Final answer:
To find the third force that puts a particle in equilibrium, we use vector addition of the given forces F1 and F2 and take their negative sum to get F3. The magnitude of F3 is found using the Pythagorean theorem, resulting in approximately 8.31 N.
Step-by-step explanation:
The student is asking about finding the magnitude of forces that keep a particle in equilibrium. To achieve equilibrium, the net external force acting on the particle must be zero. This means that we need to find a third force, F3, that when combined with the given forces F1 and F2, results in a net force of zero. We can represent these forces as vectors and use vector addition to solve for F3. Given the vectors F1 = (3î + 5ì − 6Ę) N and F2 = (4î - 7ç + 2k) N, we can calculate F3 by taking the negative sum of F1 and F2 to ensure the net force is zero:
-
- F1 + F2 + F3 = 0
-
- F3 = - (F1 + F2)
-
- F3 = - ((3î + 5ì − 6k) + (4î - 7ç + 2k))
-
- F3 = - (7î - 2ç - 4k) N
-
- F3 = (-7î + 2ç + 4k) N
The magnitude of F3 can be calculated using the Pythagorean theorem:
-
- |F3| = √((-7)^2 + 2^2 + 4^2)
-
- |F3| = √(49 + 4 + 16)
-
- |F3| = √(69)
-
- |F3| ≈ 8.31 N
The acceleration of the flea can also be calculated using Newton's second law of motion (F = ma). With the provided forces and the mass of the flea, we can find the acceleration's direction and magnitude.