Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

1
Chapter 4Making Sense of the Universe
Understanding Motion, Energy, and Gravity

• Chapter Outline
• Describing Motion
• Newtons Laws of Motion
• Conservation Laws in Astronomy
• The Force of Gravity

2/7/2005 258 PM
2
4.1 Describing Motion Examples From Daily Life

1. How do we describe motion?
2. How is mass different from weight?

3
Describing Motion - Kinematics
Precise definitions to describe motion

• speed rate at which object moves

• 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)

4
Frame of Reference for Measuring Motion

• Frame of reference - place from which motion is
  observed and measured
• Origin - point in frame from which measurements
  begin
• Fundamental reference direction - direction in
  space defining orientation of reference frame
• Secondary reference directions - define
  dimensionality and nature of space

5
Position, Velocity, Acceleration
4
Non-uniform motion
3
2
Uniform motion

• Position - measured location from a specified
  origin
• Velocity - time rate of change of position in
  particular direction
• Unit is meters per second, abbreviation is m/s
• Acceleration - time rate of change of velocity in
  a particular direction
• Unit is meters per second squared, abbreviation
  is m/s2

1
Position
Body at rest
0
0
1
2
3
4
5
6
Time
4
3
2
1
Velocity
0
0
1
2
3
4
5
6
Time
6
Acceleration of Gravity

• Gravity causes falling bodies to accelerate
  downward at about 10 m/s2
• Each second, the velocity of the falling body
  increases by about 10 m/s

7
Mass and Force

• Mass - measure of body's inertia
• Inertia is a resistance to change in state of
  motion, not to motion itself
• Fundamental measure of amount of matter in body
• Unit for mass is kilogram, abbreviation kg
• Force - push/pull that changes body's state of
  motion
• Unit for force is newtons
• 1 N 1 (kg)(m/s2)

8
Mass Verses Weight

• mass the amount of matter in a body
• weight the force that acts upon a body

Mans mass remains constant independent of
location or motion. Weight is the gravitational
force of the Earth or other body on your mass.
9
Why are astronauts weightless in space?

• There IS gravity in space
• Weightlessness is due to a constant state of
  free-fall.

10
State of Motion

• Momentum - fundamental measure of quantity of
  motion body possesses
• Momentum equals mass times velocity, i.e., P
  mv
• Depends on both magnitude and direction
• A net force produces a change in momentum, which
  generally means an acceleration or change in
  velocity.
• State of motion - momentum body possesses in some
  frame of reference

11
4.2 Newtons Laws of Motion

1. How did Newton change our view of the universe?
2. What are Newtons three laws of motion?

12
Isaac Newton (1642-1727)

• Entered Trinity College, Cambridge University, in
  1661
• 1665-1666 were plague years Cambridge closed
  during which period he developed at home
• Binomial theorem
• Differential calculus (fluxions)
• Theory of colors, theory of light
• Gravity as inverse square law, first two laws of
  motion
• In 1669, Newton appointed Lucasian Professor of
  Mathematics
• In 1684, Edmund Halley encouraged Newton to
  publish his research on mechanics
• 1687, Mathematical Principles of Natural
  Philosophy

13
Newton's Principia

• Parts published between 1667 and 1687
• Bulk of work done between 1684 and 1686
• No more encompassing treatise ever published
• Lays out mathematical formulation of theory
• Application to many long-standing problems of
  planetary motion, lunar motion, tides, etc.
• Provides standard for doing scientific
  investigations
• Establishes for all times mathematics not only as
  language of science, but as a means of knowing
• Contains Newtons laws of motion (terrestrial and
  celestial)

14
What are Newtons Laws of Motion?

• They are part of a general theory of motion,
  known as Newtons Theory of Motion
• Postulatory-deductive system of mathematical
  logic
• Assumption known as action-at-a-distance, which
  is the ability of bodies not in contact to
  manifest forces which alter each others states of
  motion

