Recent content by SeanGillespie

Homework Statement A simple cubic crystal with lattice parameter 0.5 nm has a plane which intersects atoms at the points (-0.5,-0.5,0), (1,-0.5,0.5) and (1,2.5,-1.5), where the coordinates have units of nm. What are the miller indices of the plane? Having read the relevant chapters of...

If the numerator and denominator of a fraction both tend to zero, you can use L'Hopital's rule to find the limit. This is often useful for finding the a0 coefficient in Fourier series. I believe you can also use a taylor series method to find a0 also. l'hospital's rule is quite simple to use...

I'll take it that the answer I was given on the problem sheet is wrong then, and that my method of calculating it is correct. Thank you very much.

see attached image. The shaded region is the region of integration. For the sake of making it easier to draw I've taken a to be 1. 'a' will simply be where the curve: y = \sqrt{a^2 - x^2} crosses the axes, as it is also the radius of the circle. So for the y part of the integral, the...

Original integral: \int^{a/\sqrt{2}}_{0}dx\int^{\sqrt{a^2-x^2}}_{x}\sqrt{x^2+y^2}dy Replace dxdy with r dr d(theta) and change the limits: \int^{\pi/2}_{\pi/4}d\theta\int^{a}_{0}\sqrt{x^2+y^2} r dr By replacing the square root with r, I then have: \int^{\pi/2}_{\pi/4}d\theta\int^{a}_{0}...

I've sketched the region of integration, and it is clear what the new limits should be. However, as you said, by substituting the sqrt for r and evaluating the integral I obtain an answer of: a^3\pi/12 The answer expected is: a^2\pi/8 Either the question is wrong, or I'm wrong, I assumed...

Homework Statement Transform to polar coordinates and evaluate... \int^{a/\sqrt{2}}_{0} dx\int^{\sqrt{a^2-x^2}}_{x}\sqrt{x^2 + y^2}dy Homework Equations x^2 + y^2 = r^2 x = r cos \theta y = r sin \theta I've been struggling to make sense of this problem, it should be easy, I'm...

Will someone please explain why my textbooks/lectures have taught me that the uncertainty principle is (delta x)(delta p) = (h-bar). While wikipedia states that (delta x)(delta p) >= (h-bar)/2.

This isn't actually a homework/coursework question, but rather a need to clarify a discepancy between my lecturer's notes and a textbook. My lecturer's notes state that for an "organ" pipe, closed at one end, the 1st harmonic frequency will be 4L. For the 2nd harmonic the frequency will be...

Homework Statement A car pulls a trailer along a level road at a steady speed of 10 m/s and the pull on the trailer is 100N. When the car accelerates at 0.5 m/s2 the pull on the trailer is 150N. Assuming the resistance to motion to be constant, find the mass of the trailer. Homework...

Oh yes, sorry. I skipped part of that calculation in my notes, was an error I made while typing it up on here. Confident that I've got it right now, thank you.

Okay, I'll use vector notation. Particle A: (^{2W}_{ 0}) + (^{ 0}_{-W}) - T_{1} = 0 Particle B: (^{2W}_{-W}) + (^{0}_{-W}) - T_{2} = 0 I've come to some answers using this, I'm not sure if I'm right or wrong though. I've arrived at T1 being 2.24W (2 d.p.), and T2 being...

Homework Statement A light inextensible string ABC is fixed at point C. Two particles, each of weight W are attached to the string by A and B. The system is held in equilibrium by a horizontal force of magnitude 2W acting on particle A. Find (a) the tensions in AB and BC, and (b) the...

I disagree; If an object is hung from a point, as described, it will come to rest by balancing it's mass evenly towards the centre of the earth. If you were to hang a plumbline on the same point, the plumbline will likewise hang towards the center of the earth. It is the same principle of a...

The total momentum before a collision must equal the total momentum after a collision. Before the collision, both are traveling towards each other at 10m/s... As momentum is a vector quantity it will have a direction; you can say that object A = 10 m/s, while object B = -10 m/s. The "system"...