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    I Partitioning a whole number in a particular way

    Another example is: w1 = 11 w2 = 39 w3 = 3 W = 53 P = 25 ROUND(P*w1/W) = 5 ROUND(P*w2/W) = 18 ROUND(P*w3/W) = 1 This sums to 24 but we have 25 pieces.
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    I Partitioning a whole number in a particular way

    I'm not sure what round off means. If round off means raise anything with a decimal >= .5 the next whole number and anything with a decimal <.5 to the next whole number down, then the example will still lead to 18 pieces being assigned.
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    I Partitioning a whole number in a particular way

    Thanks for the replies. I don't mind so much favoring someone more than others as long as: (ai<=wi) is not violated we assign exactly P pieces of pizza. no more, no less only whole slices can be assigned (no fractions for ai) For example, if we have w1 = 25 w2 = 9 W = 34 P = 17 Then...
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    I Partitioning a whole number in a particular way

    Hi, Let W be the sum of all the people's weights, let P be the total number of pizza slices available. If: I have P slices of pizza (P<=W) I have n people I want to split the pizza with I want to use people's weight to determine how many slices they get (more weight -> more slices) I don't...
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    I Physics of a bell siphon

    In the past i've made these bell siphons following these instructions: http://www.affnanaquaponics.com/2010/02/affnans-valve-detailed-explanations-of_9459.html I've had good success but that was just blindly following instructions and now I am just very interested in knowing the effects of...
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    I Physics of a bell siphon

    It's definitely growing in popularity! I think it's fun because you get to combine 3 hobbies: raising fish, growing plants, and building hydraulic systems (siphons, pumps, waterfalls, filtration, etc.) Apparently the physics of a bell siphon are pretty complicated, but do you think you can help...
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    I Physics of a bell siphon

    I'm trying to build a home aquaponics system, and a key component of the design I got off the internet is a bell siphon. So I'm trying to understand the physics of this siphon effect so I can optimize the weight and dimensions of the siphon to fit the size of my system. From what I read on the...
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    Measuring torque acting on motor shaft?

    I have an electric motor that I am using to turn an auger to dispense pet food. I want to measure the average torque required to turn this auger at a given rpm. I know Powerin = Voltage into motor * Current into motor and Powerout = Torque exerted by shaft * RPM of auger and Powerout...
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    Piezoelectric Crystal Shoes?

    It takes 120 J of energy to light two 60-watt light bulbs for 1 second, right? And the average phone takes 18000 Joules of energy to completely charge so that's only 150 steps! ... I'm sure there is something wrong with that line of thought, haha
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    Piezoelectric Crystal Shoes?

    I was inspired by this article http://science.howstuffworks.com/environmental/green-science/house-music-energy-crisis1.htm to wonder if one could put piezoelectric crystals in the sole of a shoe and perhaps harness the energy to charge their iPod? Can someone let me know if this is feasible...
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    Calculate attractive force between Cu2+ and O2- ions.

    The equation F= ke(|q1q2|)/r2 looks good. So if I plug in 3.204 × 10^-19 coulombs for q1 and -3.204 × 10^-19 coulombs for q2 (because O2- has a net charge equal to -2 times the charge of an electron and Cu2+ has a net charge equal to twice the charge of an electron), then I get 2.307*10-8...
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    Calculate attractive force between Cu2+ and O2- ions.

    Well I don't know the force equation, my teacher only gave us the equation for bonding energy... Perhaps since energy=force*distance we can find force by dividing our energy equation by some distance? I'm still stuck but I see now that z_1= 2 and z_2=-2. Any more help?
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    Calculate attractive force between Cu2+ and O2- ions.

    Homework Statement Calculate the attractive force between a pair of Cu2+ and O2- ions in the ceramic CuO that has an interatomic separation of 200pm. Homework Equations E_A= -\frac{(z_1\cdot e)(z_2\cdot e)}{4\pi\cdot\epsilon_o\cdot r} Where z_1 and z_2 are the valences of the two ion...
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    Finding number of atoms per cm^3 of zinc?

    Homework Statement Zinc has a density of 7.17 Mg/m^3. Calculate (a) the number of Zn atoms per cm^3, (b) the mass of a single Zn atom and (c) the atomic volume of Zn. Homework Equations atomic mass of zinc = 65.39 g/mol The Attempt at a Solution For part (a) I use the fact that...
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    Finding the energy of an electron from n=4 to n=2?

