Force diagram worksheet for physics education, illustrating scenarios like a bird in flight, a hockey player, and a baseball player sliding.

Let's solve each of the three force diagram problems step by step. We'll analyze the situation, identify all forces acting on the object, draw a proper force diagram (free-body diagram), write the net force equations for both horizontal and vertical directions, and define any necessary sign conventions.

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Problem 1: A bird sitting motionless on a perch

#### Step 1: Identify Forces
- The bird is motionless, so it is in equilibrium.
- Two forces act on the bird:
- Gravitational Force (Fg): Pulls downward due to gravity.
- Normal Force (Fn): Exerted by the perch upward, supporting the bird.

#### Step 2: Draw the Force Diagram
- Draw a dot to represent the bird.
- Draw a downward vector labeled Fg (gravity).
- Draw an upward vector labeled Fn (normal force).
- Since the bird is not moving, these two forces are equal in magnitude and opposite in direction.

#### Step 3: Sign Conventions
- Let’s define:
- Upward as positive (+)
- Downward as negative (−)

#### Step 4: Net Force Equations
Since the bird is at rest:
- Vertical direction:
∑Fy = Fn − Fg = 0 → Fn = Fg
- Horizontal direction:
No horizontal forces → ∑Fx = 0

#### Subscript Definitions
- Fg: Gravitational Force
- Fn: Normal Force

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✔ Answer for Problem 1

| Sign Conventions: | Force Diagram: |
|------------------------|--------------------|
| ↑ + | [Draw a dot with two arrows: one upward (Fn), one downward (Fg), equal length] |
| ↓ − | |

| Net Force Equations: |
|--------------------------|
| ∑Fx = 0 |
| ∑Fy = Fn − Fg = 0 |

| Subscript Definitions: |
|----------------------------|
| Fg: Gravitational Force |
| Fn: Normal Force |

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Problem 2: A hockey player moving at constant velocity across frictionless ice

#### Step 1: Identify Forces
- The player is moving at constant velocity → no acceleration → net force = 0
- Surface is frictionless, so no frictional force.
- Forces:
- Fg: Downward gravitational force.
- Fn: Upward normal force from the ice.
- No horizontal forces — since there's no friction and no mention of pushing/pulling (assuming they're coasting).

> Note: Even though the player is moving, if velocity is constant and no external horizontal forces, no push or pull is needed.

#### Step 2: Force Diagram
- Dot for the hockey player.
- One downward arrow: Fg
- One upward arrow: Fn
- Equal length (since in equilibrium)

#### Step 3: Sign Conventions
- Up: +
- Down: −
- Right: +
- Left: −

#### Step 4: Net Force Equations
- ∑Fx = 0 (no horizontal forces)
- ∑Fy = Fn − Fg = 0 → Fn = Fg

#### Subscript Definitions
- Fg: Gravitational Force
- Fn: Normal Force

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✔ Answer for Problem 2

| Sign Conventions: | Force Diagram: |
|------------------------|--------------------|
| ↑ + | [Dot with Fg down, Fn up, same length; no horizontal arrows] |
| ↓ − | |
| ← − | |
| → + | |

| Net Force Equations: |
|--------------------------|
| ∑Fx = 0 |
| ∑Fy = Fn − Fg = 0 |

| Subscript Definitions: |
|----------------------------|
| Fg: Gravitational Force |
| Fn: Normal Force |

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Problem 3: A baseball player who slows as he slides into the base

#### Step 1: Identify Forces
- The player is slowing down → decelerating → acceleration is opposite to motion
- He is sliding → kinetic friction acts between his body and the ground.
- Forces:
- Fg: Downward gravity
- Fn: Upward normal force
- Ff: Frictional force — opposes motion → acts backward (opposite to direction of motion)
- No applied force (he’s just sliding)

> Note: Friction is the only horizontal force here.

#### Step 2: Direction of Motion
Assume the player is moving to the right and slowing down.
→ So, Ff acts to the left (retarding the motion)

#### Step 3: Force Diagram
- Dot for player
- Downward arrow: Fg
- Upward arrow: Fn
- Leftward arrow: Ff
- Fg and Fn are equal (vertical equilibrium), but Ff is separate horizontally

#### Step 4: Sign Conventions
- Up: +
- Down: −
- Right: +
- Left: −

#### Step 5: Net Force Equations
- Vertical: No acceleration → ∑Fy = Fn − Fg = 0
- Horizontal: Slowing down → acceleration is negative (left), so:
∑Fx = −Ff = ma (but we don’t need mass here — just equation form)

So:
- ∑Fx = −Ff (if right is positive)
- ∑Fy = Fn − Fg = 0

#### Subscript Definitions
- Fg: Gravitational Force
- Fn: Normal Force
- Ff: Frictional Force

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✔ Answer for Problem 3

| Sign Conventions: | Force Diagram: |
|------------------------|--------------------|
| ↑ + | [Dot with Fg down, Fn up (equal), Ff pointing left] |
| ↓ − | |
| ← − | |
| → + | |

| Net Force Equations: |
|--------------------------|
| ∑Fx = −Ff |
| ∑Fy = Fn − Fg = 0 |

| Subscript Definitions: |
|----------------------------|
| Fg: Gravitational Force |
| Fn: Normal Force |
| Ff: Frictional Force |

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✔ Summary of Key Concepts

| Situation | Acceleration? | Net Force? | Forces Present |
|---------|---------------|------------|----------------|
| Bird at rest | No | Zero | Fg, Fn |
| Hockey player at constant velocity | No | Zero | Fg, Fn |
| Player sliding & slowing | Yes (decelerating) | Not zero | Fg, Fn, Ff |

> Remember: Force diagrams show all forces on the object, not forces the object exerts. Use dots to represent objects. Arrows show magnitude and direction of forces. Label clearly!

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