15
Newton's 1st Law of Motion

• Body remains in its state of motion unless acted
  on by an external force
• Galileo's principle of inertia defining "natural
  motion"
• Equation, momentum constant
• Symbolic, P
  constant

16
Newton's 2nd Law of Motion

• Body acted on by an external force will change
  its momentum in direction of the force
• Greater the force the greater the change in
  momentum
• Equation, force time rate of change
  of momentum
• Symbolic, F d(P)/dt ma

17
Newton's 3rd Law of Motion

• Forces always occur in pairs
• For every action there is an equal and opposite
  reaction
• Equation, force of action force
  of reaction
• Symbolic, Faction
  Freaction

18
4.3 Conservation Laws in Astronomy

1. What keeps a planet rotating and orbiting the
   Sun?
2. Where do objects get their energy?

19
Conservation of Linear Momentum
Linear momentum quantity of motion in straight
line motion product of mass and velocity
conserved locally and globally
Green ball possesses some of red balls momentum
Red ball has momentum
Blue ball possesses some of red balls momentum
1. Assume red ball comes to rest after
collision 2. Assume green ball has no momentum
before collision 3. Assume blue ball has no
momentum before collision
20
Conservation of Angular Momentum
Angular momentum quantity of angular motion
product of mass, velocity, and radial distance
conserved locally and globally
21
Conservation Principle
Galaxy Interactions

• Conservation of translational momentum - total
  translational momentum in the universe is a
  constant
• Interaction of bodies redistributes momentum
  among interacting bodies
• Bodies may exchange quantities of motion, but may
  neither create nor destroy motion
• Total momentum of the universe is a finite
  constant
• Conservation principle also exists for angular
  momentum, quantity of rotational motion

22
Concept of Energy

• Energy - measure of ability of physical system to
  perform work when system undergoes change
• Change in system - must be able to describe
  system accurately before and after
• Energy can be measured and quantified
• Unit for energy is the joule, amount of energy
  needed to accelerate mass of 1 kilogram at rate
  of 1 meter per second squared as it moves
  distance of 1 meter
• 1 J 1 (kg)(m2/s2)

23
Energy Forms and Properties

• Energy is a physical quantity
• Properties
• Can be quantified
• Mass is just one more manifestation of energy
• Can be transformed from one form to another
• Can be transported from one position to another
• Energy Forms
• Kinetic energy - energy body possesses by virtue
  of its state of motion
• Potential energy - energy body possesses by
  virtue of its position in field of force
• Energy Transport - energy is always transported
  by natural physical processes from regions of
  high energy content to regions of low energy
  content
• Conservation of Energy - energy can neither be
  created nor destroyed

24
(No Transcript)
25
Kinetic and Potential Energy

• Kinetic energy - energy body possesses by virtue
  of its state of motion
• Examples
• Particle moving along x-axis of graph
• Car moving along interstate
• Rock falling in Earths gravitational field
• Potential energy - energy body possesses by
  virtue of its position in field of force
• Examples
• Book held above ground
• Car parked on top of hill

26
Kinetic and Potential Energy
27
Energy Transport

• Energy Transport - energy is always transported
  by natural physical processes from regions of
  high energy content to regions of low energy
  content

28
Energy Transport Processes
Mechanical Wave - propagation of disturbance
through material medium
Rope
Electromagnetic Waves - propagation of
electromagnetic disturbance that does not require
material medium for transport
Light Source
Gas Molecules
Random Thermal Motion - random motion producing
collisions of atoms and molecules that compose
body
29
Random Thermal Motion

• Random thermal motion - continuous random motion
  and consequent interaction of constituent
  particles
• Gas particles dart about, collide frequently with
  other gas particles or walls of container
• Collide millions of times per second (108
  collisions/s)
• Change direction of motion just as frequently

30
Kinetic Energy of a Gas

• Kinetic energy of gas particles - proportional to
  product of their masses and square of their
  velocities
• Equation KE 1/2mv2
• Velocities either greater or smaller after
  collision than before collision
• Kinetic energy of each particle changes in
  repeated collisions

