Recent content by Aaron7

Homework Statement Mass M traveling at v=c/3 decays into 2 photons in x and -x directions. Mass M orginally formed by mass m traveling at v=3c/5 hitting a stationary mass m. This gives M v=c/3 and M=3m/√2. Homework Equations E=K + mc^2 p = gamma m v E = gamma m c^2 K =...

Homework Statement With X and Y being sets, I need to show that there is a bijection between the set of functions (X->P(Y)) and the set of relations P(X x Y) where P(..) is the power set symbol. Homework Equations P(Y) = {Z | Z subset of Y} The Attempt at a Solution I know a bijection...

Thank you for the help. I think I was too worried about the complexity of the set rather than using the definition to simply prove it. I should be able to move on to some more complex ones now. Thanks again.

Homework Statement I am on the final part of a question and I have to prove that the following is a irreflexive symmetric relation over A or if it is not then give a counter example. R is given as an irreflexive symmetric relation over A. Relation: {(X, Y) | X ⊆ A ∧ Y ⊆ A ∧ ∀x ∈ X.∀y ∈...

Homework Statement A rubber string when unstretched has length L0 and mass per unit length μ0. It is clamped by its ends and stretched by ΔL. The tension is T=κΔL / L0. Show that the wave speed on the rubber string when stretched by ΔL is 1/L0 √( (κ/μ0) ΔL(L0+ΔL) ) Homework...

So I have f=(L- a/2)k => fd = dk(L-a/2) / L => fd = dk - dka/2L Can I then say cosθ = a/L and since d<<L then cosθ = 1 - θ2/2 so a/L = 1 therefore fd = dk/2 and then complete it from there?

Ok, so with the triangle with sides a and d, I would work out the force in the d direction by saying: The force in the a direction is k(a/2) so the force in the d direction is k(d/2) because the distances a and d are similar to the forces acting in the a and d directions. This gets the correct...

Homework Statement There is a rod of length L pivoted on one end. It is originally at rest horizontally then released. When vertical, an impulse is applied to bring the rod to rest. Throughout the question I have worked out I = 1/3 mL^2 w= √(3g/L) at the vertical position and an...

Homework Statement The mass is connected to 4 springs, each connected to a corner of a square with sides √2 a. The springs have spring constants k and natural length a/2. Show the frequency of the mass when it is displaced by d << a towards one of the corners is √(3k/m) Homework...

Thanks for both of your help.

Homework Statement What is the probability of 4 independent dice summing to 20 or more? Homework Equations N/A The Attempt at a Solution I am not too sure how to approach this in an exam. I have attempted to do it this way but it would be easy to miss out a term: (I have put...

I got it :smile: Thanks for the help.

Homework Statement An aeroplane makes a round trip between two airports A and B located on the same line of longitude. On a windless day the aeroplane travels with constant speed v and the round trip time is T0. On the following day the same journey is made but there is a wind blowing at...

Homework Statement There is a step barrier at x=0, V_0 > E I am given: ψi = e^i(kx−ωt) ---> ψr = R e^i(−kx−ωt) <--- ψt = T e^(−αx−iωt) ---> Part of question I am confused about: State the two boundary conditions satisfied by the wave function at x = 0 and hence find...