Chapter 4 Making Sense of the Universe: 4.1 Describing ...astro.wsu.edu/hclee/Chap_4.pdfin the...

1

Copyright © 2009 Pearson Education, Inc.

Chapter 4Making Sense of the Universe:

Understanding Motion, Energy, and Gravity


4.1 Describing Motion: Examplesfrom Everyday Life

Our goals for learning:• How do we describe motion?• How is mass different from weight?


How do we describe motion?Precise definitions to describe motion:

• Speed: Rate at which object moves

!

speed = distancetime

units of ms"

# $

%

& '

Example: speed of 10 m/s

• Velocity: Speed and direction Example: 10 m/s, due east

• Acceleration: Any change in velocity; units of speed/time (m/s2)


Acceleration of Gravity

• All falling objectsaccelerate at thesame rate (notcounting friction ofair resistance).

• On Earth, g ≈ 10m/s2: speedincreases 10 m/swith each second offalling.


Acceleration of Gravity (g)

• Galileo showed thatg is the same for allfalling objects,regardless of theirmass.

Apollo 15 demonstration

Feather and Hammer DropCopyright © 2009 Pearson Education, Inc.

Momentum and Force

• Momentum = mass × velocity.• A net force changes momentum, which generally

means an acceleration (change in velocity).• The rotational momentum of a spinning or orbiting

object is known as angular momentum.

2


Thought Question

• A car coming to a stop: Yes• A bus speeding up: Yes• An elevator moving up at constant speed:

No• A bicycle going around a curve: Yes• A moon orbiting Jupiter: Yes

Is there a net force for each of the following?(Answer yes or no.)


How is mass different from weight?

• Mass—the amount of matter in an object• Weight—the force that acts upon an object

You are weightlessin free-fall!


Thought Question

On the Moon,A. your weight is the same; your mass is less.B. your weight is less; your mass is the

same.C. your weight is more; your mass is the

same.D. your weight is more; your mass is less.


• There is gravity inspace.

• Weightlessness isdue to a constantstate of free-fall.

Why are astronauts weightlessin space?


What have we learned?• How do we describe motion?

— Speed = distance/time— Speed and direction => velocity— Change in velocity => acceleration— Momentum = mass × velocity— Force causes change in momentum, producing

acceleration.


What have we learned?• How is mass different from weight?

—Mass = quantity of matter—Weight = force acting on mass—Objects are weightless in free-fall.

3


4.2 Newton’s Laws of Motion

Our goals for learning:• How did Newton change our view of the

universe?• What are Newton’s three laws of motion?


• He realized the same physicallaws that operate on Earth alsooperate in the heavens:⇒ one universe

• He discovered laws of motionand gravity.

• Much more: Experiments withlight; first reflecting telescope,calculus…

Sir Isaac Newton (1642–1727)

How did Newton change ourview of the universe?


What are Newton’s three laws ofmotion?

Newton’s first law ofmotion: An objectmoves at constantvelocity unless a netforce acts to change itsspeed or direction.

Law of inertia


Newton’s second law ofmotion: Force = mass ×acceleration.


Newton’s third law ofmotion: For every force,there is always an equaland opposite reactionforce.


Thought Question

A. Earth exerts a larger force on you.B. You exert a larger force on Earth.C. Earth and you exert equal and opposite

forces on each other.

Is the force that Earth exerts on you larger, smaller,or the same as the force you exert on it?

4


Thought Question

• The force of the car on the truck is equal andopposite to the force of the truck on the car. T

• The momentum transferred from the truck to thecar is equal and opposite to the momentumtransferred from the car to the truck. T

• The change of velocity of the car is the same asthe change of velocity of the truck. F

A compact car and a large truck have a head-oncollision. Are the following true or false?


What have we learned?• How did Newton change our view of the universe?

— He discovered laws of motion and gravitation.— He realized these same laws of physics were identical

in the universe and on Earth.• What are Newton’s three laws of motion?

1. An object moves at constant velocity if no net force isacting.

2. Force = mass × acceleration.3. For every force, there is an equal and opposite reaction

force.


4.3 Conservation Laws in Astronomy

Our goals for learning:• What keeps a planet rotating and orbiting

the Sun?• Where do objects get their energy?


Conservation of Momentum

• The total momentumof interacting objectscannot change unlessan external force isacting on them.

• Interacting objectsexchange momentumthrough equal andopposite forces.


What keeps a planet rotating andorbiting the Sun?


Conservation of AngularMomentum

• The angular momentum of an object cannot changeunless an external twisting force (torque) is actingon it.

• Earth experiences no twisting force as it orbits theSun, so its rotation and orbit will continueindefinitely.

angular momentum = mass × velocity × radius

5


Angular momentum conservation also explains why objectsrotate faster as they shrink in radius:


Where do objects get their energy?

• Energy makes matter move.

• Energy is conserved, but it can…—transfer from one object to another.—change in form.


