High School

In the pipe assembly shown, points B and C lie in the xy plane, and force F is parallel to the z-axis. If [tex]F = 150 \, \text{N}[/tex], determine the moment of F about lines OA and AB.

Answer :

Final answer:

The moment of force F about line OA is equal to 150 N times the perpendicular distance from the line of action of force F to line OA. The moment of force F about line AB is equal to 150 N times the perpendicular distance from the line of action of force F to line AB.

Explanation:

To calculate the moment of force F about line OA, we need to determine the perpendicular distance from the line of action of the force to line OA. Since point B and C lie in the xy plane, the line of action of force F is perpendicular to the xy plane. Therefore, the perpendicular distance from the line of action of force F to line OA is the distance between point B and line OA.

To calculate the moment of force F about line AB, we need to determine the perpendicular distance from the line of action of the force to line AB. Since point B and C lie in the xy plane, the line of action of force F is perpendicular to the xy plane. Therefore, the perpendicular distance from the line of action of force F to line AB is the distance between point C and line AB.

Now, let's calculate the moment of force F about line OA and line AB.

The moment of force F about line OA is given by the formula:

Moment of F about OA = F * d

where F is the magnitude of force F and d is the perpendicular distance from the line of action of force F to line OA.

Similarly, the moment of force F about line AB is given by the formula:

Moment of F about AB = F * d

where F is the magnitude of force F and d is the perpendicular distance from the line of action of force F to line AB.

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