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3.47 A crane is oriented so that the end of the 25-m boom AO lies in the yz plane. At the instant shown, the tension in cable AB is 4 kN Determine the moment about each of the coordinate axes of the force exerted on A by cable AB.

User Solrac
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1 Answer

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13 votes

Final answer:

The moments about each coordinate axis are determined by taking the cross product of the position vector from the origin to point A and the force vector along the cable AB. Given the boom's orientation in the yz plane and the tension in the cable, we can calculate the individual moments about the x, y, and z axes.

Step-by-step explanation:

The question asks to determine the moment about each of the coordinate axes of the force exerted on point A by cable AB. To calculate this, we need to know the position vector from the origin to point A where the force is applied and the force vector along the cable AB. Once we have the position vector (which can be derived from the geometry of the crane) and the force vector (given as the tension in the cable), we can compute the moment about each axis using the cross product formula M = r × F, where M is the moment vector, r is the position vector, and F is the force vector.

Given the boom lies in the yz plane, the x-coordinate of the position vector will be zero, and the moment about the x-axis will be calculated from the y and z components of the force vector. Similarly, the moments about the y and z axes can be calculated using the appropriate components of the position and force vectors.

User Cmpickle
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