Final answer:
The values of constants a and b can be found by setting the sum of the given forces equal to zero (since the particle is at rest), and solving for a and b. The acceleration of the particle when the force F3 is reversed is given by -F3/m.
Step-by-step explanation:
To solve this problem, we must first apply Newton's second law of motion that states the vector sum of the forces acting on a body is equal to the mass of the body times its acceleration vector (i.e. Fnet = ma). As the particle is at rest, the net force (and hence, the acceleration) is zero. Considering the given forces:
- F1 = -8i - 2j
- F2 = -ai + bj
- F3 = -a1 - a
The sum of these forces must be equal to zero, hence:
-8i - 2j - ai + bj - a1 - a = 0
This equation can be separately solved for i and j coordinates to find the values of constants a and b. After finding a and b, we know that the force F3 is reversed, therefore the resultant acceleration will be -F3/m. This can be written in vector form as a = -(-a1 - a)/m = a1/m + a/m.
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