31
Temperature of a Gas

• Total energy (heat or thermal energy) - sum of
  kinetic energies of particles
• Equation E ? ( KE )i ? ( 1/2mv2 ) i
• Temperature - measure of average kinetic energy
  of particles ( ltKEgt )
• Equation T ? ltKEgt
• Average kinetic energy changes only when total
  energy increases or decreases
• Absolute zero is when average kinetic energy is
  zero

Higher Temperature
Lower Temperature
Higher Total Energy
Smaller Total Energy
32
Temperature Measurement

• Kelvin system - 100 degrees between waters
  freezing point (273 K) and boiling point (373 K)
• Temperatures in astronomy usually measured on
  Kelvin (K), scale

33
Gravitational Potential EnergyOn Earth

• On Earth, depends on
• objects mass (m)
• strength of gravity (g)
• distance object could potentially fall

34
Gravitational Potential EnergyIn Space

• 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.

35
MassEnergy Equivalence

• Albert Einstein (1879-1955)
• 1905, published 4 papers in Annalen der Physik
• Quantum theory of light and photoelectric effect
• Special theory of relativity
• On the Electrodynamics of Moving Bodies"
• Mass is one more form of energy
• Equation E mc2
• Mass particles can be transformed directly in to
  energy particles, and energy particles can be
  transformed directly in to mass particles.

E mc2
Mass is a form of potential energy.
36
Conservation of Energy

• Energy can be neither be created nor destroyed.
• Energy can change from one form to another.
• Energy can be exchanged between objects.
• The total energy content of the universe was
  established at the instance of initiation of
  spacetime (Big Bang) and remains the same today.

37
4.4 The Force of Gravity

1. What determines the strength of gravity?
2. How does Newtons law of gravity extend Keplers
   laws?
3. How do gravity and energy together allow us to
   understand orbits?
4. How does gravity cause tides?

38
Newtons Law of Gravity

• Gravity - objects attract each other with force
  that varies directly as product of their masses
  and inversely as square of their separation from
  each other

39
Fields of Force

• James Clerk Maxwell (1831-1879)
• Field of force - body manifests at every
  geometrical point surrounding a body a force
  called gravity that depends on mass and inversely
  as distance squared

Fg ? 1/d2
Gravitational field about body
40
Launching a Satellite

• If an body gains enough kinetic energy, it may
  escape (change from a bound to unbound orbit).

• 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 an even faster speed, it may escape the
  earths gravity altogether.

Escape velocity from Earth 11 km/s from sea
level (about 40,000 km/hr)
41
Planetary Motion
42
Escape Velocity

• Orbital energy sum of kinetic and potential
  energies
• Orbital energy must be conserved throughout
  bodys motion
• Adding or subtracting orbital energy will alter
  bodys orbit
• During a gravitational encounter between two
  bodies orbital energy may be exchanged
• Escape velocity sufficient velocity (hence
  kinetic energy) to escape gravitational
  attraction of another body

43
Tidal Force and Tides
Tidal force different values of the
gravitational force across the diameter of a body.
44
Tidal Friction
Tidal friction frictional dissipation of energy
because of tidal force
Synchronous rotation adjustment of rotation and
revolution periods to be the same because of
tidal friction
45
The Big Picture

• Understanding the universe requires understanding
  motion. Motion may seem very complex, but it can
  be understood simply through Newtons three laws
  of motion and his law of universal gravitation.
• Today, we understand Newtons laws of motion
  through deeper principles, including the laws of
  conservation of angular momentum and energy. We
  can understand many processes in the universe by
  following how energy is exchanged between
  different bodies.
• Newton also discovered the universal law of
  gravitation, which explains how gravity holds
  planets in their orbits and much moreincluding
  satellites can reach and stay in orbit, the
  nature of tides, and why the Moon rotates
  synchronously with Earth.
• Perhaps most important, Newtons discoveries
  showed that the same physical laws we observe on
  Earth apply throughout the universe. The
  universality of physics opens up the entire
  cosmos as a possible realm of human study.