1 = 1.40 m, As shown, a member is fixed at the origin, point O, and has two applied forces, F1 and F2, applied at the free end, point B. (Figure 3) The forces are given by F1 = 105 N i - 150 N j + 55 N k and F2 has magnitude 165 N and direction angles a = Y1 1.75 m, and z = 1.20 m. What is the moment about the origin due to the applied forces? Express the individual components of the Cartesian vector to three significant figures, separated by commas. View Available Hint(s) Mo =[ Submit V JA vec i,j,k] N. m Figure < 3 of 3 > B F2