Consider the L-shaped beam illustrated in Fig. 3.37. The beam is mounted to the wall at...

   

  

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Consider the L-shaped beam illustrated in Fig. 3.37. The beam is mounted to the wall at point A, the arm AB extends in the z direction, and the arm BC extends in the x direction. A force F is applied in the z direction at the free-end of the beam. (a) If the lengths of arms AB and BC are a and b, respectively, and the magnitude of the applied force is F, observe that the position vector of point C relative to point A can be written as r= bi + ak and the force vector can be expressed as F = Fk, where i,j, and k are unit vectors indicating positive x, y, and z directions, respectively. (b) Using the cross product of position and force vectors, determine an expression for the moment generated by F about point A in terms of a, b, and F. (c) If a = b = 30 cm and F = 20 N, calculate the magni- tude of the moment about point A due to F. %3D C А B F Fig. 3.37 Problem 3.9 Consider the L-shaped beam illustrated in Fig. 3.37. The beam is mounted to the wall at point A, the arm AB extends in the z direction, and the arm BC extends in the x direction. A force F is applied in the z direction at the free-end of the beam. (a) If the lengths of arms AB and BC are a and b, respectively, and the magnitude of the applied force is F, observe that the position vector of point C relative to point A can be written as r= bi + ak and the force vector can be expressed as F = Fk, where i,j, and k are unit vectors indicating positive x, y, and z directions, respectively. (b) Using the cross product of position and force vectors, determine an expression for the moment generated by F about point A in terms of a, b, and F. (c) If a = b = 30 cm and F = 20 N, calculate the magni- tude of the moment about point A due to F. %3D C А B F Fig. 3.37 Problem 3.9