Lecture 2- Newton Laws and Motion in 2D_05

Understanding Concepts: By the end of this lecture, you should be able to:
- Define key terms: force, mass, weight, inertia, momentum.
- Understand the influence of gravity and its effects on an object’s weight.
- Apply Newton’s 3 laws of motion in everyday contexts.
- Analyze 2D motion (projectile motion) by applying Newton's Laws and SUVAT equations.

Weight (W): The force due to gravity acting on mass (m). Formula: W = mg (N).
Momentum (M): Defined as the product of mass and velocity, M = mv (kg·m/s). It's a vector quantity aligned with velocity.
Inertia: The resistance of an object to change its velocity. Defined mathematically by I = mr² (kg·m²).
Mass (m): The quantity of matter in an object, measured in kilograms (kg).
Force (F): The rate of change in momentum. Formula: F = ma (N). A Newton is the force needed to accelerate a 1 kg mass at 1 m/s².

Magnitude on Earth: Gravity varies; g averages around 9.81 m/s², but it can vary depending on location due to Earth's shape and density.
- Equator vs Poles: A 1 kg mass weighs 9.78 N at the equator, 9.81 N at the poles.
Variation in Gravitational Force: Influenced by height, depth, and Earth's curvature. Variation can be ±50 milligals (1 milligal = 0.01 m/s²).
Universal Gravitational Constant (G): Approximately 6.67 x 10⁻¹¹ m³·kg⁻¹·s⁻².

Free Fall: Objects in free fall experience acceleration equal to g. In a vacuum (no air resistance), all objects fall at the same rate.
Terminal Velocity: When weight balances air resistance, an object reaches terminal velocity, resulting in zero net force.

An object at rest or in uniform motion will remain so unless acted upon by a resultant force.
Example: An ice puck gliding on ice continues at constant velocity in the absence of friction.
Inertia Relation: Greater mass leads to greater inertia, thus requiring more force to change motion.

The rate of change of momentum is proportional to the resultant force acting on an object.
Mathematical Representation: F = ma; if mass remains constant, Force is proportional to acceleration.
Newton's Definition: 1 Newton is the force necessary to accelerate 1 kg by 1 m/s².

For every action, there is an equal and opposite reaction.
Example: When pushing a wall, the wall pushes back. If the wall breaks, the push is no longer there, and one can fall through.
Action-Reaction Pairs: Forces come in pairs acting on different objects.

Mass: Constant regardless of location in the universe.
Weight Variations: Weight changes with gravity; 1 kg has a weight of 9.81 N on Earth but only 1.7 N on the Moon.
Gravitational Force: Depends on the distance from the planet's center and the planet's mass.

In Descending Elevators: As the elevator slows down, apparent weight increases due to acceleration.
The relationship integrates Newton's laws: FN = m(g + aelev) when accelerating up, and FN = m(g - aelev) for downward acceleration.

Involves motion across two dimensions influenced by gravitational force.
Two components of projectile motion: horizontal (x) and vertical (y).
The initial velocity can be broken down into x and y components, recognizing how gravity influences vertical motion but not horizontal.

Equations of Motion in 2D: When analyzing motion, treat x and y units separately.
Key SUVAT Equations:
- s = vt (average velocity)
- v = u + at
- s = ut + ½at²
- v² = u² + 2as