Free-body diagram of a book at rest on a table, illustrating balanced forces.

You've uploaded a worksheet titled “Worksheet #1 Free-Body or Force diagrams…” which teaches how to draw free-body diagrams (FBDs) — simplified diagrams showing all the forces acting on an object.

Let’s go through each of the 4 problems, solve them, and explain the reasoning step by step.

---

## ✔ GENERAL RULES FOR FREE-BODY DIAGRAMS:

1. Represent the object as a dot, box, or circle.
2. Draw arrows (vectors) starting from the center of the object, pointing in the direction the force acts.
3. Label each force with its symbol (e.g., F_g for gravity, F_N for normal force, F_T for tension, F_f for friction, F_air for air resistance).
4. The length of the arrow should reflect the relative magnitude of the force.
5. Only include forces acting ON the object, not forces the object exerts on other things.

---

# 🔹 PROBLEM 1:
> A book is at rest on a table top. Diagram the forces acting on the book.

📌 Forces:

- F_g (gravity) – Acts downward (toward Earth’s center). Always present near Earth’s surface.
- F_N (normal force) – The table pushes *up* on the book to support it. Since the book is at rest, this must be equal in magnitude and opposite in direction to gravity.

✍️ Diagram:

```
↑ F_N
●
↓ F_g
```

💡 Explanation:

The book is at rest, so net force = 0 → forces are balanced. Gravity pulls down; the table pushes up with equal force (normal force). No motion → no friction or other forces needed.

---

# 🔹 PROBLEM 2:
> A girl is suspended motionless from the ceiling by a rope. Diagram the forces acting on the girl as she holds onto the rope.

📌 Forces:

- F_g (gravity) – Downward.
- F_T (tension in the rope) – Upward. The rope pulls her up to counteract gravity.

✍️ Diagram:

```
↑ F_T
●
↓ F_g
```

💡 Explanation:

She is motionless → net force = 0. Tension force from the rope balances her weight (gravity). Since she’s holding the rope, we assume the rope is taut and providing upward tension.

*(Note: Sometimes people draw “F_R” for rope force — but “F_T” for tension is more standard.)*

---

# 🔹 PROBLEM 3:
> An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it falls.

📌 Forces:

- F_g (gravity) – Only force acting! Since air resistance is neglected, nothing else opposes or assists gravity.

✍️ Diagram:

```
●
↓ F_g
```

💡 Explanation:

“Free-fall” means only gravity acts — no air resistance, no contact forces. So the egg accelerates downward at g ≈ 9.8 m/s². This is the simplest FBD — just one force!

---

# 🔹 PROBLEM 4:
> An egg is falling (not freely, do not neglect air resistance) from a nest in a tree. Diagram the forces acting on the egg as it falls.

📌 Forces:

- F_g (gravity) – Downward.
- F_air (air resistance / drag) – Upward. Opposes motion. Since the egg is falling down, air resistance acts *up*.

✍️ Diagram:

```
↑ F_air
●
↓ F_g
```

💡 Explanation:

Now we do NOT neglect air resistance. As the egg falls, air pushes *up* against it. Initially, gravity > air resistance → egg accelerates. Eventually, if falling long enough, they may become equal (terminal velocity), but at any moment during fall, both forces are present.

> ⚠️ Important: Air resistance is often labeled as F_d (drag) or F_air — your worksheet uses F_F (maybe “force of friction” or “fluid force”) — check what symbol was used in class. In the example diagram, they used F_frict, F_norm, F_grav, F_applied — so perhaps here they’d use F_air or F_f for fluid friction.

Since the worksheet example shows “F_frict”, maybe they want F_f for air resistance? But technically, air resistance is a type of drag, not solid friction. However, for simplicity in intro physics, sometimes F_f is used broadly.

✔ So if following worksheet style:
Use F_g down, F_f up.

```
↑ F_f
●
↓ F_g
```

---

## ✔ SUMMARY OF ALL 4 DIAGRAMS:

| Problem | Object | Forces Present | Diagram |
|---------|--------------|----------------------------|-----------------------------|
| 1 | Book on table| F_g (down), F_N (up) | ↑ F_N<br>●<br>↓ F_g |
| 2 | Girl hanging | F_g (down), F_T (up) | ↑ F_T<br>●<br>↓ F_g |
| 3 | Egg (free fall)| F_g (down) | ●<br>↓ F_g |
| 4 | Egg (with air res.)| F_g (down), F_f (up) | ↑ F_f<br>●<br>↓ F_g |

---

## 🎯 KEY TAKEAWAYS:

- Always start with gravity (F_g) — unless in space or specified otherwise.
- Normal force (F_N) appears when object is in contact with a surface that supports it.
- Tension (F_T) appears when something is being pulled by a rope/cable.
- Air resistance (F_air or F_f) opposes motion — acts *opposite* to velocity.
- At rest or constant velocity → net force = 0 → forces balance.
- Accelerating? Then forces are unbalanced.

---

If you’re submitting this worksheet, make sure to:

✔️ Draw clean arrows from the center of the object
✔️ Label each force clearly
✔️ Use consistent symbols (check what your teacher prefers — e.g., F_g vs. W for weight, F_N vs. N, etc.)

Let me know if you want these drawn visually or need help labeling based on your class symbols! 😊