Final answer:
The second force has a magnitude of 613 N in the positive a direction, which is calculated using Newton's second law of motion and the known force of 170 N in the negative y direction.
Step-by-step explanation:
To find the magnitude of the second force acting on a 29 kg mass which is accelerating at 27 m/s² in the positive a direction, with one of the forces acting in the negative y direction with a magnitude of 170 N, we use Newton's second law of motion. Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
Firstly, we calculate the net force required to produce the given acceleration using F = ma, which gives us F = 29 kg × 27 m/s² = 783 N. This force is the vector sum of the two individual forces acting on the mass. Since we know one force is 170 N in the negative y direction, the second force must be in the positive direction with a magnitude sufficient to achieve the net force of 783 N.
To find the magnitude of the second force, we subtract the force in the negative y direction from the net force: 783 N - 170 N = 613 N. Therefore, the second force has a magnitude of 613 N in the positive direction.