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...
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...
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...