Homework Statement
Given that b_{n}\rightarrow\infty and \frac{a_{n}}{b_{n}}\rightarrow C (where C>0) as n\rightarrow\infty, prove that a_{n} must also diverge to \infty, that is, a_{n}\rightarrow\infty as n\rightarrow\inftyHomework Equations
As above.
The Attempt at a Solution
I could...
I'm preparing for the "Sixth-Term Examination Papers" (STEP) this June by going through the past papers. Unfortunately there isn't any solution available for the older past papers AND I've already finished high school which basically means I can't verify my solutions. So I thought it might be a...
I wonder if anyone here has experiences with the mathematical tripos/natural sciences tripos at Cambridge. I'm currently holding an offer for Maths there (conditional on STEP) and opting to do maths with physics, and if I get in I MAY transfer to do physics in the natural sciences tripos in the...
I was playing around with complex exponentials and came to this result:
$\begin{eqnarray*}
e^{\frac{2\pi i}{5}}&=&e^\left(\frac{2}{5}\right)\left(\pi i\right)\\
&=&\left(e^{\pi i}\right)^{\frac{2}{5}}\\
&=&\left(-1\right)^{\frac{2}{5}}\\
&=&1\end{eqnarray*}$
But obviously e^{\frac{2\pi...
Perhaps I was at fault to have worded my post so poorly. I meant, personally, I don't like experimenting much, but I'm not saying that in general physics experiment should be discouraged. After all the wacky postulates of quantum theories were accepted due to the experimental results, not to...
I don't know.. I'm a high school physics student and I love the theory bit and I would prefer as few experimental works as possible, but I understand other people do like experiments and "get" the subject better with the practical works. I'm just more of a theorist type..
Hmm.. I might have missed something.. after all I'm just another high school physics student still..
Anyway, I thought Newtonian mechanics is supposed to be entirely deterministic and hence under this idealism such continuous random variables wouldn't exist. Random frictional effects wouldn't...
Hmm... why so? Consider the masses are initially static "matter" (especially in the Newtonian framework) cannot travel "through" one another.
Or will it concern the force due to the impulse upon collision? Since the velocity when the two particles collide is very high the impulse force which...
Ahh, thanks a lot guys! Yes I was indeed picturing the "initially stationary" situation but I also did forget about the initial relative velocities and orbitting situation. A lot clearer now!
I was just reading through stuff about Newtonian gravitation and this question popped up in my head and I can't answer myself.
Consider two uncharged point masses with mass M and m respectively, independently suspended far away from each other in a space that would otherwise consist of...
What if, say to prevent that, I fix a pipe from the hole right down to the rig below it? So now the flow rate would depend on the *depth* of the water (which now includes the pipe length too)? And so then what calculation would this turn into?
*And I editted the original post, inserted one...
Well I did do some quick kinematic calculation on it but, while I can find out the velocity of falling "droplets" of water when it reaches the rig, the continuum of water flow stream just confuses me.
*EDIT: So can I just go: v of water = sqrt(2*h*g) at the device, but water is let flowing...
Hi,
I'm trying to get the rig for my physics project set up which requires some constant water flow through the system. Unfortunately it's requiring a bit more water inflow than the tap can provide. I measured the tap's flow rate to be somewhere around 0.1L/sec to 0.3L/sec
Now because I...
Hmm.. I didn't expect the paper to deform at around 100psi actually.. I'm just planning on measuring freefall time under different pressures.. I guess I'll have to see.. (I wouldn't imagine a large amount of deformation over a 3m freefall actually, I might be wrong though)
I'm just looking...