Question

which free body diagram below does not show an object at equilibrium?
50 n
30 n 30 n
50 n
50 n
75 n 75 n
50 n
50 n
25n 30 n
5 n
50 n
50 n
75 n 70 n
10 n
50 n

Explanation:

Step1: Recall Equilibrium Condition

For an object to be in equilibrium, the sum of forces in the horizontal direction (\(F_x\)) and vertical direction (\(F_y\)) must both be zero.

Step2: Analyze First Diagram

• Vertical forces: \(50\,\text{N (up)} + (-50\,\text{N (down)}) = 0\)
• Horizontal forces: \(30\,\text{N (left)} + (-30\,\text{N (right)}) = 0\)
• Equilibrium: Yes.

Step3: Analyze Second Diagram

• Vertical forces: \(50\,\text{N (up)} + (-50\,\text{N (down)}) = 0\)
• Horizontal forces: \(75\,\text{N (left)} + (-75\,\text{N (right)}) = 0\)
• Equilibrium: Yes.

Step4: Analyze Third Diagram

• Vertical forces: \(50\,\text{N (up)} + (-50\,\text{N (down)}) = 0\)
• Horizontal forces: Left forces: \(25\,\text{N} + 5\,\text{N} = 30\,\text{N}\); Right force: \(30\,\text{N}\)
• Sum of horizontal forces: \(30\,\text{N (left)} + (-30\,\text{N (right)}) = 0\)
• Equilibrium: Yes.

Step5: Analyze Fourth Diagram

• Vertical forces: \(50\,\text{N (up)} + (-50\,\text{N (down)}) = 0\)
• Horizontal forces: Left force: \(75\,\text{N}\); Right forces: \(70\,\text{N} + 10\,\text{N} = 80\,\text{N}\)
• Sum of horizontal forces: \(75\,\text{N (left)} + (-80\,\text{N (right)}) = -5\,\text{N}

eq 0\)

• Equilibrium: No.

Answer:

The free - body diagram with 75 N (left), 70 N (right), 10 N (right), 50 N (up), and 50 N (down) (the fourth diagram) does NOT show an object at equilibrium.