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!
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?
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?
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...
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...
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...
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...
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?
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...
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.
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...
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)...
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...
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...
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...
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?
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...
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?
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...
: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.
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?
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...