forces and motion

What is a force?
- An interaction between two objects; a force acts on each object involved.
- Forces are pushes, pulls or twists.
- They can:
- Start objects moving
- Stop objects moving
- Change the speed of moving objects
- Change the direction of moving objects
Two broad categories of forces (for simplicity):
- contact forces
- non-contact forces

Definition: forces that can act over a distance without touching.
Examples:
- Magnetic forces between magnets
- Gravity pulling objects toward the Earth
Important point: interaction does not require contact

Magnetic poles:
- Opposite poles attract
- Same poles repel
Direction of magnetic field lines: from north (N) to south (S) outside the magnet
Visualizing field: draw lines showing the pattern of the magnetic field

How to visualize magnetic fields:
1. Sprinkle iron filings next to the magnet (not on the magnet) to reveal the field
2. Draw several lines in your booklet to show the field shape (similar to the red diagram lines)
Compass needles and magnets:
- Compass needles have poles; the needle’s north end points toward the magnetic south pole of the Earth/magnet
- Opposites attract; test with your magnet and compass
Field line direction with two magnets:
- Field lines connect the north of one magnet to the south of another
- Even with two magnets, the lines show connections between N and S

Looking at field diagrams, you can infer magnetic north and south poles on Earth
The north end of a compass needle points toward the Earth’s magnetic south pole (field direction convention)

Paper-clip maze: place a paper clip on cardboard, move a magnet underneath to guide it through a maze
Rescue a paper clip from water: use a magnet on the outside of a glass to pull the paper clip without getting wet
Paper-clip up a ruler: use a magnet under the ruler to pull the clip toward the end of the ruler

Definition: a point representing the average position of the matter in a body or object; useful for stability analysis
Mass distribution determines the center of mass, which helps predict stability

Methods shown:
- Plumb line
- Pivot
- Intersection of lines from the object’s geometry (centre of mass located where a vertical line through the COM passes through the base)
If the vertical line through the centre of mass does not pass through the base, the object topples

Thrust Force
- A force applied to an object by another object or by a person
- Examples:
- Pushing a desk across a room
- The thrust force is the force exerted on the desk by the person (action on the desk)
Support Force
- Normal reaction from a surface supporting an object
Friction Force
- The force that opposes motion between two contacting surfaces
- Occurs when an object moves across a surface or attempts to move across it

Balanced forces:
- Two equal forces push/pull in opposite directions
- Net force is zero; object remains at rest or continues moving at constant velocity (Newton’s first law context)
Unbalanced forces:
- One force is larger than the other
- Net force is not zero; object changes speed or direction

Speed (scalar) and velocity (vector)
Speed: distance traveled per unit time
Velocity: speed with direction
Common equation (scalar form):
- v = \frac{d}{t}
- where v is speed (or speed along a path), d is distance, and t is time
Velocity direction convention: positive forward, negative backward

Axes: Distance from the start (Y-axis) vs Time (X-axis)
Key features:
- A steeper line indicates larger distance moved in a given time (higher speed)
- Constant speed: straight line with constant slope
- Distance increasing with time: moving forward
- Stationary: horizontal line (distance constant, speed 0)
When distance-time lines curve (not a straight line):
- Upward curvature indicates acceleration (increasing speed)
- Downward curvature indicates deceleration (decreasing speed)
Gradients:
- The gradient on a distance-time graph equals the speed, i.e. v = \frac{\Delta d}{\Delta t}

These graphs show how speed changes over time
Typical interpretations:
- A-B: object moving at a steady speed (constant v)
- B-C: decelerating (speed decreasing)
- C-D: stationary (speed = 0)
- D-E: accelerating (speed increasing) [example sections may vary by diagram]
The gradient on a speed-time graph correlates with acceleration (change of speed per unit time)

Example 1: Ball moving 5 meters in 2 seconds
- Speed = v = \frac{d}{t} = \frac{5}{2} = 2.5\ \text{m s}^{-1}
Example 2: Car travels 10 km in 6 minutes; convert to hours
- 6 minutes = 0.1 hours
- Speed = v = \frac{d}{t} = \frac{10}{0.1} = 100\ \text{km h}^{-1}
Example 3: Cyclist 2.1 km in 5 minutes
- 5 minutes = 300 seconds
- Speed = v = \frac{2100}{300} = 7\ \text{m s}^{-1}
Example 4: Triathlete total race time 2 h; total distance 51.5 km
- Average speed = \frac{51.5}{2} = 25.75\ \text{km h}^{-1}

Distance-time graphs illustrate how distance changes with time and reveal speed via slope
Speed-time graphs illustrate how speed changes with time and reveal acceleration via slope or curvature