SCNC1112: Motion and Gravity

• SCNC1112: the course covers Unifying Principles and Concepts of Science (I), specifically Motion and Gravity.
• The formulae presented are for understanding, not computation.
• Grasp the meaning and implications of formulae for quantitative reasoning and qualitative arguments, such as how force changes with mass in Newton's 2nd law (F=ma).
• The lecture explores observed phenomena, the principles behind them, and how science describes them.
• Length, time, temperature, energy, and entropy serve as descriptors of science.
• Motion is linked to Newton's Laws of Motion, Gravitation, and the Laws of Thermodynamics governing motion and energy.
• Newton's laws of motion and gravity apply universally to objects on Earth and in space.

Outline of Lecture

• The plan includes describing state and change (length, time, velocity, acceleration), motion (Newton's laws), Newton's law of gravitation, the importance of numbers in science, and universal laws.
• Focus is given to the language of motion.
• To understand motion, learning the language of motion is required
• Science refines everyday terms for exact meaning
• Misconceptions and misunderstandings arise.

Language of motion

• Speed measures distance traveled over time, in meters per second (m/s).
• Velocity, measured in m/s, is a vector quantity, indicating both speed and direction.
• Acceleration, in m/s², is the rate of change of velocity, affecting either speed or direction
• Scientific definition of acceleration includes change in speed or direction, not just increase in speed
• Objects moving at a constant speed in a circle accelerate towards the center, known as centripetal acceleration, because their direction changes.

Feather-Hammer Experiment

• Previously, heavier objects were believed to fall faster.
• Galileo stated all objects accelerate at same rate downward

Isaac Newton's Contributions

• Galileo did not discover what drives acceleration
• Isaac Newton's work synthesized Galileo's, establishing motion laws
• Newton's Laws of Motion and theory of gravity explain planetary motion.
• It demonstrates Earthly and celestial motions obey the same laws.

Newton's First Law of Motion

• An object maintains constant speed in a straight line, or stays at rest, unless acted upon by an unbalanced force.
• Naturally objects move in a straight line
• A force needed to move in a circle

Newton's Second Law of Motion

• Acceleration is proportional to force, and inversely proportional to mass.
• Net unbalanced force causes acceleration.
• If initial positions, velocities, masses, and forces known the motions become definitively determined

Newton's Third Law of Motion

• For every action, there is an equal and opposite reaction.
• An object exerting a force experiences an equal and opposite force.
• Forces always act in pairs simultaneously.
• All of Newton's laws interplay constantly in universe
• Laws interlock as aspects of an object's behavior
• Newton's laws are counter-intuitive.

Newton's Discovery of Gravity

• Newton saw an apple fall and the Moon, realizing a shared force
• Newton's first law shows the Moon experiences a forces to orbit the Earth
• The same force pulling the apple pulls the Moon.
• Gravity is a universal force governing motion on Earth and in space.
• The force is universal across objects and mass scales.
• Gravity, where the force (F) between two masses (m₁, m₂) is F = Gm₁m₂/d², with 'd' as separation, and 'G' is gravitational constant (6.67 x 10⁻¹¹ N m² kg⁻²) (inverse square law).

Gravity and the Earth

• Gravitational forces point toward the Earth's center (centripetal).
• Earth acts on apple, the apple acts on the earth (same magnitude)
• Acceleration is identical for all objects, such as at Earth's surface (g = 9.8 m/s²).
• Acceleration varies with distance from the Earth.
• It also demonstrated that gravity is a force between two masses.
• The gravitation force for two everyday objects is usually small, unless one object is the Earth

Mass vs Weight

• Newton distinguished mass from weight
• Mass measures resistance to motion changes per Newton's first law
• Weight measures the force of gravity, dependent on location.
• An object with mass 100kg weighs 980 N on Earth due to gravity
• Mass remains constant, while weight varies.
• Mass is fundamental, unlike weight.
• Weightlessness: no support and no gravity.
• Apollo 15 tested feather-hammer drop on Moon in 1971
• In comparison on Earth: Air resistance is much higher.

Preparation for Lectures 4 and 5

• Read Trefil & Hazan Chapters 3 & 4 on Energy, Heat, and the Second Law of Thermodynamics.
• Understand the second law of thermodynamics and entropy