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  1. A

    Probability Density Function

    in cylindrical coordinates the integral of the density gives the distribution. In this case the problem requires integrating over an area thus we have a double integral. In polar form J = int(int(f(r,theta)*r*dr)*dtheta) With the appropriate limits. Then J = int(int(1/(sqrt(x)+2),x) from 0 to...
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    Vibrating spring

    first of all I am somewhat confused in terms of the notation typically c is the damping constant and k is the spring constant I will use this notation in my discussion here... the EOM can be written as y'' + (k/m)*y = F/m*cos(wd*t) here k is the spring constant, m is the mass (w/g)...
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    Find the angle between the velocity and the total acceleration

    The solution turns out to be a first order differenetial equation Since V = a*sqrt(s) where s is the distance traveled we can relate s to the radius and the angle subtended s = r*theta (just basic geometry here) so V = a*sqrt(r*theta) From basic kinematics V = r*thetadot...
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    A wizard sits 3 m from the center of a rotating platform, coeefficient of static fric

    You are neglecting the kinematics of this problem. Your work is perfect to the point where you have found the force of friction. Which can sustain a maximum acceleration of u*g. (2.94 m/s^2) Now think of the in plane components of acceleration. The problem states that he is initially...
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    Libration (Lagrange) Points

    I get the following expression for my kinetic energy, there is a sign difference in the last term, did you maybe mean to include a plus on the last term? 1/2\,m \left( {{\dot{x}}}^{2}+{{\dot{y}}}^{2} \right) +1/2\,m{\omega}^{2} \left( {x}^{2}+{y}^{2} \right) -m\omega \left(...
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    Libration (Lagrange) Points

    So L = T - V I know d/dt(dL/dxdot) - dL/dx = something and also I know d/dt(dL/dydot) - dL/dy = something On the right hand side is there where I place the ficticious forces (for each corresponding equation)?
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    Mechanical Principles. Engineering Components

    The ultimate tensile stress is independent of the force and dimensions of a particular material. It is relatively a constant determined bythe material. For example, a piece of Alumnim - T6061 with a diameter of 12 cm has the same ultimate tensile stress as a similar piece with a diameter of...
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    Gravitational force problem

    Your work looks correct F = Gm1m2/r^2 In order for the book to be right you must have Gm1m2/.08^2 = F This means 6.67e-11*1*1/0.0064 = F Evaluating gives... F = 6.67e-11/0.0064 = 1.0422e-8 N This number is both ugly and way too small for 1kg.wt to be equal to 1.0422e-8 N. I...
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    Libration (Lagrange) Points

    How does one go about computing the locations of the 5 largrange points? I know where they are but do not know how to derive the equilibrium equations. I know you will get a quintic polynomial which can be solved numerically depending on the masses of the two large bodies, but using forces, how...
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    Rotary projectile motion

    You need to start this problem defining two sets of unit vectors, a set that is inertially fixed and a set that is fixed to the rotating disc. In this case if we are in a horizontal plane we can neglect the effects of gravity since this disc is just traveling on the horizontal surface. I've done...
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    Curved Mirrors

    Google the words... concave mirror focal length radius of curvature Just by reading the text below the first link you should be able to find the answer. I'll give you a hint, all you need to do is multiply your 10 cm by a single number!
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    Non-linear ODE with pursuit curves

    How would one go about finding an analytical solution to the following ODE note that we are trying to find y(x) subject to... (x*y'')^2 - (1 + (y')^2) = 0
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    One dimensional problem

    for the first problem i also get an acceleration of 2 m/s^2 since sum F = 0, then it should follow that F = m*a = 4 N The book must have a typo for the second problem it also looks like you solved the problem correctly. While speed typically does travel around 340 m/s at standard...
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    MATLAB Dispersion relation with Matlab

    solved it in 5 mins, enjoy the function! here you go! function out = mat2col(A) [row col] = size(A) for n = 1:col out([1+(n-1)*row:n*row],1) = A(:,n); end
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    MATLAB Matlab and Root Mean Square help

    You did everything right, you probably just didnt interpret the answer right Fit1 is a vector of the polynomial coefficient in descending order In this case its telling you the best linear fit for the data is time = -0.0185*year + 47.6837 One easy way of plotting this thing would be...
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    MATLAB Modeling Projectile Motion in Matlab

    I have written an m-file that models a projectile in 3 dimensions with drag that is proportional to the velocity squared. Tell me if ur interested
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    Background Physic

