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Describing Motion

- Speed: How Fast.
- Velocity: How fast in which direction.
- Acceleration: How fast and in which direction velocity changes.

Sometimes, acceleration is a constant

- Example: Acceleration due to gravity is constant near the surface of the Earth.
- Since it is a constant, the acceleration due to gravity is given the special symbol g.
- For the earth, g = 9.8 m/s/s or approximately 10 m/s/s.

When Acceleration = g, we have Free Fall Motion.

Notice that the V arrow gets longer while the g arrow does not. It remains constant in length and direction.

V = 0m/s

t = 0 seconds

g

V(t) = V(0) + g(t)

V(2sec) = 0 + (10m/s2)(2s)

V(2sec) = 20m/s

V = ?

t = 2 seconds

g

Gravitational Acceleration Near the Surface of the Earth.

On the Earth, the acceleration due to gravity is ~ 10m/s2 (9.8 m/s2).

Momentum and Force

- Momentum = Mass x velocity
- Force = (Change in Momentum)/(Change in time).

V

p – linear momentum

m

p = mV

Example: If m = 10kg and V = 10m/s (East)

P = (10kg)(10m/s) = 100 kg m/s (East)

Mass and Weight

- Mass : Amount of matter a body possesses.
- Weight : Force of gravity acting on the mass.
- Apparent weight = Net force that acts on the mass.

Weight is not the same as mass. The man’s weight changes, but his mass remains constant.

Free-fall, Weightlessness, and Orbit

- Free-Fall- the condition of an accelerating mass when the acceleration = g.
- Weightless- If the only force acting is that due to gravity, and there is no reaction force from a floor, for example, pushing up against you, then one is in a state of free-fall and experiences weightlessness.

Astronauts are in a prolonged period of weightlessness when they are in orbit

Newton’s Cannon

- The faster the cannonball is shot, the farther it goes before hitting the ground.
- If it goes fast enough, it will continually “fall around” or orbit, the Earth.
- With a fast enough speed, it may escape the Earth’s gravity altogether.
- Escape velocity – The minimum velocity needed to escape from the gravitational field of a moon, planet or star.

Newton’s Three Laws of Motion

- 1) Law of Inertia: In the absence of a net force, the motion of an object remains constant.
- 2) Net Force = Rate of change of momentum.
- Momentum = mass x velocity
- 3) For every force, there is always an equal and opposite reaction force.

Conservation of Linear Momentum and Conservation of Angular Momentum

- Conservation of Linear Momentum:
- In the absence of a net external force, linear momentum remains constant.
- Conservation of Angular Momentum:
- In the absence of a net torque (twisting force), the total angular momentum of a system remains constant.

Newton’s Law of Universal Gravitation

- Every mass attracts every other mass through the force called gravity.
- The force of attraction is directly proportional to the product of their masses.
- The force of attraction decreases with the square of the distance between the mass centers. This is called an inverse square law.

The “Why” of Kepler’s Laws, and More

- Newton found that Kepler’s first two laws apply not only to planets, but to any object going around another object under the force of gravity.
- He found that orbits do not have to be bound orbits as they are with elliptical orbits. Unbound (hyperbolic) orbits are also possible.
- Newton found that Kepler’s third law could be generalized in a way that allows us to calculate the mass of one or both orbiting objects.

Tides

- The tidal bulges face toward and away from the moon because of the difference in the strength of the gravitational attraction in parts of the Earth at different distances from the Moon.
- There are two daily high tides at any location on Earth, as it rotates through the two tidal bulges.

Tides also depend on tidal forces from the Sun, which are about 1/3 as strong as the moon’s.

Highest high tides.

Lowest low tides.

Tidal Friction causes three important effects

- It causes the Earth’s rotation to gradually slow down, resulting in a longer day.
- It makes the Moon move gradually away from the Earth (The Moon has a slight tangential component to its acceleration vector)
- Synchronous rotation is a natural consequence of tidal friction.

Radial acceleration

It can be shown, by conservation of angular momentum, that the radial distance of the moon must increase as the rotation rate of the Earth decreases by tidal friction.

Orbital Energy and Escape Velocity

- A comet in an unbound orbit of the Sun, passes near Jupiter.
- The comet loses some of its orbital energy to Jupiter, which changes the comet’s path to a bound orbit around the Sun.

unbound orbit

bound orbit

The escape velocity is the velocity necessary for an object to completely escape the gravity of a large body such as a moon, planet or star.

