How do I find net force when something has arrows all four directions with different N values for each? In the free-body diagram shown above, which of the following is the net force on the balloon?
1570 N
-570 N
1212 N
1070 N
Image shows arrows:
Pointing to right=950N
To left=1520N
up=5120N
down=4050N

In the vertical direction, take up to be positive and down to be negative. Then the net vertical force would be

5120 N - 4050 N = 1070 N

(it's positive, so the net vertical force is pointing upward)

In the horizontal direction, take right to be positive and left to be negative. Then the net horizontal force would be

950 N - 1520 N = -570 N

(negative means the net horizontal force points to the left)

So the net force on the balloon is the vector

F = (1070 N) i + (-570 N) j

(where i and j are the unit vectors in the horizontal and vertical directions, respectively)

The magnitude of the net force on the balloon is the magnitude of this vector:

F = √((1070 N)² + (-570 N)²)

F ≈ 1212 N

e/c, where e is its total energy