Homework 3

Unit 18 Problem 10, 12, 13(only b), 17, 18, 20Unit 19 Problem 17, 20

Escape Velocity is for more than just Rockets!

• The concept of escape velocity is useful for more than just rockets!

• It helps determine which planets have an atmosphere, and which don’t– Object with a smaller mass (such as the

Moon, or Mercury) have a low escape velocity. Gas particles near the planet can escape easily, so these bodies don’t have much of an atmosphere.

– Planets with a high mass, such as Jupiter, have very high escape velocities, so gas particles have a difficult time escaping. Massive planets tend to have thick atmospheres.

The Origin of Tides

• The Moon exerts a gravitational force on the Earth, stretching it! – Water responds to

this pull by flowing towards the source of the force, creating tidal bulges both beneath the Moon and on the opposite side of the Earth

High and Low Tides

As the Earth rotates beneath the Moon, the surface of the Earth experiences high and low tides

The Sun creates tides, too!

• The Sun is much more massive than the Moon, so one might think it would create far larger tides!

• The Sun is much farther away, so its tidal forces are smaller, but still noticeable!

• When the Sun and the Moon line up, higher tides, call “spring tides” are formed

• When the Sun and the Moon are at right angles to each other, their tidal forces work against each other, and smaller “neap tides” result.

The Conservation of Energy

• The energy in a closed system may change form, but the total amount of energy does not

change as a result of any process

• Kinetic Energy is simply the energy of motion

• Both mass (m) and velocity (V) contribute to kinetic energy

• Imagine catching a thrown ball.– If the ball is thrown gently, it hits your hand

with very little pain– If the ball is thrown very hard, it hurts to

catch!

Kinetic Energy

Thermal Energy

• Thermal energy is the energy associated with heat

• It is the energy of the random motion of individual atoms within an object.

• What you perceive as heat on a stovetop is the energy of the individual atoms in the heating element striking your finger

Potential Energy

• You can think of potential energy as stored energy, energy ready to be converted into another form

• Gravitational potential energy is the energy stored as a result of an object being lifted upwards against the pull of gravity

• Potential energy is released when the object is put into motion, or allowed to fall.

Conversion of Potential Energy

• Example:– A bowling ball is lifted from the floor

onto a table• Converts chemical energy in your

muscles into potential energy of the ball– The ball is allowed to roll off the table

• As the ball accelerates downward toward the floor, gravitational potential energy is converted to kinetic energy

– When the ball hits the floor, it makes a sound, and the floor trembles

• Kinetic energy of the ball is converted into sound energy in the air and floor, as well as some heat energy as the atoms in the floor and ball get knocked around by the impact

Definition of Angular Momentum

• Angular momentum is the rotational equivalent of inertia

• Can be expressed mathematically as the product of the objects mass, rotational velocity, and radius

• If no external forces are acting on an object, then its angular momentum is conserved, or a constant:

Conservation of Angular Momentum

• Since angular momentum is conserved, if either the mass, size or speed of a spinning object changes, the other values must change to maintain the same value of momentum

– As a spinning figure skater pulls her arms inward, she changes her value of r in angular momentum.

– Mass cannot increase, so her rotational speed must increase to maintain a constant angular momentum

• Works for stars, planets orbiting the Sun, and satellites orbiting the Earth, too!

The Nature of Light

• As a wave…– A small disturbance in an electric field creates

a small magnetic field, which in turn creates a small electric field, and so on…

• Light propagates itself “by its bootstraps!”– Light waves can interfere with other light

waves, canceling or amplifying them!– The color of light is determined by its

wavelength.

• As a particle…– Particles of light (photons) travel

through space.– These photons have very specific

energies. that is, light is quantized.– Photons strike your eye (or other

sensors) like a very small bullet, and are detected.

• Light is radiant energy.• Travels very fast –

300,000 km/sec!• Can be described either

as a wave or as a particle traveling through space.

The Effect of Distance on Light

• Light from distant objects seems very dim– Why? Is it because the photons

are losing energy?– No – the light is simply

spreading out as it travels from its source to its destination

– The farther from the source you are, the dimmer the light seems

– We say that the object’s brightness, or amount of light received from a source, is decreasing

This is an inverse-square law – the brightness decreases as the square of the distance (d) from the source

The Nature of Matter

• The atom has a nucleus at its center containing protons and neutrons

• Outside of the nucleus, electrons whiz around in clouds called orbitals– Electrons can also be

described using wave or particle models

– Electron orbitals are quantized – that is, they exist only at very particular energies

– The lowest energy orbital is called the ground state, one electron wave long

• To move an electron from one orbital to the next higher one, a specific amount of energy must be added. Likewise, a specific amount of energy must be released for an electron to move to a lower orbital

• These are called electronic transitions

The Chemical Elements

• The number of protons (atomic number) in a nucleus determines what element a substance is.

• Each element has a number of electrons equal to the number of protons

• The electron orbitals are different for each element, and the energy differences between the orbitals are unique as well.

• This means that if we can detect the energy emitted or absorbed by an atom during an electronic transition, we can tell what element the atom belongs to, even from millions of light years away!

Measuring Temperature

• It is useful to think of temperature in a slightly different way than we are accustomed to

– Temperature is a measure of the motion of atoms in an object

– Objects with low temperatures have atoms that are not moving much

– Objects with high temperatures have atoms that are moving around very rapidly

• The Kelvin temperature scale was designed to reflect this

– 0 K is absolute zero –the atoms in an object are not moving at all!

Results of More Collisions

• Additional collisions mean that more photons are emitted, so the object gets brighter

• Additional hard collisions means that more photons of higher energy are emitted, so the object appears to shift in color from red, to orange, to yellow, and so on.

• Of course we have a Law to describe this…

Wien’s Law and the Stefan-Boltzmann Law

• Wien’s Law: – Hotter bodies emit more

strongly at shorter wavelengths

• SB Law: – The luminosity of a hot

body rises rapidly with temperature