Free-Body Diagrams - Free Printable

It looks like you've uploaded a worksheet titled "Free-Body Diagrams", which asks you to draw accurate free-body diagrams (FBDs) for various situations involving rocks being acted on by forces. The instructions say:

> "In each case, a rock is acted on by one or more forces. All drawings are in a vertical plane, and friction is negligible except where noted. Draw accurate free-body diagrams showing all forces acting on the rock. Please use a ruler, and do it in pencil so you can correct mistakes. The first one is done as an example."

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Let me go through each scenario, analyze what forces are acting on the rock, and explain how to correctly draw the free-body diagram (FBD). Since I can't see your image directly, I'll interpret based on the description of each case from the text and typical physics problems.

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🔹 1. Static – Rock suspended by two ropes at angles

- Given: Rock is stationary (static), held by two ropes at angles (T₁ and T₂), with tension forces.
- Forces:
- Weight (ω) downward (gravity).
- Tension T₁ pulling left-upward.
- Tension T₂ pulling right-upward.
- ✔ FBD:
- Draw a dot for the rock.
- Arrow down: ω (weight).
- Arrow up-left: T₁.
- Arrow up-right: T₂.
- ✔️ This is already shown as an example — correct.

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🔹 2. Static – Rock hanging vertically from a single rope

- Given: Rock hangs from a rope, stationary.
- Forces:
- Weight (ω) downward.
- Tension (T) upward from the rope.
- ✔ FBD:
- Dot for rock.
- Arrow down: ω.
- Arrow up: T.
- ✔️ Already drawn — correct.

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🔹 3. Rock is falling. No air friction

- Given: Rock in free fall; no air resistance.
- Forces:
- Only gravity (weight, ω) acts downward.
- No other forces (no tension, no normal force, etc.).
- ✔ FBD:
- Dot for rock.
- Single arrow pointing down: ω.
- No other forces!
- ✘ Common mistake: Adding a "force of motion" or upward arrow — not valid.
- ✔️ Your diagram shows only ω — correct.

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🔹 4. Static – Rock suspended by two ropes forming a V-shape

- Given: Rock held by two ropes attached to a ceiling, symmetric or asymmetric.
- Forces:
- Weight (ω) downward.
- Tension T₁ in left rope (upward and left).
- Tension T₂ in right rope (upward and right).
- ✔ FBD:
- Dot.
- Down: ω.
- Up-left: T₁.
- Up-right: T₂.
- ✔️ Already shown — correct.

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🔹 5. Static – Rock suspended by three ropes (triangular setup)

- Given: Rock held by three ropes connected to a central point.
- Forces:
- Weight (ω) downward.
- Three tension forces: T₁, T₂, T₃, each pulling along the rope direction.
- ✔ FBD:
- Dot.
- Down: ω.
- Three arrows pointing away from dot along rope directions: T₁, T₂, T₃.
- Note: These tensions must balance the weight and keep the system static.
- ✔️ If your diagram shows these three vectors properly aligned with the ropes — good.

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🔹 6. Static – Rock resting on a horizontal surface

- Given: Rock on flat surface, not moving.
- Forces:
- Weight (ω) downward.
- Normal force (N) upward from surface.
- ✔ FBD:
- Dot.
- Down: ω.
- Up: N.
- ✔️ Already shown — correct.

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🔹 7. Static – Rock on an inclined plane

- Given: Rock on ramp, not sliding (static), no friction mentioned → but if it's static, friction might be implied.
- Wait: The problem says "friction is negligible except where noted." But here it's static, so must have friction to prevent sliding.
- However, since friction is *not* mentioned as present, we assume no friction — but then the rock would slide unless there's another force.

But wait: If it's static and no friction, then it must be held by another force — perhaps a rope?

Looking at your FBD:
- You have:
- ω (down).
- N (perpendicular to slope).
- T (pulling parallel to slope?).
- So likely, the rock is held by a rope pulling up the incline.

✔ Forces:
- Weight (ω): down.
- Normal force (N): perpendicular to incline.
- Tension (T): along the incline (upward, to hold it).
- Friction: not included (negligible).

So the FBD should show:
- ω: straight down.
- N: perpendicular to incline (into the page? No — outward from surface).
- T: up the incline.

✔️ Your diagram shows this — good.