Basic Types of Energy

• Kinetic (motion)• Radiative (light)• Stored or potential

Energy can change type butcannot be destroyed.


Thermal Energy:The collective kinetic energy of many particles

(for example, in a rock, in air, in water)

Thermal energy is related to temperature but it is NOTthe same.Temperature is the average kinetic energy of the manyparticles in a substance.


Temperature Scales


Thermal energy is a measure of the total kinetic energy of allthe particles in a substance. It therefore depends on bothtemperature AND density.

Example:

6


Gravitational Potential Energy

• On Earth, it dependson…— an object’s mass (m).— the strength of gravity

(g).— the distance an object

could potentially fall.


Gravitational Potential Energy• In space, an object or gas cloud has more gravitational energy

when it is spread out than when it contracts.⇒A contracting cloud converts gravitational potential energy to

thermal energy.


Mass-Energy• Mass itself is a form of potential energy.

EE = = mcmc22

• A small amount of mass canrelease a great deal of energy.• Concentrated energy can

spontaneously turn intoparticles (for example, inparticle accelerators).


Conservation of Energy

• Energy can be neither created nor destroyed.• It can change form or be exchanged between

objects.• The total energy content of the universe was

determined in the Big Bang and remains thesame today.


What have we learned?• What keeps a planet rotating and orbiting the Sun?

— Conservation of angular momentum• Where do objects get their energy?

— Conservation of energy: Energy cannot becreated or destroyed but only transformed fromone type to another.

— Energy comes in three basic types: kinetic,potential, and radiative.


4.4 The Force of GravityOur goals for learning:• What determines the strength of gravity?• How does Newton’s law of gravity extend

Kepler’s laws?• How do gravity and energy together allow

us to understand orbits?• How does gravity cause tides?

7


What determines the strength of gravity?The Universal Law of Gravitation:1. Every mass attracts every other mass.2. Attraction is directly proportional to the product of

their masses.3. Attraction is inversely proportional to the square of

the distance between their centers.


How does Newton’s law of gravity extend Kepler’s laws?

• Ellipses are not the onlyorbital paths. Orbits canbe:— bound (ellipses)— unbound

• parabola• hyperbola

• Kepler’s first two laws apply to all orbitingobjects, not just planets.


• Newton generalized Kepler’s third law:Newton’s version of Kepler’s third law:If a small object orbits a larger one and youmeasure the orbiting object’s

orbital period AND average orbital distanceTHEN you can calculate the mass of the larger object.

Examples:• Calculate the mass of the Sun from Earth’s orbital period (1

year) and average distance (1 AU).• Calculate the mass of Earth from orbital period and distance of

a satellite.• Calculate the mass of Jupiter from orbital period and distance

of one of its moons.


Newton’s version of Kepler’s third law

p = orbital perioda = average orbital distance (between centers)(M1 + M2) = sum of object masses

22 3

1 2

4!( )

p aG M M

=+


How do gravity and energy togetherallow us to understand orbits?

• Total orbital energy(gravitational +kinetic) staysconstant if there isno external force.

• Orbits cannotchangespontaneously.

More gravitational energy;less kinetic energy

Less gravitational energy;more kinetic energy

Total orbital energy stays constant.


⇒ So what can make anobject gain or loseorbital energy?

• Friction or atmosphericdrag

• A gravitationalencounter

Changing an Orbit

8


• If an object gains enoughorbital energy, it may escape(change from a bound tounbound orbit).

• Escape velocity from Earth ≈11 km/s from sea level (about40,000 km/hr).

Escape Velocity


Escape andorbital velocitiesdon’t depend onthe mass of the

cannonball.

Relationship Between Cannonball's Mass and Orbital Trajectory


How does gravity cause tides?

• The Moon’s gravity pulls harder on near side of Earththan on far side.

• The difference in the Moon’s gravitational pullstretches Earth.


Tides and Phases

Size of tides depends onthe phase of the Moon.

Tides


Tidal Friction

• Tidal friction gradually slows Earth’s rotation (and makes theMoon get farther from Earth).

• Moon once orbited faster (or slower); tidal friction caused it to“lock” in synchronous rotation.


What have we learned?• What determines the strength of gravity?

— Directly proportional to the product of the masses (M ×m)

— Inversely proportional to the square of the separation• How does Newton’s law of gravity extend Kepler’s laws?

— Applies to other objects, not just planets— Includes unbound orbit shapes: parabola, hyperbola— Can be used to measure mass of orbiting systems

9


What have we learned?• How do gravity and energy together allow us to

understand orbits?— A change in total energy is needed to change

orbit.— Add enough energy (escape velocity) and the

object leaves.• How does gravity cause tides?

— The Moon’s gravity stretches Earth and itsoceans.

Chapter 4 Making Sense of the Universe: 4.1 Describing ...astro.wsu.edu/hclee/Chap_4.pdfin the...

Documents

Transcript of Chapter 4 Making Sense of the Universe: 4.1 Describing ...astro.wsu.edu/hclee/Chap_4.pdfin the...