Using the net force rules from the 'Free Body Diagram, Net Force (Total Force), Balanced vs. Unbalanced' notes, determine whether each free body diagram is balanced or unbalanced and find the net force and its direction for: (a) 10 N left and 2 N right, (b) 5 N left and 3 N right, (c) 6 N up and 2 N up, (d) 7 N left, 2 N right, and 4 N right, (e) 0 N right and 100 N right.

What you are doing with each free body diagram

Each diagram is just a list of forces with directions. If forces point the same way, you add them. If they point in opposite directions, you subtract the smaller total from the larger total, and the net force points in the direction of the larger total.

Diagram (a): 10 N left and 2 N right

Opposite directions, so subtract: $$F_{net} = 10 - 2 = 8\text{ N}$$ Direction is left (the larger force was left). Net force is not $0\text{ N}$, so it is unbalanced.

Diagram (b): 5 N left and 3 N right

Opposite directions: $$F_{net} = 5 - 3 = 2\text{ N}$$ Direction is left. Not $0\text{ N}$, so unbalanced.

Diagram (c): 6 N up and 2 N up

Same direction, so add: $$F_{net} = 6 + 2 = 8\text{ N}$$ Direction is up. Not $0\text{ N}$, so unbalanced.

Diagram (d): 7 N left, 2 N right, and 4 N right

First combine the rightward forces: $$F_{right} = 2 + 4 = 6\text{ N}$$ Now compare left vs right (opposite directions): $$F_{net} = 7 - 6 = 1\text{ N}$$ Direction is left. Not $0\text{ N}$, so unbalanced.

Diagram (e): 0 N right and 100 N right

Same direction, so add: $$F_{net} = 0 + 100 = 100\text{ N}$$ Direction is right. Not $0\text{ N}$, so unbalanced.

Quick check for balanced vs. unbalanced

Balanced means $F_{net} = 0\text{ N}$ (no acceleration). Every case here has a nonzero net force, so every case is unbalanced.