    Homework Statement Find the energy of a He+ electron going form the n=4 state to the n=2 state. Homework Equations E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2} Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level. ^ I think those are...
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    Computing energy in the electron of Li 2+?

    Homework Statement Using the Bohr model of the atom, compute the energy in eV of the one electron in Li2+. Homework Equations E_n=\frac{m\cdot e^4 \cdot z^2}{2n^2 \cdot \hbar^2} Where m= mass of electron, z= atomic number, e= charge of an electron, n is the energy level. ^ I think...
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    Period of an Oscillating Particle

    Sorry, how do we have ## \frac {dt} {dx} = f(x) ##?
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    Period of an Oscillating Particle

    "Period" is the time it takes for the particle to make one cycle. The particle traveling from 0 to A takes 1/4 of the time it would take to travel the whole period. But I don't see how we can find the time it takes the particle to travel from 0 to A? We have this equation that gives us time...
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    Period of an Oscillating Particle

    If ##\frac{dx}{dt}=a+x## then ##\frac{1}{a+x}dx=dt## (whatever that means), so ##\int \frac{1}{a+x} dx = \int dt = t##. So ##ln(a+x)=t##. If ##\frac{dx}{dt}=x^2## then ##\frac{1}{x^2}dx=dt## (once again idk what exactly i'm doing there), so ##\int \frac{1}{x^2}dx = \int dt##. So...
  20. R

    Period of an Oscillating Particle

    I'm afraid I don't get what it means to take ##\frac{dx}{dt}=f(x)## and turn it into ##\frac{1}{f(x)}dx=dt. And thus I don't get what it means to then take the integral of both sides of that... can you help me make sense of what those procedures mean?
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    Period of an Oscillating Particle

    oh whoops the integral of velocity is displacement so we would have x(t). So we could solve x(?)=A and then multiply it by 4 to get the period?
  22. R

    Period of an Oscillating Particle

    ##\frac{dx}{dt}=f(x)## ##\frac{1}{f(x)}dx=dt## ##\int f(x)^{-1} dx = \int 1 dt=t## is that right? That would give us time as a function of velocity which can give us velocity as a function of time? Then we can integrate that with respect to t to find displacement as a function of time...
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    Period of an Oscillating Particle

    Since the input into our velocity equation we found is x not t, I should edit: ... to say: See how as we make Δt smaller and smaller, the above becomes a better and better approximation of displacement x as a function of time? But I don't know how to turn that method into an integral...
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    Period of an Oscillating Particle

    Homework Statement A particle oscillates with amplitude A in a one-dimensional potential that is symmetric about x=0. Meaning U(x)=U(-x) First find velocity at displacement x in terms of U(A), U(x), and m. Then show that the period is given by ##4\sqrt{\frac{m}{2U(A)}}\int_0^A...
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    Help Understanding Quotient Groups? (Dummit and Foote)

    I don't understand, why can't we just say: If ##aK=a'K## and ##bK=b'K##, then ##(aK)(bK)=(a'K)(bK)=(a'K)(b'K)##. ?
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    Help Understanding Quotient Groups? (Dummit and Foote)

    I don't see why K needs to be normal? In order for ##(G/K,\cdot)## to be a group we need: i) ##g_1K\cdot(g_2K\cdot{g_3K})=(g_1K\cdot{g_2K})\cdot{g_3K}##. ii) ##\exists{e\in{\frac{G}{K}}}## s.t. for all g in ##\frac{G}{K}##, ##e\cdot{gK}=gK##. iii) for every ##gK\in{\frac{G}{K}}## we need...
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    Help Understanding Quotient Groups? (Dummit and Foote)

    I left out one part of the definition. It should say "Let ϕ:G→H be a homomorphism with kernel K. The quotient group G/K is the group whose elements are the fibers of ϕ (sets of elements projecting to single elements of H) with group operation defined above: namely if X is the fiber above a...
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    Help Understanding Quotient Groups? (Dummit and Foote)

    The definition given is... "Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group ##G/K## is the group whose elements are the fibers (sets of elements projecting to single elements of H) with group operation defined above: namely if ##X## is the fiber above...
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