Note: Weight should be decomposed into components in some cases, but in a free-body diagram, we only show actual forces, not components. So:
- Do not break ω into components unless asked.
- Just show ω downward, N normal to surface, T along the rope.

So if your diagram has those three — it’s correct.

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🔹 8. Static – Rock on an inclined plane with no rope

- Given: Rock on incline, static, no friction mentioned.
- But again: if no friction and no rope, and it's static, that's impossible unless the incline is horizontal.

Wait — but the diagram shows:
- ω down.
- N normal to incline.
- Two arrows labeled Nₓ and Nᵧ — probably components of normal force?

✘ That’s incorrect.

The normal force is one force, perpendicular to the surface. We don’t split it into components unless analyzing.

But here, the FBD shows:
- ω down.
- N (normal force).
- Then Nₓ and Nᵧ — which are not real forces, just components.

⚠️ Mistake: In a free-body diagram, we only show real forces. Components are used in calculations, not in FBDs.

Also, if the rock is static on an incline with no friction and no tension, it cannot stay static — it will slide.

So either:
- There’s friction (but problem says “negligible” unless noted), or
- There’s a tension or support holding it.

But your diagram shows no friction, only:
- ω
- N
- Nₓ and Nᵧ (which are not real forces)

✘ So this FBD is incorrect.

✔ Correct FBD for a rock on an incline, static, with friction:
- ω: down.
- N: perpendicular to incline.
- f: parallel to incline, upward (friction preventing motion).
- (If no friction, it wouldn’t be static.)

But since the problem says "friction is negligible", and it's static, then there must be another force — perhaps a rope?

But the diagram doesn’t show one.

So likely, the intended situation is:
- Rock on incline.
- Static.
- Friction is present despite saying "negligible" — but maybe it's an exception.

Wait — the instruction says: "friction is negligible except where noted."

But in this case, it’s not noted as having friction.

So friction should be neglected.

Then the only forces are:
- ω
- N

But these cannot balance unless the incline is horizontal.

Therefore, this situation is physically impossible unless:
- There is a rope pulling it up the incline.
- Or friction is acting.

But since friction is not mentioned, and the diagram shows Nₓ and Nᵧ, which are not real forces, the FBD is wrong.

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✔ Final Corrections & Summary

| Case | Forces Present | Correct FBD? | Notes |
|------|----------------|-------------|-------|
| 1 | ω, T₁, T₂ | ✔ | Correct |
| 2 | ω, T | ✔ | Correct |
| 3 | ω only | ✔ | Correct (free fall) |
| 4 | ω, T₁, T₂ | ✔ | Correct |
| 5 | ω, T₁, T₂, T₃ | ✔ | Correct |
| 6 | ω, N | ✔ | Correct |
| 7 | ω, N, T | ✔ | Correct (if T is tension) |
| 8 | ω, N, Nₓ, Nᵧ | ✘ | Incorrect — Nₓ and Nᵧ are not real forces |

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🔧 Fix for Case 8:

If the rock is static on an incline with no friction, then it cannot be static unless there’s a tension or other force.

But if it’s static and friction is negligible, then either:
- The incline is horizontal (but it’s not), or
- There is another force (like a rope or hand pushing).

Assuming the rock is held in place by a rope (even if not shown), then:
- Add T (tension) up the incline.
- Remove Nₓ and Nᵧ.
- Keep ω and N.

✔ Corrected FBD:
- Dot.
- Arrow down: ω.
- Arrow perpendicular to incline: N.
- Arrow up the incline: T.

Alternatively, if friction is present, then:
- Add f (friction) up the incline.
- Remove Nₓ and Nᵧ.

But since friction is said to be negligible unless noted, and it’s not noted, don’t include friction.

So best assumption: There is a tension force.

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✔ Conclusion

Your FBDs for cases 1–7 are correct.

Case 8 is incorrect because:
- It shows Nₓ and Nᵧ, which are components, not forces.
- It lacks tension or friction to balance the component of weight down the incline.

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🛠️ How to Fix Case 8:

Draw:
- A dot for the rock.
- One arrow down: ω (weight).
- One arrow perpendicular to the incline: N (normal force).
- One arrow parallel to the incline, upward: T (tension, if present).
- Do not show Nₓ and Nᵧ.

If the problem intends for friction to act, then add:
- One arrow parallel to incline, upward: f (friction).

But only if explicitly stated.

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Let me know if you'd like a sketch description or want me to generate a corrected version!