Announcements
• Reading Week 10:
• Gregory, Chapters 15; 16, pp. 326-331, 339-end;
and Chapter 20, pp. 419-25.
Conservation of Mechanical Energy
• HW7 due 3 November
• Midterm mean was 85
• Grades posted on canvas later today
• Midterm solutions and essay grading remarks
posted on Tests page.
• Acceleration problem
Last time
18th cent. vis viva controversy: does the universe run down?
Descartes: universe consists of many parts colliding
with each other, but in each collision God ensures
that “no motion is lost”
His guess for what physical quantity stayed the same
in a collision: “force of motion” mv
[today: mv=momentum]
Huygens: yes, but remember to include the sign of v!
Inelastic collision:
before
m
v
v
+mv – mv = 0
m
after
2m
2m(0) = 0
Last time
Leibniz: doesn’t like Cartesian proposal, since
inelastic collisions will still run universe down.
Proposed instead vis viva, mv2
Vis viva survives inelastic collisions, since
clay particles move afterwards (clay heats up)
‘sGravesande corrected to ½ mv2
[today: ½ mv2 =kinetic energy]
Clicker question
Which of the following was a challenge to his 1/r2 law
of gravitation that Newton survived in the 18th century?
•
•
•
•
•
shape of the Earth: prolate or oblate
date of return of Halley’s comet
influence of sun on moon’s motion
slowing down of moon’s orbit
all the above
Flammarion engraving 1888
We may regard the present state of the universe as the effect of its past and
the cause of its future. An intellect which at a certain moment would know all
forces that set nature in motion, and all positions of all items of which nature
is composed, if this intellect were also vast enough to submit these data to
analysis, it would embrace in a single formula the movements of the greatest
bodies of the universe and those of the tiniest atom; for such an intellect
nothing would be uncertain and the future just like the past would be
present before its eyes.
— Pierre Simon Laplace, A Philosophical Essay on Probabilities
The infinite universe that Laplace showed was stable and eternal
It was a mechanical clockwork universe that had and would continue to tick along
As Halley had shown in the problem sof the shrinking of the Moon’s orbit
and the prediction of his comet’s reappearance, you could run the Newtonian
mechanism of the heaven backwards as well as forwards
Newtonian celestial mechanics was, in other words, reversible
This week we’re going to give you the facts of life
We’ll replace Laplace’s well-ordered, stable, eternal
clockwork universe with one that ends with a whimper
This is because there are irreversible processes at work
“This is the End”
From Camille Flammarion (1842 -1925)
Goals for today
1. To lay the groundwork for the undoing of Laplace’s universe
2. To do that we have to look at some of the other forces of nature
than just the contact forces we have been considering
Electrical
Magnetic
Chemical
Optical
Thermal
3. To see some examples of how these “forces” were interconvertible
4. To begin to see how there was something special about heat
Descartes’ cosmos underscored the central importance of matter in motion
It was “the name of the game”
Natural philosophers wanted to learn all they could
about how matter comes to be in motion
Descartes was concerned with contact motive
forces – collisions of masses already moving
In the wake of debates about vis viva, natural philosophers became
interested in other forces that were a counterpart to “living forces”
These “dead” forces were exerted on matter but did not result in
the motion of matter unless they were converted into motive force
As they investigated these forces they discovered that there
were numerous ways in which they were interconvertible
What were these forces?
Electrical force
Magnetic force
Chemical force
Thermal force
Optical force
What was electricity?
Franklin thought of it as a
weightless fluid that
repelled itself but was
attracted to normal matter
Invention of the Leyden Jar
Lucia Galeazzi
Force conversions ??
Force conversion??
Dissociated water into two gases
using current from a battery, 1800
William Wollaston
Herschel experimented on the temperature of colored light
Noticed that region below red was hottest of all
Force conversion ??
Ritter experimented with darkening of the muriate of silver (AgCl) by colored light
Prevented darkening
No effect
Darkened
Darkened most of all
Force conversion ??
Heat
The transformation of heat into motive force
was a major factor of the Industrial Revolution
Sadi Carnot
Newcomen steam engine
Carnot noted that to use heat to produce mechanical force
required that something at a higher temperature fell to a
lower temperature. Without a temperature difference
the heat was “useless”
He also thought that heat was conserved
Carnot imagined that heat was merely
used to create the motion of the piston
like water is used in a water wheel
(so the water is not used up but can be
used again)
Others said Carnot was wrong -the heat
actually turned into mechanical force
In England James Joule determined experimentally
how much heat corresponded to how much
mechanical force, settling the question of whether
heat was conserved or not (it was not)
James Joule
In Germany Rudolf Clausius said
Joule and Carnot were both right
Joule was right that heat became mechanical
force (heat not conserved)
Carnot was right that the temperature
must fall for heat to become mechanical force
Because of this not all of the heat became
mechanical force. There was always some
that was merely transferred from a warm
body to a colder one.