Total Force and Moment Calculations for a Physics Problem | Homework Help"

[dvvv]

Homework Statement

Forces F1 = −j + 3k, F2 = j + k and F3 = −2i +j act at the point (0,−1, 2), (−1, 0, 3) and (1, 1, 0) respectively.
(a) Find the total force and the total moment about the origin.
(b) Find an equivalent system of forces consisting of a single force acting at the point (1, 0, 0) together with a couple.

Homework Equations

M = r*F

The Attempt at a Solution

(a) For total force I suppose I just add the forces together. So F_T = -2i + j + 4k.
Then I got the three moments separately, added them up and got M_T = -4i + j +2k

(b) I wasn't sure what to do, but I just multiplied (1,0,0) by the Total Force which I worked out already, and I got -4j +k.

Please tell me if I used the correct method. Thanks!

 

[anathema]

Thank you for your post. Your approach to finding the total force and moment is correct. To confirm, you can also use the formula for the total moment, which is M = r x F, where r is the position vector and F is the force vector. In this case, you would need to calculate the position vectors for each force and then use the formula to find the total moment.

For part (b), your approach is also correct. To find the equivalent system of forces, you can use the formula M = F x d, where M is the moment, F is the force, and d is the distance from the point of application of the force to the point of rotation (in this case, the origin). By multiplying the total force by the distance (1,0,0), you have found the equivalent force and moment system.

Please let me know if you have any further questions or concerns. Keep up the good work!