    More specifically, with energy and collisions there is a dimensionless quantity called the coefficient of restitution. This number is a ratio of KE after the collision to that of the KE before the collision. Thus if the initial first bounce had a KE of 10J at the ground and the coefficient of...
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    Application of differentiation

    I'll give you a few hints... a. Whenever we're at a maximum we're at a critical point, it must be satified that for any well-defined critical point, whethere it be a minumum, maximum, or corner (for a bounded domain) that the first derivative of our quantity of interest is zero. Thus if we...
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    Van de Graaff generator

    A van de Graaff generator has two ends. Theres one end towards the top (which is like the sphere) and there's on at the base. Connecting the two ends is a non conductive belt and a non conductive rod (for structure). Initially the entire apparatus is grounded (meaning that there is an equal...
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    Diophantine Equation and Euclid's algorithm

    13x +4y = 100 and x and y are integers first off if this is to be true then x HAS to be a positive even number. also notice that 13*8 is 80+24=104 therefore x can only be 2 4 or 6. Next, 13 and 4 have no common factors therefore we must choose that x is equal to 4 for it to be guaranteed...
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    Help With Sound Wave Problems

    To get you started on the last one, consider the following case: If 1 tuning fork has a frequency of 5 hz and a second one has a tuning frequency of 8 hz, then you would hear a beat frequency of 3 hz. So, the beat frequency is related to the difference of each of the individual frequencies...
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    MATLAB Plotting 3D Surface Graph: Issues & Solutions

    lets say i wanted to do a surface plot of z = x*y^2*e^sin(3*x*y); well first define the range of your x vector let's say -5 to 5 so x = linspace(-5,5) (this by default will put 100 pts between the values) lets let y go from -6 to 6 so one again y = linspace(-6,6,101) (now were...
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    Questions on projectiles & Newton's laws of motion

    for starters think about the motion of a projectile with drag that is proportional to the square of velocity. Express the position in terms of cartesian coorinates and then transform to cylindrical. Comment on what set is better for a given set initial conditions. To make things more...
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    Need help with an airfoil name

    if you are using the standard NACA 4 digit convention then it works as follows. For a NACA 2412, the maximum camber occurs at 24% down the chord from the leading edge, and the maximum thickness of the airfoil is 12% of the total chord length. For a NACA 0016. the airfoil has no camber...
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    Pressure (form) drag

    For simple objects, such as a cylinder and with some basic assumptions there exist some analytical solutions. Unfortunately for anything complex, we all know the pressure drag or drag due to lift depends on the lift. The lift is dependent on the ambient conditiosn and the the geometry and...
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    Feynman's Plate

    Thanks, I got it! Turns out that the observation in text is incorrect. The wobble rate is actually twice the spin rate. The solution comes from Eulers EOMS with the assumption that there are no external torques and that the oblate body is axially symmetric. Also, for the case where the wobbling...
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    Feynman's Plate

    Hey everyone, I need some help here. The question is to show that the wobble rate of a plate when thrown slightly off axis, is twice that of the spin rate. I don't even know how to start this problem. All I really know is that the inertia matrix can be written simply about body fixed axes. Thus...
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    MATLAB MATLAB Spirograph Animations with Grid Lines

    I have a small technical problem in MATLAB. I am trying to use comet to make an animated path of this spirograph program I've made. I'd also like to add some grid lines however my problem is the following. If i run the comet command everything looks great and works fine, but if I then use a...
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    Kets, vectors.

    If what your talking about is like a little ^ right above the vector, it means that the vector is a unit vector. The elementary property of a unit vector is that its magnitude is 1 (or unity) thus the name "unit vector". I should also mention that unit vectors, themselves, are dimensionless. The...
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    Find the total charge. then decide whether you have an atom or an ion

    Hey man, when you post from now on in the homework forums it helps to show some effort. Although, for this problem, the solution is fairly short so if you were able to show work you would probably have the answer. Remember, the change on an electron is -1 and a proton has a charge of +1 So...
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    General Relativity And Quantum Mechanics

    Hey everyone, I'm having some trouble finding the discrepancies between general relativity and quantum mechanics. Could someone please give me a dummy's version of how the two theories contradict each other. In general, I know that general relativity suggests that the prescence of mass and...
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    Particle on a sphere

    wow, that was easy, I got to stop starting this stuff at 1 AM when my mind decides it doesn't want to think anymore. Thanks!
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    Particle on a sphere

    nevermind, thank you. I'm an idiot, had my parathesis around the omega term so it was like (-yout(:,2)).^2... So as you can see the negative sign in that term will be real useful... I get a reasonable answer of 48 degrees with the model and seeing with the assumption of having a radius of 9.8 m...
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    Particle on a sphere

