Answer:
Blank #1: 12
Blank #2: 8
Blank #3: 20
Blank #4: 6
Blank #5: 10
Blank #6: 4
Please see attached image
Explanation:
Notice that in the first case, you are supposed to include two forces directed towards the right (same direction). In such cases the vectors that represent those forces simple add their magnitudes to give you the resultant (larger) net force.
We can use as an example 12 N for the first blank, 8 N for the second blank (since the vector shows somewhat shorter that the first one), and the resultant force would be the addition of these two: 12 N + 8 N = 20 N
For the second cart, you are to include two forces but in opposite directions (one pointing right and the other one pointing left). I such case, the magnitudes of the forces subtract. Notice also that the resultant force is expected to be directed towards the right, so we are careful to include a larger value for the force pointing to the right (blank 5) than for the force pointing to the left (blank 4). We use for example 10 N for blank 5, and 6 N for blank 4, that gives us a difference: 10 N - 6 N = 4 N, pointing to the right.
