Question

PLEASE HELP! which free body diagram represents a box in equilibrium?

Answer 1

Second option- explanation in comments.

Answer 2

The box is in equilibrium when the sum of forces on the box in vertical as well as horizontal direction is zero.

Assuming the force in right as positive and force in left direction as negative.

Assuming the force in up as positive and force in down direction as negative.

For Box 1:

`\sum F_(x)` = Net force along horizontal direction = 5 - 3 = 2 N

`\sum F_(y)` = Net force along vertical direction = 5 - 3 = 2 N

Since
`\sum F_(x)` ≠ 0 and
`\sum F_(y)` ≠ 0

hence the box is not in equilibrium

For Box 2:

`\sum F_(x)` = Net force along horizontal direction = 5 - 5 = 0 N

`\sum F_(y)` = Net force along vertical direction = 2 - 2 = 0 N

Since
`\sum F_(x)` = 0 and
`\sum F_(y)` = 0

hence the box is in equilibrium

For Box 3:

`\sum F_(x)` = Net force along horizontal direction = 5 - 5 = 0 N

`\sum F_(y)` = Net force along vertical direction = 0 - 5 = - 5 N

Since
`\sum F_(x)` = 0 and
`\sum F_(y)` ≠ 0

hence the box is not in equilibrium

For Box 4:

`\sum F_(x)` = Net force along horizontal direction = 2 - 2 = 0 N

`\sum F_(y)` = Net force along vertical direction = 2 - 5 = - 3 N

Since
`\sum F_(x)` = 0 and
`\sum F_(y)` ≠ 0

hence the box is not in equilibrium

hence only second box is in equilibrium.