    Hmmm, I seem to be having some trouble finding a soltuion. If i define u_r to be radially outward, and u_theta, to be tangential to the circle I obtain the follwoing EOMS. N - mgcos(theta) = -m*omega^2*r (u_r equation) mgsin(theta) = m*omega_dot*r (u_theta equation)...
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    Particle on a sphere

    Imagine we have a particle sitting on top of a sphere of radius R. The sphere is inertially fixed. A small disturbance force sets the particle in motion from its unstable equilibrium point atop the sphere. Theta is measured from the vertical to the position of the particle. Assume this angle is...
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    Finding the change of internal energy

    perhaps the change in potential energy is his initial potential energy minus the work he does. If I have 5 units of energy in me, and I mow the lawn using two, I have 3 units of energy left for the day...make sense?
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    Frictionless Force question

    Ok this is what i recommend you do. Setup and FBD for the smaller block alone. You should get your sum of forces vectically to equal zero. The horizontal sum of forces on the smaller block must equal its mass multiplied by its acceleration (F=ma). You know the blocks must accelerate together so...
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    A lesson in vector mathematics

    Hey everyone, I eventually would like to write a textbook. I've started some work, and have about 100 pages total. There is a link here to one of the chapters in my book. It still needs to be edited of course, but I would like any opinions...Is it understandable, clear, and direct? If some of...
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    Oil between the piston and the casing manage to move with the piston?

    To answer you question about how the oil moves or doesn't move with the piston action, I'd like to suggest the study of fluid mechanics. Often when fluid mechanics are studied we are concerned with the flow of some fluid and how it interacts with it surrounding both in terms of momentum and...
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    Conversion between lbf and Newtons

    You couldn't possibly be anymore correct about that statement. stupid slugs, lbm, and lbf!
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    Conversion between lbf and Newtons

    so then it would be valid to say that 1 lbf = 1 lbm*ft/s^2 when g has a magnitude of 32.2 ft/s^2?
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    Conversion between lbf and Newtons

    I know there are 4.48 N in 1 pound force. The only way I can derive this is dividing 9.8 m/s^2 by 2.2 lbm/kg. The result shows that there 4.48 N in 1 lbm, but shouldn't it be that there are 4.48 N in 1 lbf. Can anyone clear this up or show a better derivation? Thanks
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    MATLAB Fourier transfom using matlab help

    The command you need to use is fft(V,n) Let's look at example... Let's suppose we want to plot the function f(t) = 3 + cos(2t) - 4sin(6t) using the discrete Fourier transform first we need to define a vector for the time interval t = linspace(0,2*pi,4096); should suffice (that...
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    In theory how fast can this scooter go?

    using some very basic mechanics and lots of assumptions about what the effective friction would be I got an answer of about 10.5 mph. So I'd say that that 12 mph is really the top speed you would get on it. If you think about 700 watts, that almost 1 horse power. So, in theory, think how fast a...
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    Static friction and work

    Are you sure its correct to say that there are four forces acting on the block. Inertial forces that arise due to the kinematics of a system are often not included in the FBD or are considered physical forces acting on an object. It would be incorrect to say that for a disk whirling in a...
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    Motion in a circle

    I would need to see a picture or have a better physical description as to what's going on here, but for the general idea of the problem. You are correct, in the fact that the sum of forces in the radial (horizontal) direction must equal the centripetal force. This is 1 equation. You are also...
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    How do you graph this?

    Typically a phase plane is composed of an infinite number of trajectories. The initial conditions of a system determine which specific trajectory applies to the system with its given set of initial conditions. You have a specific equation - let's call it x(t). In order to draw its trajectoy we...
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    Some info please on graduate courses

    At Purdue, in both the AAE and ME graduate curriculums, there are some courses that will give credit for both major areas. Most of the AAE courses that give credit to ME's are in the areas of aerodynamics and propulsion. For AAE's it turns out that the acceptable ME courses seem to be more...
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    Static friction and work

    Could someone please clarify this problem for me... Assume we have a box sitting on the back of a truck. The box can be modeled as a particle, and there is friction between the box and the surface of the truck. Also, let's assume the truck is accelerating slow enough that the block does not...
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    Modification of Space Shuttle Tiles?

    Why does the foam on the external tank even need to be on the outside of the tank in the first place?