letters to nature
20. Beck, S. L. & Ruff, L. J. Rupture process of the great 1963 Kuril Islands earthquake sequence: asperity interaction and multiple event rupture. J. Geophys. Res. 92, 1412314138 (1987). 21. Kanamori, H. Mechanism of tsunami earthquakes
ME 152A (Fall 2013) Prof. Sumita Pennathur
HW #3
1. HYDROSTATICS
Oil spills may occur in ports where oil tankers are loaded. The density of oil o is less than that of
water, w, and the two fluids are immiscible, so that when a spill occurs, the oil simply
5
Surface tension
At the interface between two materials physical properties change rapidly over distances comparable to the molecular separation scale. Since a molecule at the interface is exposed to a
different environment than inside the material, it w
transferred as a result of a temperature difference. CONTENTS M.
Delalija, Physics Work 2 CONTENTS M. Delalija, Physics Heat The
heat transferred into or out of a system is also found to depend on the
process. This can be demonstrated by the situations de
substance appears as heat. This is because the energy agitates the atoms
of the object, increasing their vibrational or translational motion, and the
result is a temperature rise. Physical therapy and infrared photography
are some practical applications.
contains two wires, with one carrying current to the switch and the other
away from the switch, the net magnetic field would be very small and
fall off rapidly. The second reason is that the current is alternating at 50
Hz. As a result, the magnetic field
let x and v be the compression and initial marble speed for Bobbys
attempt. Then we have: v = (1.10 102 m)s k m (6.29) The marbles
trip from the edge of the table to the floor is (by now!) a fairly simple
kinematics problem. If the time the marble spends
in both directions or that have an inhomogeneous DE (through heat generation).
Separation of
variables, however, can only work if a separated ODE and the associated BCs
conform to the
SturmLiouville system, which constrains the method to conduction proble
Note that the choice of T1 as the characteristic temperature resulted in
homogeneous BCs on all
surface except the top surface. This is desired the more homogeneous the
problem, the easier it
is to solve.
As was done before, the temperature T(x, y) is spl
Why you should you avoid alamming on your brakes when you want to
stop in the shortest possible distance? The brakes may lock and the car
will slide farther than it would if the wheels continued to roll because the
coefficient of kinetic friction is less
Hertz was the first to generate and detect electromagnetic waves in a
laboratory setting. CONTENTS M. Delalija, Physics (Part 14)
Production of Electromagnetic Waves . Electromagnetic waves are
radiated by any circuit carrying an alternating current. The
pole. If a compass needle is suspended in bearings that allow it to rotate
in the vertical plane as well as in the horizontal plane, the needle is
horizontal with respect to the Earths surface only near the Equator. As
the device is moved northward the ne
effect can also play a major role in determining the Earths temperature.
Earths atmosphere is a good transmitter of visible radiation and a good
absorber of infrared radiation. Carbon dioxide in the Earths atmosphere
allows incoming visible radiation from
roadway as the automobile attempts to push the roadway backward. 7
CONTENTS M. Delalija, Physics Exercises . What force causes a
propeller airplane to move? The force driving a propeller airplane
forward is the reaction force of the air on the propeller a
reactions of oxygen with ultraviolet radiation. This ozone shield converts
lethal high-energy ultraviolet radiation to heat, which warms the
stratosphere. X-rays are electromagnetic waves with wavelengths from
about 10 nm to 0.1 pm. The most common source
to the positive and negative terminals of some voltage source. When this
connection is made, electrons are pulled of one of the plates, leaving it
with a charge of +Q, and other plates with Q. The capacitance,C, of a
capacitor is defined as the ratio of t
antenna, the strengths of he electric and magnetic fields become very
weak. CONTENTS M. Delalija, Physics (Part 14) Properties of
Electromagnetic Waves 3 CONTENTS M. Delalija, Physics (Part 14)
The Spectrum of Electromagnetic Waves . All electromagnetic w
Furthermore, convection is not important in this situation because the
hands are not above the flame in the path of convection currents. The
important process in this case is the radiation of heat energy. All objects
continuously radiate energy in the for
Delalija, Physics (Part 12) Insulators and Conductors It is convinient to
classify substances in terms of their ability to conduct electric charge.
