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# Mathematical Physics

### Moments of Inertia

Show that none of the principal moments of inertia can exceed the sum of the other two.

### Representative Integral/Complex Plane/Closed Loop Contour

Representative Integral/Complex Plane/Closed Loop Contour See attached file for full problem description.

### Calculus between two planes in a straight line

Using the calculus of variations show that the shortest distance between two points on a plane is a straight line.

### Density of an unknown material 10/19

A solid cube of unknown composition is seen floating upright in water with 30% of it above the surface. What is the density of the material? I believe the answer is 0.70 g/cm^3.

### What is the x coordinate of the center of mass of the system

See attached file for full problem description with diagram. What is the x coordinate of the center of mass of the system described in Part D? Express your answer in terms of . =

### Mathematical Methods in Physical Sciences

I need some help on this question, it is from the book "The mathematical methods in the physical sciences". 7. Given v = x^2i + y^2j + z^2k a. Integrating v*ndo for surface of the cube which its length is 1 and is consisted of 4 vertexes of (0,0,0), (0,0,1), (0,1,0), (1,0,0). b. Using divergence theorem, calculate the abov

### Rotational inertia

A solid cylinder of mass 8kg and diameter of 20 is rotated about an axis paralle to its central axis at a distance of 10 cm from the cylinders central axis. The rotational inertia about the parrale axis is what?

### Using dimensional analysis, which equation is (a -> m/^2, v -> m/s, x -> m , t -> s)

Using dimensional analysis, which one of the following equations is (a -> m/^2, v -> m/s, x -> m , t -> s) a. x = v/t b. v = 2ax t2 = x/a c. x2 = 2av d. x = at

### A person moves: What is the displacement from the original position?

A person moves 30m north, then 20m east and then 30 H (square root 2) m 45 degrees south of west. His displacement from the original position is a. 14m south west b. 10m west c. 28 m south d. 15 m east

### 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

### Compare a graph of someone walking toward a motion detector and a graph of someone walking away.

For a distance vs. time plot, A) Compare a graph of someone walking at a constant slow pace and a graph of someone walking at a constant fast pace. How are they similar? How are they different? B) Compare a graph of someone walking toward a motion detector and a graph of someone walking away. How are they similar? How are

### 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[&#61537;], cos[&#61538;] 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.

### Given x,y coordinates of three point masses, find the center of mass, c.m.

Three point masses are located in an x,y plane as follows: M1= 7 kg, at (x1, y1)= (5, 6); M2= 8 kg, at (x2, y2)= (-4, 6); and M3= 9 kg, at (x3, y3)= (3, -2). Find the coordinates (xcm, ycm) of the c.m. of the system.

### Total distance traveled by girl delivering newspapers

A girl delivering newspapers travels three blocks west, four blocks north, then six blocks east. B. What is the total distance she travels?

### 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^ ?

### mathematical description of a wave, direction, displacement

The displacement (in meters) of a wave is y= 0.26 sin (pi *t-3.7 pi *x), where t is in seconds and x is in meters. (a) Is the wave traveling in the +x or -x direction? (b) What is the displacement y when t= 38 seconds and x= 13 meters?

### position of the center of mass of a thin parabolic shell

Determine the position of the center of mass of a thin parabolical shell defined by z = a^2 - r^2 in cylindrical polar coordinates, glued to a flat bottom where z = 0, r < a of the same thickness.

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

### Important to grasp when dealing with many physics problems

Various questions to practice with integration. Integrate the following; a) x^6 b) 3x + x^2 c) 1/(x^2) d) ax + b e) x^p + x^q View the pdf file for the best clarity.