Calculate the net force for each of the 6 force diagrams (arrows in N), and identify which diagrams have the same net force: (1) 4 N left, (2) 7 N right and 2 N right, (3) 4 N left and 4 N left, (4) 5 N right and 3 N right, (5) 8 N right and 4 N left, (6) 4 N left and 5 N left.

What you are doing in each diagram

Treat right as positive and left as negative, then add the forces. The result is a single net force with both a magnitude and a direction.

Net force calculations (right = +, left = -)

1. One force: $$F_\text{net}=-4\,\text{N} \Rightarrow 4\,\text{N left}$$

2. Both to the right: $$F_\text{net}=+7\,\text{N} + +2\,\text{N}=+9\,\text{N} \Rightarrow 9\,\text{N right}$$

3. Both to the left: $$F_\text{net}=-4\,\text{N} + -4\,\text{N}=-8\,\text{N} \Rightarrow 8\,\text{N left}$$

4. Both to the right: $$F_\text{net}=+5\,\text{N} + +3\,\text{N}=+8\,\text{N} \Rightarrow 8\,\text{N right}$$

5. Opposite directions: $$F_\text{net}=+8\,\text{N} + -4\,\text{N}=+4\,\text{N} \Rightarrow 4\,\text{N right}$$

6. Both to the left: $$F_\text{net}=-4\,\text{N} + -5\,\text{N}=-9\,\text{N} \Rightarrow 9\,\text{N left}$$

Which diagrams match?

• Including direction (true net force as a vector): none match.
• Ignoring direction (matching magnitude only): diagrams 3 and 4 both have magnitude $8\,\text{N}$.