Recent content by danyull

Ah I remember this now! This also reminds me that I should study up on distinguishable and indistinguishable particles too. Thanks a bunch!

Let's say your ellipse has axes of length ##A## and ##B##, and center ##(h,k)##, and is rotated by angle ##\theta##. This is represented by the equation $$\frac{((x-h)\cos(\theta)+(y-k)\sin(\theta))^2}{A^2}+ \frac{((x-h)\sin(\theta)-(y-k)\cos(\theta))^2}{B^2} =1.$$ If ##A>B## then I suspect the...

Hello, I'm doing some refreshers before going back to school. Stat mech is my shakiest and I'd appreciate some help on this problem. I know that for a single particle, the partition function will be $$Z = 1 + 2e^{-\beta\Delta} + 2e^{-4\beta\Delta}$$ and so its internal energy is $$\frac{1}{Z}...

Homework Statement Two identical bodies of constant heat capacity ##C_p## at temperatures ##T_1## and ##T_2## respectively are used as reservoirs for a heat engine. If the bodies remain at constant pressure, show that the amount of work obtainable is ##W = C_p (T_1 + T_2 − 2T_f)##, where...

Homework Statement Find the average energy ##\langle E \rangle## for (a) an n-state system in which a given state can have energy 0, ε, 2ε, 3ε... nε. (b) a harmonic oscillator, in which a state can have energy 0, ε, 2ε, 3ε... (i.e. with no upper limit). Homework Equations Definition of...

Oops, yeah I realized that wouldn't work after trying it. Do you think I could set ##\vec {\mathbf v}' \cdot \hat {\mathbf x}' = 0## instead? Evaluating the velocity at the time I solved for, the vector points "down" in the coordinate system, which is perpendicular to the coordinate's unit...

Ah, right I did. Thank you! I believe I have the second part too now. I'll just set ##\vec {\mathbf r}' \cdot \hat {\mathbf y} = 0## because the dot product is zero when the vectors are orthogonal. The x-component drops out, and the position ##y'## will be from the equation I just used...

Thanks for your input! My professor wants us to practice rotated reference frames using matrix transformations, hence this homework problem. I think I figured out part (a). I just used the equation ##y' = v_{0,y}' t + \frac 1 2 a_y' t^2## and set it equal to 0, then solve for ##t##. I'm still...

Thanks for the warm welcome! and for the compliment. I have a lot of friends from mixed backgrounds.

Homework Statement A ball is thrown with initial speed v0 up an inclined plane. The inclined plane makes an angle of π/6 above the horizontal line and the ball is launched at an angle θ above the inclined plane. No air resistance in this problem. (a) How long does the ball stay in the air? (b)...

Hello! I'm a physics and mathematics major hoping to go into theoretical physics. Besides physics and math, I like languages and I've taught myself Spanish, Japanese, and some German and Chinese. I also like playing piano, dancing, cooking, and watching nice TV shows. It's nice to meet you~