Transcript Thermodynamic modeling of the formation of aerosol particles

Chapter 2 continuation...
Tuesday, January 29
Spring 2008
Galileo’s Kinematic Equations
Equations of “pure” motion – without reference to mass of
object or forces acting on it
With constant acceleration, a, and initial velocity, vi,
at any time, t:
Velocity:
v = vi + at
Distance:
d = vit + (½)at2
In freefall, the acceleration (a) due to gravity, g, is
constant:
g = 9.8 m/s2 ≈ 32 ft/s2
Galileo and Projectile Motion
vi,x
g
Sir Isaac Newton &
Classical Mechanics
• Newton and the Universal Laws of Motion
"Gravity explains the motions of the planets,
but it cannot explain who set the planets in
motion. God governs all things and knows all
that is or can be done."
Which path will the ball follow?
Isaac Newton
(1642 – 1727)
The First Law
• An object will continue moving in a straight
line at a constant speed, and a stationary
object will remain at rest, unless acted upon
by an unbalanced force
• Uniform motion vs. acceleration
• Inertia
F1
F2 = –F1
F2
F1 + F 2 = 0
The Second Law
• The acceleration produced on an object
by a net force is proportional to the
magnitude of the force and inversely
proportional to the mass of the object
• Equation:
F
a= m
F = ma
Units of Force
F = ma
Unit of force = unit of mass × unit of acceleration
= kg · (m/s)/s
= kg · m/s2
(metric system)
1 newton = 1 N = 1 kg·m/s2
1 N is the amount of force required to accelerate
1-kg mass at a rate of 1 m/s2.
a
The Third Law
• Interacting objects exert equal but opposite
forces upon each other
• The reactions may not be equal and opposite
The two forces are called an
“action-reaction pair.”
What force produces the forward
motion of a car?
Identifying Forces & Resultant Motion
Forces that are
perpendicular to one
another are usually treated
separately.
Motion in the vertical
direction: no acceleration,
F = ma so total force = 0,
W = –N
Motion in horizontal
direction: F = ma,
so F = P – f > 0 to get
chair moving.
Free Fall and Air Resistance
Air resistive force, R, acts
in opposite direction of
gravitational force, W.
R depends on the velocity.
F
W–R
a=—=
m
m
Eventually, the magnitude
of R equals that of W, and
the object reaches
“terminal velocity.”
Centripetal Acceleration
v2
v1
v2
a
a
v2
-v1
v1
v2
a
-v1
a
effect of velocity: lesser speed = smaller Dv value
As the speed decreases, ac decreases.
v
a
As the speed increases, ac increases.
v
a
Centripetal Acceleration
v2
v2
v1
v1
v2
-v1
v2
a
-v1
a
effect of radius: larger radius = less rapid change in direction of v
As the radius increases, ac decreases.
As the radius increases, ac decreases.
r
a
r
a
Centripetal Forces
The net force that produces a centripetal
acceleration is referred to as the centripetal force.
v2
Fc = mac = m—
r
Centripetal Forces
The tension force from a pull on a string, produces
the necessary centripetal force to keep a ball on
the end of the string in circular motion.