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  1. R

    Linear velocity of a rotating body

    how did you get the x, y and z to equal those three? and where did the t's come from? thanks for the help!
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    Linear velocity of a rotating body

    Homework Statement A flat rigid body is rotating with angular velocity 3 rads-1 about an axis in the direction of the vector (i + 2 j + 3 k) and passing through the point (1, 1, 0) on the body. Find the linear velocity of the point P = (1, 0, 1) on the body. (You may use the result v =...
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    Applications of vector algebra to physics

    Homework Statement A ball of mass 1 kg is acted upon by three forces: Fl = (2i + 4j - 3k) N, F2 = (-3i - j + 2k) Nand F3 = (i - 5j - k) N. Determine a vector expression for the acceleration of the particle. If, at time t = 0, it has position r = (i +j) m and velocity u = (i +3j)m/s...
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    Finding the mass of an atom - bainbridge mass spectrometer question

    Q. In a particular spectrometer, doubly ionised \stackrel{12}{6}C and singly ionised \stackrel{6}{3}Li atoms are detected. The ratio of the path radii is 1.00252, the Li having the larger value. The fields are constant. Find the mass of of the lithium atom. I can only think of the equation...
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    Fourier Transformation integral

    I'm trying to integrate a function which is given as F(u)= \int f(x)e^{-2}^{\pi} ^{i} ^{x} ^{u} dx with limits of +ve and -ve infinity integrating by parts gives me \frac{1}{2} f(x)^{2}e^{-2}^{\pi}^{i}^{x}^{u}-\frac{1}{2} \int f(x)^{2}xe^{-2}^{\pi}^{i}^{x}^{u}dx fisrt off, is the...
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    Differential Equation

    oh right, my mistake lol so, the last line should be ln(3x+4)=\frac{1}{2}ln(t^{\frac{1}{2}}) I have no idea where to go from here with the initial value that I was given x(0)=2! would I sub in x=2 into the equation?
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    Differential Equation

    [edit] - there should be 'dt' s on the RHS in the 2nd and 3rd line of work
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    Differential Equation

    I'm trying to solve this firrst order diff. equation, where I'm given the initial value, x(0)=2 \frac{dx}{dt}=\frac{3x+4}{\sqrt{t}} \frac{dx}{3x+4}=\frac{1}{\sqrt{t}}dt \int\frac{1}{3x+4}dx=\int\frac{1}{\sqrt{t}}dt ln(3x+4)=ln(t^{\frac{1}{2}}) this is as far as I got, do I sub in x(0)=2...
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    Integration problem

    is \int\frac{dx}{1+x^{2}} the same as \int\frac{1}{1+x^{2}}dx ?
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    F=ma calculation in vector format

    brilliant, thanks for that guys.
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    F=ma calculation in vector format

    I am given F=(3i + 2j + 4k) N and mass = 2kg I need to calculate acceleration, so I plugged it into F=ma, am I right in saying (3i + 2j + 4k) = 2 a \frac{(3i + 2j + 4k)}{2} = a therefore a = 1.5i + 1j + 2k ? cheers.
  12. R

    Writing an equation for a wave

    y=A sin (wt\pmkx) is the formula where A = amplitude w = angular freq. t = time k = wave vector wave vector doesnt have units as it's a vector quantity.. right?
  13. R

    Writing an equation for a wave

    I needed to write an equation for a wave with: amplitude : 2cm wave vector : 502.7 angular frequency : 125.7 Hz time : 0 sec and I used the general equation for waves to come up with: y = 0.02 sin (125.7 - 502.7x) is that alright?
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    De Broglie wavelength calculations

    I ended up discussing something with friends when we were going through this question - why is it that we don't see wave like properties in larger bodies i.e. in macroscopic levels? is it because the larger the mass, the smaller the de Broglie wavelength, and so the wave like properties are just...
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    De Broglie wavelength calculations

    brilliant - just another quicky, some of the answer guides ignored the whole square root part of the equation.. is that because that part of the equation is always roughly equal to 1?
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    De Broglie wavelength calculations

    I had a go at 2 Q's and wanted to make sure I'm doing this right. so here's the first one, and maybe if i went wrong with it I was going to redo the 2nd Q on my own. \lambda = h/p = h/mv (\sqrt{1-((v^2)/(c^2))}) so, an Alpha Particle travelling @ 2x106m/s (mass = 6.645x10-27 kg)...
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    Another quick integration q

    oh right, so i've got du=2xdx, intergral sec^2 u du = tan u + c sub back u=x^2 =tan x^2 +c how does that look?
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    Another quick integration q

    the question is \int 2x sec^2 (x^2) dx do i sub u= sec (x^2) ? I so far have got to trying to sub u= sec(x^2) and getting du= 2 (sec x^2 tan x^2)... i have a strong feeling i fudged the "du" part. hmm.
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    Intergrating e

    great - cheers for that i get it now :)
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    Intergrating e

    intergrating "e" I'm doing some intergration q's and I'm stuck on one which involves e [x^2 e^(x^3) ]dx I know to integrate you "add one to the power and divide by the new power.. would that make the solution ((x^3)/3) ((e^(x^4))/(x^4)? hope that makes a bit of sense..
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    Consevation of energy in collisions

    so would i be right in saying, "If the collision between the two bodies is an elastic collision, all momentum, kinetic energy and total energy will be conserved as elastic collisions do not convert any original energy forms into another." I am struggling to understand this, but I really...
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    Consevation of energy in collisions

    I am going through some questions for resits in August, and I have no idea what this question is wanting me to explain : "Briefly discuss the circumstances under which (i) momentum, (ii) kinetic energy and (iii) total energy are conserved in collisions between two bodies. [3]" it's only a...
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