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Mathematical Physics

A floating spherical shell in water

A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 54.0 cm, and the density of iron is 7.87 g/cm3. Find the inner diameter. I have no clue how to start or solve this problem. Thanks for the help!

Working with flow rate

A rectangular open tank is 4.5' wide, 3' deep and 6' long. We wish to fill the tank using a 1" diameter hose that delivers water at a speed of 100 inch/s. a) Determine the volume of the tank in gallons and liters. b) Compute the volume of water delivered by the hose in bothe quarts and liters per second. c) How long will i

Kinetic Friction Expressions

Which of these mathematical expressions have the appropriate dimensions of the coefficient of kinetic friction? Please see attached for mathematical expressions. Type the letters corresponding to correct answers alphabetically. Do not use commas. For instance, if A, B, and D have the appropriate dimensions, enter ABD.

Locating the Centroid Areas

Question: Locate the centroid y of the area whose equation is y=1/x bounded by the x axis, and the line x=.5 inches. The height of the area starts at 2 inches high at x=.5 inches, and slopes down to 0.5 inches high at x=2 inches. The length of the shape is 1.5 inches.

Centroid of ellipse

Half of an ellipse is centered with x, y, and z axis' passing through. The nose extends out towards the y axis at a distance b. It's circular base has radial height 'a' from the x axis. Locate the centroid of the ellipsoid of revolution whose equation is y^2/b^2 + z^2/a^2 = 1.

Finding the Direction Cosines

Okay I have been racking my brain with this one for over a week and still have no clue how to do this.I need to study this for a test I am having and can't seem to figure this out Consider an arbitrary 3D vector: A=Axx+Ayy+Azz a) Determine the direction cosines for this vector. These are cos[], cos[] and cos

Finding Speed

Two planes leave simultaneously from the same airport, one flying due north and the other flying due east. The north bound plane is flying 50 miles per hour faster than the east bound plane. After 3 hours the planes are 2,440 miles apart. Find the speed of each plane. I made a guess at it because I really don't know how to figu

Double pendulum Calculations

A double pendulum consists of a pendulum of mass m2 hanging from a pendulum of mass m1. The motion of both parts of the double pendulum is constrained to the x-y plane. Both strings are "unstretchable" and having length I2 and I1, respectively. a) How many degrees of freedom does this system have? Using the variable theta1

Working with operators

If |0> and |1> denote the two eigenstates of N corresponding to the eigenvalues 0 and 1, respectively, show that câ?  |0> = |1> and c |0> = 0

Separation of Quasi and Intrinsic Fermi Levels and Conductivity

An undoped Si sample is optically excited at 300K such that Gop=10^19 ehp/cm^3s and taun=taup=1 microseconds. (a) What is the separation of the quasi Fermi levels (Efn-Efp)? (b) Where is Efn and Efp with respect to the intrinsic Fermi level Ei? (c) What is the change in conductivity due to excess carriers? What are the a

Determining Center of Mass

Find the center of mass of a system of three particles of mass 2 kg, 3kg and 4 kg placed at the corners of an equilateral triangle of side 2 meters.

Finding the frequency of vibration of a stretched wire.

A wire of density 9gm/cm^3 is stretched between two clamps 100cm apart subjected to an extension of 0.05 cm. What is the lowest frequency of transverse vibrations in the wire, assuming the Young's modulus to be 9x10^11 dynes/cm^ ?

Problems about Centroids III

Asking problem: Divide the parabolic spandrel shown into five vertical sections and determinate by approximate means the x coordinate of its centroids; approximate the spandrel by rectangles of the form bdd'b'. Note: The drawing file is in word97 format for PC and not for MAC. My question is how can I determine the area of

fundamental definition for centroid

The asking problem: Show that when the distance h is selected to maximize the distance Y from line BB' to the centroid of the shaded area, we also have Y=h. Note: The Y is relating to the centroid Y of the area. The drawing is in word97 format for PC and not for MAC. My problem is I don't know how can I demonstrate this. Ca

Integration practice using set limits

Three problems for practice. View the pdf file below for additional clarity. a) x^5 upper limit 1, lower limit 0 b) 3x^2 upper limit 2, lower limit 1 c) x^n upper limit 1, lower limit 0