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    Determining Spring Constant in Ion Pair

    Homework Statement The force between an ion pair is given by F=-k\alpha\frac{e^{2}}{r^{2}}[1-\left(\frac{r_{\circ}}{r}\right)^{m-1}] Find the value of r where the equilibrium position is. Determine the effective spring constant for small oscillations from the equilibrium. Using...
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    Potential and Thermal Energy

    Homework Statement Starting from rest, a railroad car rolls down a hill 20 m high and hits another identical car at rest. The cars lock together after the collision. What fraction of the first car's change in potential energy is converted into thermal energy in the collision? Homework...
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    Advice and Insight for choosing between Math and Physics

    Right now I am on track to be a math and physics double major, but I just finished my freshman year, so I haven't declared yet (all male liberal arts college). I won't know my GPA until May 15th and since it is freshman year, it doesn't matter a whole lot. I may have a 4.0 (on a 4 point scale)...
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    Mathematica [Mathematica] Simple Problem with the plot function

    I have a formula for the fibonacci sequence (with 1 being the first) and I noticed that the 12th fibonacci number was 144. I thought that was a neat coincidence, so I I headed over to mathematica to see if this (and 1) were the only numbers that had this property. I was almost certain that it...
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    Current Loop in a nonuniform magnetic field

    Homework Statement A nonuniform magnetic field exerts a net force on a current loop of radius R. The figure shows a magnetic field that is diverging from the end of a bar magnet. The magnetic field B at the position of the current loop makes an angle θ with respect to the vertical, as the...
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    Uniform Tension of Rope with Mass

    I am having trouble puzzling this one out. What I am trying to understand is why the tension of a rope is uniform throughout (even when there is mass). So I have knowledge that tension is in fact not a force (as it is a scalar quantity). You have two people pulling on a rope in opposite...
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    Kinematics-acceleration in two dimensions

    Homework Statement A tennis player standing 8.0 meters from the net hits a ball 1.5 meters above the ground toward her opponent. The ball leaves her racquet with a speed of 25.0m/s at an angle of 14.0 degrees above the horizontal. The net is 1.0 meters high. The baseline is 12 meters back...
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    Easy-acceleration with unit vectors

    Homework Statement r1=(0m) r2=(2000i + 1000j)m v1=(200j)m/s v2=(200i-100j)m/s Homework Equations tantheta=vy/vx v2^2=v1^2+2ax v2=v1+at x2=x1+v1t+1/2at^2 The Attempt at a Solution Thank you for any help
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    Summation+Differentiation=Disaster. I need help with a summation problem I'm having.

    My logic is flawed somewhere, but I can't figure out where or why. So I've been playing with summation a bit and figured out a way to make equations for Ʃ^{n}_{k=1}K and Ʃ^{n}_{k=1}K^{2} That looks odd, so I'll just use Ʃ from now on, but realize that it is always from k=1 to n. ƩK is a series...
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    Sliding Ladder Velocity Problem

    1. Homework Statement [/b] This is a pretty simple calculus problem, but I can't figure out why my method fails. A ladder 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 4 ft/s. Consider the triangle formed by the side of...
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    Finding the Simplest Polynomial for a Series

    I cannot for the life of me remember where I learned to do this nor can I remember why this works, but I know a method for finding the simplest polynomial for a series. I had something half typed up and then I found this site: http://www.johansens.us/sane/technotes/formula.htm which explains a...
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    Infinite sqrt Series?

    I heard something interesting today, but I am skeptical. I heard that a certain infinite series has a finite answer and I was curious as to whether or not this was true and if we can prove it either way. This is the series: \sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\sqrt{5...}}}}} Any thoughts would be...
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    Complete Dissociation?

    This is probably an easy question, but I can't get it straight and searching has not helped. So when salts go into solution they completely dissociate if they contain anions of strong acids or cations of strong bases, right? I'm still shaky on this concept though. Take Sodium carbonate for...
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    The Physics of Fire by Friction

    I wasn't sure where to post this, so hopefully I didn't post it in the wrong place and hopefully I won't get flamed. Anyway, I am a boyscout and last weekend I was doing a demonstration on fire by friction. I use a bow drill. For those of you who do not know, this is how it works: A spindle...
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    Overcoming Friction Sliding Box.

    Homework Statement A 75 kg box slides down a 25 degree ramp with an acceleration of 3.60 m/s/s Find the coefficient of kinetic friction (I'll use "uk") between the box and the ramp. Find the acceleration for a 175 kg box. Homework Equations F=ma Fg= mXg (g=9.81 m/s/s in my...
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