Question

add two east-west and two north-south forces to the force diagram in order for the 2.0-kg object to have a westward acceleration of 4.0 m/s/s.
2 n north
2 n west
2 n east
2 n south

Explanation:

Step1: Calculate net westward force

Use $F_{net}=m \cdot a$. Substitute $m=2.0\ \text{kg}$, $a=4.0\ \text{m/s}^2$.
$F_{net}=2.0 \times 4.0 = 8.0\ \text{N west}$

Step2: Balance north-south forces

Current north/south forces are equal (2 N each), so add equal magnitude forces (e.g., 3 N north and 3 N south) to keep net north-south force 0.

Step3: Adjust east-west net force

Current east-west forces cancel (2 N each). To get 8 N west net force, add forces where west force - east force = 8 N. Example: add 10 N west and 2 N east: $(2+10)-(2+2)=8\ \text{N west}$.

Answer:

1. North-South forces to add: 3 N North and 3 N South (any equal magnitude pair works, as long as net north-south force remains 0)
2. East-West forces to add: 10 N West and 2 N East (or any pair where the total westward force exceeds total eastward force by 8.0 N)

Resulting net force: $8.0\ \text{N west}$, which produces the required $4.0\ \text{m/s}^2$ westward acceleration.