Dynamics: Newton’s Laws of Motion, Free-Body Diagrams, and Resistive Forces

Relationship Between Force and Motion: When a force is applied to an object, such as in sports like kicking a football, playing hockey, using a parachute, or playing tennis, there is an observable change in speed and/or direction over time. This implies a change in the body's velocity.
Acceleration and Deceleration: Since any change in velocity indicates acceleration or deceleration, it can be concluded that a force can cause an object to accelerate or decelerate.
Zero Acceleration Conditions: When an object is traveling at zero acceleration ( $a = 0\,m/s^2$ ), it does not necessarily mean no forces are present. Instead, it indicates that:
- The object is either stationary (at rest) or moving with a constant velocity.
- The resultant force acting on the object is zero ( $F = 0\,N$ ), meaning all acting forces are balanced.
Vector Nature of Force: Force is a vector quantity, possessing both magnitude and direction. To calculate the resultant force in a straight line, a specific direction (e.g., to the right) is assigned as positive. All directions must be considered to determine if forces are balanced (resultant is zero) or unbalanced (resultant is not zero).

Definition: Every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it.
Balanced Forces: This law applies when the forces acting on a body are balanced (resultant force $F = 0\,N$ ).
Real-World Application: Seat belts are a critical safety feature based on this law. If a driver applies the brakes suddenly, their body continues moving forward (uniform motion). The seat belt provides a necessary opposing force to stop the person from crashing into the windscreen.

Definition: When a resultant force acts on an object of a constant mass, the object will accelerate in the direction of the resultant force.
Mathematical Formula: The relationship between resultant force ( $F$ ), mass ( $m$ ), and acceleration ( $a$ ) is defined by the equation:
- $F = ma$
Units of Measurement:
- $F$ = Resultant force measured in Newtons ( $N$ ).
- $m$ = Mass of the object measured in kilograms ( $kg$ ).
- $a$ = Acceleration of the object measured in meters per second squared ( $m/s^2$ ).
Application: This law applies to objects that are either accelerating or decelerating because the forces acting on them are unbalanced ( $F \neq 0\,N$ ).

Definition: If body A exerts a force ( $F_{AB}$ ) on body B, then body B will exert an equal and opposite force ( $F_{BA}$ ) on body A.
General Maxim: For every action, there is an equal and opposite reaction.
Characteristics of Action-Reaction Pairs:
1. Forces always occur in pairs (action and reaction).
2. The forces are equal in magnitude.
3. The forces act in opposite directions.
4. The forces act on different bodies (Body A and Body B).
5. Each pair of forces must be of the same nature (e.g., both gravitational or both normal forces).
Examples:
- Balloon Propelling Upwards: When air is released from a balloon (action), the balloon moves in the opposite direction (reaction).
- Book on a Table:
  - The gravitational force ( $F_{EB}$ ) exerted by Earth on the book and the upward force ( $F_{BE}$ ) by the book on Earth form one pair.
  - The normal force ( $F_{TB}$ ) by the table on the book and the normal force ( $F_{BT}$ ) by the book on the table form another pair.

Purpose: Free-body diagrams use arrows to represent the forces acting on individual objects. They serve as visual aids to help identify forces and their effects, facilitating problem-solving.
Representation: Forces are represented by arrows showing direction and magnitude, typically for cases in one or two dimensions.
Historical Case Study: In $2012$ , Austrian skydiver Felix Baumgartner became the first human to break the sound barrier in freefall. FBDs can be used to represent the forces (weight and air resistance) acting on him when he reached terminal velocity.

Definition of Friction: Friction is the contact force that opposes or tends to oppose motion between surfaces in contact. It is caused by the irregularities of the surfaces.
Friction in Different Mediums:
- Solids: Opposes motion between two solid surfaces.
- Liquids: A swimmer is slowed by friction between the water and their body.
- Gases: A runner experience air resistance while sprinting.
Resistive Nature: Friction is categorized as a resistive force because it always acts in the opposite direction to the motion of the body.

Reducing Negative Effects: Friction causes wear and tear (e.g., shoe soles wearing out) and energy loss as heat. It can be reduced using:
- Ball bearings.
- Lubricants (e.g., on bicycle chains).
- Air cushions (e.g., hovercrafts ejecting high-pressure air to stay above water or land).
- Magnetic levitation (Maglev trains).
Enhancing Positive Effects: Friction is useful for movement and safety. It can be enhanced through:
- Tire treads (providing grip on the road).
- Talcum powder or chalk for rock climbers and weightlifters.
- Parachutes (increasing air resistance).

Scenario: Two skydivers (A and B) of equal mass leap from a plane. Skydiver A is in a "spread-eagle" position, while Skydiver B is in a "head-first" position.
Scientific Explanation:
- Air resistance depends on the surface area of the object. Higher surface area equals higher air resistance.
- Skydiver A has a larger surface area and thus experiences more air resistance than Skydiver B.
- Since weight ( $W$ ) is equal for both, the downward resultant force ( $F = W - \text{Air Resistance}$ ) is smaller for Skydiver A.
- According to $F = ma$ , a smaller resultant force results in a smaller acceleration. Therefore, Skydiver A falls slower and stays above Skydiver B.

Ancient Belief: In the past, people incorrectly believed a force was needed to keep a body in motion.
Galileo Galilei ( $1564 – 1642$ ): In the $17\text{th}$ century, Galileo discovered through experiments that a body in motion stays in motion unless a force acts on it, overturning long-held theories.
Sir Isaac Newton ( $1643 – 1727$ ): Newton built upon Galileo’s work to formalize the three Laws of Motion, showcasing scientific collaboration and the refinement of knowledge through experimental evidence.

iFly at Sentosa: How do skydivers stay suspended in the wind tunnel simulator? (Dimensions: Height = $17.2\,m$ , Diameter = $5.03\,m$ ).
Spinning Eggs: If you spin a raw egg and a hard-boiled egg, which one will stop first when you touch it?
Shoe Soles: What causes shoe soles to wear out after several months, and why must they be replaced?
Roller Coasters: Why do riders momentarily feel weightless or "airborne" on a roller coaster? Is it a sensation, or have they actually lost weight?
Paper Dynamics: If an A4-sized piece of paper is dropped when flat versus when crushed from the same height, which reaches the ground first? (Explanation: The crushed piece has less surface area, less air resistance, and thus a higher resultant downward force).
The World Without Friction: How different would the world be if there was no friction? Consider walking, stopping vehicles, or holding objects.