I was wondering whether the decay of the Pi-0 meson in QED to an electron positron pair can occur as follows:
Pi-0 -> virtual photon -> e+e-
or does it have to go via
Pi-0 -> two virtual photons -> e+e- (the Feynman diagram has a 'square' of virtual electrons/photons)?
I'm struggling with the relation between particle exchange and parity with the case of para- and ortho-hydrogen.
The overall wavefunction must be antisymmetric with respect to particle exchange and so for para-hydrogen (an antisymmetric spin state) the spatial part of the wavefunction must be...
Firstly, apologies for the notation.
The 4-momentum of a massive particle (rest mass m) is defined by
where u is the 4-velocity. Thus in a frame S in which a particle has 3-velocity u the components of p are
How can we then identify the zeroth component of...
I guess you have a two cylinder system with an incompressible fluid?
For a) you may call, generally, the diameter of the red cylinder D, and thus the diameter of blue cylinder 2D. What are the areas associated with diameters? We thus may work out the volume V=Area x distance through which the...
I would start by drawing a diagram of the situation. Draw the 4 forces in, i.e. weight W, reaction force R from the floor, friction F' and the force we are pulling with F.
Since the trunk isn't moving the vertical direction, we may equate the 'downwards' forces with the 'upwards' forces, i.e...
A stone is dropped from a stationary helicopter 500m above the ground, at the equator. How far from the point vertically below the helicopter does it land?
Conversation of AM
The Attempt at a Solution
Let the height above the ground it is...
The Coulomb is the SI unit of charge. It is just a standard against which we can compare the relative charges of difference objects; just like we might say this object has a mass of 1kg, and this object has a mass of 3kg, we could say one object has 1 coulomb (C) of charge, and another has 10C...
So, the rocket equation is
F_ext = m(dv/dt) + u(dm/dt)
where m is the mass of the rocket, v the velocity, u the effective exhaust gases speed, and F_ext the external forces on the system.
If we take a constant mass ejection rate p, and take the external force to be the gravitational...
You've recognised the general equation of a parabola to be y = Ax^2 + Bx + C. Because we're dealing with gradients, I suggest you differentiate this equation with respect to x. In this situation, y is the elevation, and x is the horizontal distance.
A sensible co-ordinate system would be to...
Remember, you're trying to PROVE that tan(x/2) = sinx/(1+cosx), so don't start the proof by writing this!
I would suggest by writing down the right hand side (i.e. sinx/(1+cosx)) because this looks intuitively like it can be simplified, and then manipulate this to find it equal to tan(x/2)
Okay so you know the identity cos2A=(cosA)^2-(sinA)^2, as you've written above.
Remember (sinA)^2+(cosA)^2=1 ?
Try substituting (cosA)^2 from the second equation into the first, then rearrange to find the denominator. Use sin2A=2sinAcosA for the numerator, and you should be okay! Hope this...
You need to know the accleration to find the time using the s = ut - 0/5at^2 equation, so that's no good surely, because that's ultimatley what you're trying to find. Use your initial velocity as the one you calculated, and write down what the final velocity must be. You know the displacement...
Try using one of the equations of motion which doesn't involve time, that is,
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the average acceleration and s is the displacement between when vel = u and vel = v
The answer is 1, if you didn't already know. Try again but write sinx as S, and cosx as C; this makes the expression a whole lot more manageable. I suggest taking a factor of 1/S^2 out and then forming a single fraction. Hope this helps.
Draw yourself a little diagram of the situtation. Include the forces acting. You should have a force(say, F) coming out of the loco, between the loco and the first car call the tension T1; remember to draw two arrows for this tension, one pulling the loco towards the car, the other pulling the...
There are two ways of approach. One is using the constant accleration equation
where a is the acceleration of the crate and s is the displacement caused by the accleration, i.e.
v1 = 0, a = F/m (Newton's Second Law) = 25/4.5 = 50/9, s = 1.2, so
v2 = sqrt (2.4*50/9)...
Okay, your first question was to show that
|y + x|^2 = |y|^2 + |x|^2 + 2|yx|cos(a1-a2)
Using the definitions of y and x given. Start by writting down that
y = |y|exp(ia1) = |y|(cos(a1)+isin(a1))
x = |x|exp(ia2) = |x|(cos(a2)+isin(a2))
Using the series definitions of the exponential, sine and...
Cheers that makes things clearer. I'm afriad my experience at differentials is sufficiently small that I don't know how to derive both sides. V_t goes to a_t by definition of acceleration I suppose, but I haven't got any t's on the RHS of the equation, and as its differentiating w.r.t t, I'm...