Question

A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second is pointing right, labeled F Subscript p Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing left, labeled F Subscript f. The upward vector is the same length as the downward vector. The right vector is the same length as the left vector.

A free body diagram with 3 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing right, labeled F Subscript p Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. All three vectors are of equal length.

A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing right, labeled F Subscript f Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing up to the left, labeled F Subscript P Baseline.

A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing left, labeled F Subscript f Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing down to the right, labeled F Subscript P Baseline. All vectors are the same length.

Answer 1

I’m not sure exactly what you want done with these diagrams, so I’ll assume you want to know which ones give translational equilibrium (net force = 0). I’ll state any assumptions and show which are/aren’t in equilibrium.

1) Four forces: Fg downward, Fp right, FN upward, Ff left. “Upward vector is the same length as the downward vector. The right vector is the same length as the left vector.”
- Vertical: FN = Fg → vertical components cancel.
- Horizontal: Fp = Ff → horizontal components cancel.
Conclusion: net force = 0 → translational equilibrium.

2) Three forces: Fg downward, Fp right, FN upward. “All three vectors are equal length.”
- Vertical: FN = Fg → vertical components cancel.
- Horizontal: Fp remains unbalanced to the right.
Conclusion: net force points right (Fp) → not equilibrium; object would accelerate to the right.

3) Four forces: Fg downward, Ff right, FN upward, FP up-left. (No lengths specified.)
- You cannot decide without magnitudes. Write components (take θ = angle of FP above the negative x-axis):
- x: Ff + FP cos(180−θ) = Ff − FP cos θ must equal 0 → Ff = FP cos θ
- y: FN − Fg + FP sin θ must equal 0 → FN + FP sin θ = Fg
- If FP and the others satisfy those two equations, net force = 0; otherwise not. So equilibrium only if the magnitudes satisfy the two component equations above.

4) Four forces: Fg down, Ff left, FN up, FP down-right. “All vectors are the same length.”
- Let each magnitude = 1 and take 45° for the diagonal down-right.
- x: −1 (left) + cos45° ≈ −1 + 0.707 = −0.293
- y: −1 (down from Fg) + 1 (up from FN) − sin45° ≈ 0 − 0.707 = −0.707
- Net vector ≠ 0 (net down-left). Conclusion: not equilibrium.

If you meant something else (e.g., which diagrams are possible for an object at rest, or about friction direction, or about torque/rotation), tell me which and I’ll analyze that specifically.