Question

1. which of the following diagrams represents a box in equilibrium?

(diagrams showing different force configurations on a box: first diagram with 5n left, 5n right, 2n up, 2n down; second with 5n left, 3n right, 2n up; third with 2n left, 2n right, 2n up)

Explanation:

Step1: Recall Equilibrium Condition

For an object to be in equilibrium, the net force in both horizontal and vertical directions must be zero. This means the sum of forces in the horizontal direction ($F_{net,x}$) and vertical direction ($F_{net,y}$) should each equal zero.

Step2: Analyze First Diagram

• Horizontal Forces: $5\,\text{N}$ (right) and $5\,\text{N}$ (left). So, $F_{net,x} = 5 - 5 = 0\,\text{N}$.
• Vertical Forces: $2\,\text{N}$ (up) and $2\,\text{N}$ (down). So, $F_{net,y} = 2 - 2 = 0\,\text{N}$.

Both net forces are zero, so this box could be in equilibrium.

Step3: Analyze Second Diagram

• Horizontal Forces: $5\,\text{N}$ (right) and $3\,\text{N}$ (left). $F_{net,x} = 5 - 3 = 2\,\text{N}$ (right, non - zero).
• Vertical Forces: $2\,\text{N}$ (up) and $0\,\text{N}$ (down, assuming no other vertical force). $F_{net,y}=2\,\text{N}$ (up, non - zero).

Net forces are non - zero, so not in equilibrium.

Step4: Analyze Third Diagram

• Horizontal Forces: $2\,\text{N}$ (right) and $2\,\text{N}$ (left). $F_{net,x}=2 - 2 = 0\,\text{N}$.
• Vertical Forces: $2\,\text{N}$ (up) and $0\,\text{N}$ (down, assuming no other vertical force). $F_{net,y}=2\,\text{N}$ (up, non - zero).

Net vertical force is non - zero, so not in equilibrium.

Answer:

The first diagram (with $5\,\text{N}$ left - right and $2\,\text{N}$ up - down forces) represents a box in equilibrium.