Recent content by ConorDMK

Oh yeah, of course, thank you! It's been a while since I've done this stuff. So I use, which makes sense as to why the hint says to use Pauli Matrices and Spinors.

So what I'm not sure on, is calculating the matrix elements for part (iii) with Pauli spinors and Pauli matrices, and then finding the form of the corresponding states. As I don't see how using the hint helps. The following is using the eigenvalues of the spin-operators. Provided what I...

Thank you very much! I'll keep the advice noted as well. These sorts of questions always trip me up, I guess I just need to be more confident with my workings.

Finding the neutrons per second. Uncluttering the question: ##P = 6 \times 10^{7} J/s, E_{1} = 149.7 MeV/event, A = 10^{-4} m^{2}, R = 5 m ##. Number of events per second = ##\frac{P}{E_{1}}## = escaping neutrons per second Area of ##5m## sphere around reactor = ## 4 \pi R^{2} ## Fraction of...

Sorry, I kept thinking ∇ had to be a vector. (∇T)r = (∂T/∂r) (∇T)θ = (∂T/∂θ)(1/r) (∇T)φ = (∂T/∂φ)(1/(r*sin(θ)))

(∇T)r(dl)r = (∂T/∂r)(dr/dr)rˆ = (∂T/∂r)rˆ (∇T)θ(dl)θ = (∂T/∂r)(dθ/dθ)θˆ = (∂T/∂θ)(1/r)θˆ (∇T)φ(dl)φ = (∂T/∂φ)(dφ/dφ)φˆ = (∂T/∂φ)(1/(r*sin(θ)))φˆ ∇T(r) = (∇T)r(dl)r + (∇T)θ(dl)θ + (∇T)φ(dl)φ = (∂T/∂r)rˆ + (∂T/∂θ)(1/r)θˆ + (∂T/∂φ)(1/(r*sin(θ)))φˆ This is what I had before, but I didn't think...

Homework Statement Let T(r) be a scalar field. Show that, in spherical coordinates ∇T = (∂T/∂r) rˆ + (1/r)(∂T/∂θ) θˆ + (1/(r*sin(θ)))(∂T/∂φ) φˆ Hint. Compute T(r+dl)−T(r) = T(r+dr, θ+dθ, φ+dφ)−T(r, θ, φ) in two different ways for the infinitesimal displacement dl = dr rˆ + rdθ θˆ + r*sin(θ)dφ...

That's the line of thinking that we decided to go down in the end. And having done that, I decided to do the full algebraic expression for the final image and final magnification anyway, just to annoy the people marking it. I feel like Dr Frankenstein.

Homework Statement A symmetric, double-convex, thin lens made of glass with n = 1.52 has a focal length in air of 40 cm. The lens is sealed into the opening in the left-hand of a tank filled with water (n = 4/3). At the right-hand end of the tank is a plane mirror 90 cm from the lens. Find the...

Got it, thank you very much.

Homework Statement A gas bottle contains exactly 158 moles of carbon dioxide CO2. Find the change in the internal energy of this much CO2 when it is cooled from 36C down to exactly 25C at a constant pressure of 1 atm. The gas can be treated as an ideal gas with γ=1.289. The gas constant reads...

t=√[(2(57kg)(12m)+2(9.6kgm2)(12m/0.3m)2)/((57kg)(9.8N/kg)(12m))] t=2.65s

so if I continue with mgh=0.5m(2h/t)2+0.5I(2h/(rt))2 I should get the correct answer?

suvat: s=t(v+u)/2 as u=0 for both v=2s/t so v=2h/t and ω=2h/(rt) Correct? or should they be without the 2?

Energy before: Etotal=mgh Energy after: Etotal=0.5mv2+0.5Iω2 using ω=h/(rt) and v=2h/t mgh=0.5m(2h/t)2+0.5I(h/(rt))2 t2=(2mh2+0.5I(h/r)2)/(mgh) t=√[(2mh2+0.5I(h/r)2)/(mgh)] Putting in the values t=√[(2(57kg)(12m)2+0.5I(12m/0.3m)2)/((57kg)(9.8N/kg)(12m))] t=1.90s to 2 decimal places...