- The escape velocity of the Earth = 11 km/s

G = 6.67 x 10-11 m3/kg s2

M = Mass of the planet

R = Radius of the planet

Matter and Energy in Everyday Life

- Matter:
- Matter is simply material, such as rocks, water, or air.
- Mass is the amount of matter an object has.
- Energy:
- In physics, energy is defined as the ability to do work.
- Generally two types of energy:
- 1) Kinetic
- 2) Potential
- We measure energy in calories, Joules, electron volts, along with many other units.

A typical adult consumes about 2500 calories of energy each day from the food they eat.

- In science and internationally, the favored unit of energy is the joule. This is because the joule can be written in the fundamental units of kg, m, and sec.
- 1 calorie = 4,184 joules. So 2500 calories used daily by a typical adult ~ 10 x 106 J (10million joules)

Whenever matter is moving, it has energy of motion, or kinetic energy.

- Kinetic Energy = Energy of motion.
- Potential Energy = Usually energy of position, but can also be regarded as stored energy.
- Gasoline has stored chemical potential energy which is converted to kinetic energy of the car.
- Radiative Energy = Energy of light (electromagnetic energy).

A Scientific View of Energy

v

m

We can calculate the kinetic energy of any moving object with a very simple formula:

KE = ½ mv2

m : Mass of the object. v: Speed of the object. KE: Kinetic energy measured in Joules.

Thermal Energy

- The energy contained within a substance as measured by its temperature is often called thermal energy.
- Thermal energy represents the collective kinetic energy of the many individual particles moving within a substance.

Same Temperature, but less thermal energy.

Same Temperature, and more thermal energy.

Types of Potential Energy

- Gravitational Potential Energy
- The amount of gravitational potential energy released as an object falls depends on its mass, the strength of gravity, and the distance it falls.
- GPE = mgh.
- Mass-Energy E = mc2
- A small amount of mass represents a huge amount of energy.

Conservation of Energy

- A fundamental principle in science is that, regardless of how we change the form of energy, the total quantity of energy never changes. This principle is called the:

Law of Conservation of Energy

The Material World

- Matter can exist in different phases.
- Solid
- Liquid
- Gas

What is Matter?

- Today, we know that all ordinary matter is composed of atoms.
- Each different type of atom corresponds to a different chemical element.
- Atoms can form molecules which can then form a number of different material substances.
- Some molecules consist of two or more atoms of the same element.

A small dense nucleus lies at the center of an atom.

- The nucleus is made up of protons and neutrons.
- The nucleus is surrounded by particles called electrons.
- The properties of an atom depend primarily on the amount of electrical charge. (protons and electrons)

Terminology

- atomic number: The number of protons in an atom.
- atomic mass:The combined number of protons and neutrons in an atom.
- isotope: Sometimes, the same element can have more than the usual number of neutrons. We call this an isotope.
- A proton and a neutron form an isotope of hydrogen called deuterium.

Finally, at 100oC (STP), the water molecules have enough thermal energy to break free from one-another.

Evaporation begins with the production of steam (water vapor).

Phases of Matter – example: waterThe water remains a liquid over a large temperature range.

As the temperature increases, the water becomes a liquid (liquid water)

Below 0oC (32oF), water is a solid (ice)

Ref: PJ Brucat (University of Florida)

Ions and Ionization

- The loss of one or more electrons (electrons are negatively charged) leaves the remaining atom with a net positive charge.
- Such charged atoms are called ions.
- The process of stripping electrons from atoms is called ionization.
- At high temperatures, the atoms of a hot gas can become ionized, creating a plasma phase of matter.

Energy in Atoms

- Atoms contain electric potential energy in the distribution of their electrons around their nuclei.
- Consider the hydrogen atom, which is the simplest atom.

Ionization

If the electron gains enough energy, it can escape the atom completely and we have an ionized atom.

If the electron gains energy, it becomes “smeared out” over a greater volume.

When the atom contains the smallest amount of electric potential energy, we say that the atom is in the ground state.

The Discovery of the Quantum World

- The most surprising aspect of atoms was the discovery that only particular energy transitions can occur for the electron.
- This was the beginning of Modern Physics (1910 – 1935) and a theory of Quantum Mechanics was developed.

Any height is possible

I’m Continuous!

I’m Quantized!

Quantum System

Only discrete “Quantized” step heights are possible.

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