The potential energy U = mgx of an 80-kg mass is shown versus
height x near the surface of the earth.
The potential energy U = mgx of an 80-kg mass is shown versus
height x near the surface of the earth.
Graphs of acceleration, velocity, and position versus time for a body falling in a
viscous fluid, shown as solid color curves. The light color curves show the
corresponding relations if there is no viscous friction.
Graphs of acceleration, velocity, and p
(a) An object with a mass m is
on the floor of an elevator that
is accelerating upward.
(b) Forces acting on the object.
(c) Forces acting on the elevator.
(a) An object with a mass m is
on the floor of an elevator that
is accelerating upward.
(b) Forces
C O N S E RVATI O N
LAW S
1. Work
By definition
A ( F r ) F r cos Fx rx Fy ry Fz rz
Some
forces
(weight,
spring
tension, etc.) are
always
exerted
along
one
coordinate only and,
thus, are called
conservative ( FC ).
Hence:
the
work
of
conservative forces
K INETIC TH EORY O F GASES
Ideal Gas assumptions:
The number of molecules in the gas is large, and the average separation between them is
large compared with their dimensions;
The molecules obey Newtons laws of motion, but as a whole they move randomly;
FLU ID S AN D FLUI D
DYNAMICS
The microstructure (and as a result of that, the motion) of a real fluids is very complex and
not yet fully understood. In many cases the behavior of a real fluid is associated with the
ideal fluid features:
Nonviscousity (w
THERMO DYNAMICS
The First Law of Thermodynamics:
M
Is actually the law of conservation of energy: if moles of ideal gas are supplied with
M
heat (energy) Q C dT , then in general case this system internal energy is changing
M i
by dE 2 R dT while it is pe
MOTION
GENERAL APPROACH :
Any motion is relative and, hence, has to be described in a certain frame of reference.
To describe motion means to define a function of
position (coordinate r) versus time t.
The plot of this function is called trajectory
Vector
R EAS O N FO R MO TI O N FO R C E
GENERAL APPROACH :
Force is something that creates acceleration: F ~ a
The coefficient of proportionality between force and acceleration defines degree of inertia and is
called mass m .
Hence, F = ma
SI UNITS of force: [
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Molecular Collisions
Michael Fowler 7/21/08
Difficulties Getting the Kinetic Theory Moving
Oddly, the first published calculation of the average speed of a molecule in the kinetic theory of
gases appeared in the Railway Magazine, of al
Centripetal force for a particle in uniform
circular motion.
Forces on a body whirling in a vertical
circle with center at O.
The total displacement from a to b has
been divided into small intervals of x.
The straight line is a plot of the function Fx (x)
Centripetal force for a particle in uniform
circular motion.
Forces on a body whirling in a vertical
circle with center at O.
The total displacement from a to b has
been divided into small intervals of x.
The straight line is a plot of the function Fx (x)
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Oscillations
Michael Fowler 3/24/07
Introduction
In this lecture, we will be looking at a wide variety of oscillatory phenomena. After a brief recap
of undamped simple harmonic motion, we go on to look at a heavily damped oscillator. W
The graphical representation of the one-dimensional constrained potential energy function U(x) for an object.
Also shown are various values of the total mechanical energy.
Points (A, B, C, D) on the potential-energy versus position graph
with zero slope a