Motion, Gravity & Newton's Laws

Unifying Principles and Concepts of Science (I)

• The lecture focuses on Motion and Gravity.

Disclaimer

• Formulae will be presented in this chapter.
• Understanding their meaning and using them for qualitative arguments is expected.
• No computational problems need to be performed with the formulae.
• As an example, consider Newton's second law, F = ma.

Describing Motion and Change

• Descriptors of science include length, time, temperature, energy, and entropy.
• Motion involves Newton's Laws which are Newton's Laws of Motion and Gravitation, and the laws of thermodynamics.
• Energy of life and the Theory of evolution correlate with the Second Law of Thermodynamics.

The One Idea

• Newton's laws of motion and gravity are universal.
• These laws govern the behavior of objects on Earth and in space.

Outline of Lecture

• The lecture will cover describing state/change (length, time, velocity, acceleration) and motion (Newton's laws).
• The concept of force is important when understanding motion.
• It is important to differentiate between daily perception and scientific reality,
• Exploring Newton's law of gravitation, numbers, and universal laws of science will be discussed.
• Many ideas will be revisited later in the course.

Language of Science vs Daily Language

• Knowing a bit about the language of motion is key to understanding it.
• Science sharpens everyday terms for exactness but it can lead to misconceptions.

The Language of Motion

• Speed is the distance an object travels divided by the time it takes, measured in meters per second (m/s).
• Velocity is similar to speed but includes direction, making it a vector quantity, also measured in m/s.
• Acceleration is the rate of change of velocity, either in magnitude (speed) or direction, measured in m/s².
• The scientific definition of "acceleration" differs from daily usage.
• In science, any change in velocity (speed or direction) results in acceleration.

Centripetal Acceleration

• Objects moving at a uniform speed around a circular path experience acceleration.
• Acceleration experienced by the object is centripetal.
• Change in speed or direction of velocity can cause acceleration.

Feather-Hammer Drop Experiment

• It was once believed heavier objects fall faster than lighter ones.
• The acceleration 'a' was thought to depend on mass 'm'.
• Galileo stated all objects accelerate at the same rate (g) when falling downwards.

Studying a Changing Universe

• Galileo did not consider what causes acceleration.
• Isaac Newton synthesized Galileo's work into Newton's laws of motion.
• Included in Newton's laws of motion is the theory of gravity.
• Objects on Earth and celestial bodies are governed by the same natural laws.
• Isaac Newton lived from 1642-1727.

Newton's First Law of Motion

• A moving object continues in a straight line at a constant speed, and a stationary object remains at rest unless acted upon.
• Leaving an object alone will not change its state of motion, only applying a force will cause it to change.
• Force is required to keep an object moving in a circle.
• The natural motion of an object is a straight line and any other motion requires an applied force.

Newton's Second Law of Motion

• Acceleration is proportional to force and inversely proportional to mass.
• The law describes what force does when it acts.
• Expressed as F = ma, where F is force.
• The unit of force is the Newton (N): 1 N = 1 kg x 1 ms⁻².
• Net unbalanced force causes acceleration.
• Motions can be definitively determined if positions, velocities, masses, and forces are all known.

Newton's Third Law of Motion

• Every action has an equal and opposite reaction.
• When a force is applied to an object, that object exerts an equal and opposite force.
• Force always acts simultaneously in pairs.

Newton's Laws of Motion

• All motion in the universe involves the constant interplay of Newton's three laws.
• These laws never occur in isolation.

Balloon Car Example

• The balloon car illustrates Newton's laws.
• Newton's third law is exemplified by the balloon exerting a backward force, with air providing an equal forward force.
• Newton's first law states that the forward force by the air changes the car from stationary to moving.
• Newton's second law states that the car's initial acceleration is proportional to the forward force and inversely proportional to its mass.

Common Misconceptions

• Intuition and daily experience often conflict with Newton's laws.
• An object with no unbalanced force will naturally come to rest, which is incorrect.
• An unbalanced force causes an object to move with a constant velocity which is also incorrect.
• A third incorrect idea involves, larger objects applying larger force to smaller objects.

Newton's Law of Gravitation

• Newton saw an apple fall and the Moon, realizing gravity's influence.
• For the Moon to orbit Earth, it must experience force.
• His revelation was that the same force that pulls the apple also pulls the Moon.
• Universal gravitation governs motion on Earth, moons, and planets.
• Universality among all objects and mass scales applies to this force.

Newton's Law of Universal Gravitation Formula

• Deriving the formula for gravitational force required a new branch of mathematics known calculus.
• There is an attractive force between objects that is proportional to masses and inversely proportional to the square of the distances. Gm1m2 d2
• Force of gravity between two masses m1, m2 is F = .
• 'd' meaning separation between them and 'G' meaning Gravitational constant, being 6.67 ×10-11 N m2 kg-2.
• The magnitude of gravitational force is inversely proportional to square of the distance (inverse square law).

Forces Come in Pairs

• The Earth exerts a force F on the apple, and the apple exerts a force F' on the Earth.
• The magnitude (strength) of the two forces are the same.
• The Earth and the Moon are no exception as these relations are applicable to gravitational forces between any masses.

Acceleration Due to Gravity

• At the same distance from the Earth, the acceleration due to gravity is the same.
• All objects accelerate at 9.8 m/s² on Earth, though the force on each object varies.
• Acceleration is not the same at different distances from the Earth, such as for the Moon, which is much smaller than g.

Numbers

• Newton's law of gravitation requires sensitivity to numbers.
• The small value of G dictates that gravity is weak between everyday objects, and is usually ignorable.
• Except when one of the objects is the Earth (6 × 1024 kg).
• Ex: Two 100kg masses at 1m apart experience a gravitational force of 6.67 x 10-7 N, which is equivalent to a weight of 6.8 × 10-8 kg.

Mass and Weight

• Newton distinguished mass and weight.
• Mass measures an object's resistance to changes in motion.
• Weight is the force of gravity on an object depending on location.
• An object with a mass of 100kg will have a weight of 980 N (Earth's surface) but only 162 N (Moon).
• A bathroom scale measures the effect of Earth's gravity
• It determines mass and measures own weight.

Relationship Between Mass and Weight

• It's easier to change weight than mass.
• Mass remains the same while weight fluctuates in free fall or different acceleration.
• Mass is fundamental in science, however, weight is not as much.

Weightlessness

• "Weightlessness" and free call are related and can be associated with examples of weightlessness conditions in spacecrafts.
• There is no support or feeling of weight.

Feather-Hammer Drop Experiment on the Moon

• In 1971, an Apollo 15 astronaut performed the feather-hammer drop experiment on the Moon.

Lectures 4 and 5

• Lectures 4 and 5 require reading Trefil & Hazan, Chapter 3 (Energy) and Chapter 4 (Heat and the Second Law of Thermodynamics).
• The second law of thermodynamics and entropy is to be understood.
• An article by Steven Pinker and why entropy implies "an arrow of time" were assigned.