I've had a play around with that and, although it gives quite a nice number, I know the answer I need but can't seem to reach it...I've been told that I should get:
F(q^{2})=\frac{m^2}{m^2+q^2}
The problem being, my integral still has an exponential factor - I'm not sure how to make it...
Homework Statement
I'm trying to integrate the following:
\int_0^{2\pi} \int_0^\pi \int_0^r \frac{m^2r}{4\pi} e^{-r(m+iqcos\theta)} sin\theta dr d\theta d\phi
The Attempt at a Solution
Well, the question wasn't just that, my attempt was to get this far!
I know that...
Thankfully we'd already been given the half-life, and we figured we'd have to calculate the speed from gamma...thanks for verifying, you've been a great help!
Ah, I see...you work out gamma via E=\gamma*mc^{2}...since you need the speed to calculate the distance, I'm assuming you calculate the speed from the gamma factor...it certainly seems to work okay.
Homework Statement
How far will a beam of muons with kinetic energy (a) 1 MeV, (b) 100 GeV travel in empty space before its intensity is reduced by half?
Homework Equations
See below
The Attempt at a Solution
My main problem with this is that it looks like we won't be taught the...
This may seem like a really obvious question to those that know it but...
We looked at Yukawa's potential the other day, in the form W(r)=\frac{\alpha}{r}*e^{-Kr}, but our lecturer never explained what K and \alpha actually are! I've looked on the net and all I can find is that they are...
I realized that it must be Pythagoras, as that's where the equation for a circle comes from, it was more the fact that - when rearranged from the equation - the hypotenuese would be r^2d^2. Since it is normally just r^2, I wasn't sure if you were able to just put the distance (d^2) in.
I'm currently working on my final year project, and one of the little bits to do is to see if certain data points fall within a circle with my own defined radius and central co-ordinates. I've been given the equation to use:
d = \frac{\sqrt{(l-l_{0})^2 + (b-b_{0})^2}}{r}
where l_{0} and...
Thanks ever so much! We were trying to go straight from the equation without taking into account where it comes from. We also have a slight tendency to overthink things! Thanks for your help! :)
Thankfully, this question is only a couple of marks, we've been advised to ignore the Sun's motion for this. Going from the equation and making M_{0} the mass of the Sun, gives the freefall velocity the same value as the escape velocity for the Sun. Would that be correct?
Ah, I think I see what you're getting at. KE + PE = 0 therefore
\frac{1}{2}v^2 = \frac{GM_{0}}{R} - \frac{GM_{0}}{R_{0}}
meaning that our velocity would be like the equation from my original post but where R is the radius of the Sun, R_{0} is infinity, making that term disappear, and M_{0}...
Homework Statement
(b) If an object of 0.1 Solar masses fell into the Sun (starting at rest at infinity) calculate what its final speed and energy would be.
Mass of the Sun = 1.99 x 10^{30} kg
Radius of the Sun = 6.96 x 10^8 m
The Attempt at a Solution
Having done the rest of...