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    Determining Spring Constant in Ion Pair

    For the units to work out I HAVE to know r0. Maybe my value is crap, but at least my solution shows the understanding is there. It turned out to not be too hard...maybe a little convoluted. Thanks for the help!
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    Determining Spring Constant in Ion Pair

    So I took r0 to be the ion separation between na and cl which was 0.28 nm. Using this and all of the other information, I ended up with a frequency of 1.19*10^13 hertz. Is this reasonable?
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    Determining Spring Constant in Ion Pair

    Well, I end up with the spring constant being \frac{k\alpha e^{2} \left(m-1\right)}{r_{0}^{3}} and plugging this into mathematica shows the tangent, which is in good agreement for small deviations. Great...so now what?
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    Determining Spring Constant in Ion Pair

    Finding the derivative of force will show the points at which it is minimized and maximized, but I all ready know that. What good is it?
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    Determining Spring Constant in Ion Pair

    I did this! So I converted r to r_{\circ}+\Delta r and get F=-k\alpha \frac{e^{2}}{r_{\circ}+\Delta r}[1-\left(1-\frac{\Delta r}{r_{\circ}}\right)^{1-m}] and say that \frac{\Delta r}{r_{\circ}} is much less than 1 (which is reasonable for small angles). I was hoping that this would get rid of...
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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

    Thanks for looking over it. One concern was that the height doesn't factor into this ratio. That seems a little strange to me, but I can accept it as true. This isn't necessarily a difficult problem, but it was difficult to keep track of the variables as there are essentially three stages to the...
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    Potential and Thermal Energy

    Now I'm confused again :confused: Okay, step by step. Follow along and tell me where my mistake is. Momentum is conserved. Kinetic energy is not. Step 1: The potential energy of the car an earth turns completely into kinetic energy of the car (ignoring kinetic energy of the earth). Step...
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    Potential and Thermal Energy

    I got 1/2. Sorry, it is there at the bottom, just not in words.
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    Potential and Thermal Energy

    That sounds like exactly what I did! So do you think my answer is correct?
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    Potential and Thermal Energy

    So is it okay to consider the kinetic energy of the first car before and after the collision and the kinetic energy of the second car before and after the collision separately like I did?
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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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    Mathematica [Mathematica] Simple Problem with the plot function

    That's really neat and useful. I was so accustomed to just glazing over (1-Sqrt[5])/2, that I forgot that it was negative. If you raise it to the power of 1/2 for example, then the answer is imaginary. That's why it is not a real-valued function, correct? Thank you, sir.
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    Advice and Insight for choosing between Math and Physics

    Ouch. I do not claim to be awesome. I have no idea what I am doing here and I need help from people who do (and who are thereby more awesome than I am). My question is where to start. If I had a good idea about what I wanted to ask, then I wouldn't need suggestions. What things do I need to be...
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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

    I know that the answer is to be 2πRIBsinθ, but I don't see how or why. dF=IdlxB is the same as saying dF=IΔsxB or dF=IBsinθΔs integrating yields F=IBssinθ or F=2πRsinθ. But doesn't the value of theta change for each segment? Oh wait! No, it doesn't. It should remain constant as the...
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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

    So the length of rope (dx) at the bottom of the curve would experience no tension? How does this translate for the chain link at the bottom of the curve?
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    Uniform Tension of Rope with Mass

    It answers a question that I asked.
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    Uniform Tension of Rope with Mass

    Sorry, I almost missed this post. I'm following you nicely I think. So, now follow my logic: Let's say that there are links in a chain and that every link can withstand the same amount of tension except for one link (the weak link). Now, let's assign values. Each strong link can withstand 15 N...
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    Uniform Tension of Rope with Mass

    Oh, yes I've seen some of this. Doesn't it involve hyperbolic trig functions? Does this formula also apply to vertically hanging ropes? Could one, say, use this to calculate the tension on a chain link?
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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

    :facepalm: I appreciate the help. I remember running into this same problem in high school. Maybe after learning from the same mistake twice, I won't make it again. Fingers crossed.
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    Kinematics-acceleration in two dimensions

    Right, and I did. I got the equation deltaY=V.sintheta(t)-0.5gt^2 Rearranged and solve the quadratic equation. I ended up with two answers. One was 0.89 and the other was 0.3437. How am I supposed to determine which is correct and which is not?
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    Easy-acceleration with unit vectors

    It makes sense now. thank you.
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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

    If you click the first picture, you will have an understanding equal to mine. I'm sorry.
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    Easy-acceleration with unit vectors

    find the saucer's acceleration in unit vectors and in terms of magnitude and direction.
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