To determine in which situations the object’s acceleration has an x-component, we need to analyze the net force acting in the x-direction in each diagram. The force along the x-axis will directly influence the acceleration in that direction according to Newton's second law ($F = ma$).

Let's evaluate each diagram:

1. Diagram (1):

   • Forces in the x-direction: $5 \, \text{N}$ to the right and $3 \, \text{N}$ to the left.
   • Net force in the x-direction: $5 \, \text{N} - 3 \, \text{N} = 2 \, \text{N}$ to the right.
   • Therefore, there is an x-component of acceleration.

2. Diagram (2):

   • Forces in the x-direction: $3 \, \text{N}$ to the right and $2 \, \text{N}$ to the left.
   • Net force in the x-direction: $3 \, \text{N} - 2 \, \text{N} = 1 \, \text{N}$ to the right.
   • Therefore, there is an x-component of acceleration.

3. Diagram (3):

   • Forces in the x-direction: $5 \, \text{N}$ to the right and $5 \, \text{N}$ to the left.
   • Net force in the x-direction: $5 \, \text{N} - 5 \, \text{N} = 0 \, \text{N}$.
   • Therefore, there is no x-component of acceleration.

4. Diagram (4):

   • Forces in the x-direction: $5 \, \text{N}$ to the right and $5 \, \text{N}$ to the left.
   • Net force in the x-direction: $5 \, \text{N} - 5 \, \text{N} = 0 \, \text{N}$.
   • Therefore, there is no x-component of acceleration.

Conclusion:

• The object has an x-component of acceleration in Diagram (1) and Diagram (2).

Would you like further details on how to compute net forces or have any questions?

Here are 5 related questions for further exploration:

1. How does the net force in the y-direction affect the acceleration?
2. What would happen to the object’s acceleration if the forces in both directions were balanced?
3. How do you calculate the total magnitude of the acceleration using both x and y components?
4. Can an object accelerate in one direction while having zero acceleration in another?
5. What is the role of mass in determining the acceleration from a given force?

Tip: Remember, an unbalanced force in any direction will always result in acceleration in that direction according to Newton's Second Law.