Conductors are materials in which electric charges move freely, and
insulators are materials in which elect
tends to accumulate at locations where the radius of curvature of the
surface is smallest. That is, at a sharp point. Why is it safe to stay
inside an automobile during a lightning storm? Although many people
believe that this is safe because of the insul
= (4.22)
This series does not converge i.e, it has a value of infinity. This is because tanh[(2n
1)] 1
for n 1, which leaves for large n the simple series of
P
1/(2n 1) which will not converge to
a constant. Therefore, the net heat transfer rate through
a2 (x L/2)2
i
in which q0 and a are constants. Formulate the problem for the temperature
distribution
in appropriate dimensionless form, and derive a solution using the SOV method.
Note: the
boundary conditions can be simplified by exploiting the symmetry
Exercises
1. A plane wall of thickness L is initially at temperature of T1. At time t = 0 a uniform
heat
flux of strength q is applied to the surface at x = L. The surface at x = 0 is
maintained
at temperature T1. Formulate the problem in appropriate nond
and q = 1, is shown in Fig. 4.9. The sloping lines represent the temperature profile
at a constant
values of y; increasing height of the lines correspond to increasing y. This view
shows that the flux
condition is met at x = 1, in that the lines uniformly
T(a, ) (4.107)
T
r
_
1
= f() Bi2 (T(1, ) T,2) (4.108)
T(r, ) = T(r, + 2) (4.109)
where a = R1/R2, Bi1 = h1R1/k, Bi2 = h2R2/k, T,2 = (T,2 T,1)k/q0R2, and
f() =
cos(),
2
2
0,
2
<
3
2
(4.110)
The dimensionless problem has a homogeneous DE and homogeneous BC
Ann(x) cosh(ny) (4.75)
110 CHAPTER 4. TWO DIMENSIONAL STEADYSTATE CONDUCTION
At y = 1 the condition is
s(x) =
X
n=1
Ann(x)
cosh(n) (4.76)
from which we obtain
An =
Z1
0
s n dx
cosh(n)
Z1
0
2
n dx
=
2
cosh(n)
Z1
0
s n dx
The remaining integral is evaluat
x
R
so that the DE now appears as
Pe
T
x
=
1
r
r
_
r
T
r
_
+
2T
x2 (4.127)
in which Pe = uR/ is the Peclet number of the flow. The Peclet number is analogous
to the
Reynolds number; it is a ratio of the characteristic rates of axial convective and
radial
lower density. The denser regions of cooler air from above replace the
warm air. Your automobile engine is maintained at a safe operating
temperature by a combination of conduction and forced convection. 7
CONTENTS M. Delalija, Physics Example: Algal Bloo
what happens to an object when the net force acting on it is zero.
Newtons second law answers the question of what happens to an object
that has nonzero force acting on it. From observations, we can
conclude that the acceleration of an object is directly
. 5 CONTENTS M. Delalija, Physics Description of Phase Changes
Phase changes can be described in terms of rearrangements of molecules
when heat is added to or removed from a substance. Consider first the
liquid-gas phase change. The molecules in a liquid
equation for horizontal motion gives us v0 t = 2.20 m (6.32) What can
we do with these equations? If we divide Eq. 6.32 by Eq. 6.30 we get: v0
t vt = v0 v = 2.20 1.93 = 1.14 If we divide Eq. 6.31 by Eq. 6.29 we get:
v0 v = x0 q k m (1.10 102 m)q k m = x0
kg)v2 73.5 J = (4.0 kg)v2 73.5 J Now use E = Wfric and get: (4.0
kg)v2 73.5J = 17.6 J Solve for v: (4.0 kg)v2 = 55.9J = v2 = 55.9 J
4.0 kg = 14.0 m2 s2 which gives v = 3.74 m s The final speed of the 5.0
kg mass (in fact of both masses) is 3.74 m s . 16.