Question

Assume that the position vector of point A is r = i + j + k. Determine the moment about the origin O if the force F = 5i + 4j + 5k. What is the moment about the origin O of the force F?

Answer 1

The moment about the origin O of force F = 5i + 4j + 5k at the point A with position vector r = i + j + k is -i - k N·m.

Step-by-step explanation:

The moment (or torque) about the origin O of the force F applied at point A with position vector r = i + j + k can be found using the cross product of r and F. The cross product is given by:

| i j k |
| 1 1 1 |
| 5 4 5 |

Calculating the determinant of this matrix, we get:

Moment = (1(4)-1(5))i - (1(5)-1(5))j + (1(4)-1(5))k
= -i + 0j - k
= -i - k

So, the moment about the origin O of the force F is -i - k Newton-meters (N·m).