I have read this paper "http://www.pnas.org/content/113/22/6143.full" and while I found it intersting, there isn't much discussion on the future applications of the new developments (unless I zoned out and passed over it, always a possibility).
Just wondering if anyone had any thoughts as to...
Homework Statement
Prove that y(x,t)=De^{-(Bx-Ct)^{2}} obeys the wave equation
Homework Equations
The wave equation:
\frac{d^{2}y(x,t)}{dx^{2}}=\frac{1}{v^{2}}\frac{d^{2}y(x,t)}{dt^{2}}
The Attempt at a Solution
1: y(x,t)=De^{-u^{2}}; \frac{du}{dx}=B; \frac{du}{dt}=-C
2...
Homework Statement
(a) A particle is moving so fast with respect to an observer that the γ factor of its rest frame with respect to the observer’s rest frame is 108. By how much is the velocity of the particle less than that of light?
(b) A particle is moving very slowly with respect to an...
Of course, thank you :)
We determined before the F=ρAv2
In this situation, A=Lh
Considering a thin strip of height dh we can get to:
τ=v2ρL∫0hhdh
which leads to the equation needed; 0.5v2ρLh2
With the third (and final :P ) part, I can get an equation for F in terms L and h from F=τ/h...
What is the area of the block?
Let area=A, representing the section of the wall impacted by the wind.
The length of the block of air would be equal to vt, no? It makes sense that the amount of air hitting the wall is dependent of the speed of the air and the time taken.
The mass would be...
Homework Statement
Ignore turbulence and viscosity.
A cylinder with radius r is filled to depth d. There's a leak in the bottom of the cylinder.
When suspended from a rope, the depth is reduced to d/2 after 10 minutes. From this point, how long should it take to empty completely...
So A=∏r2 and r ranges from r0/2 to 2r0
But with my integral, which I thought would be R=ρ∫0L (1/A)dx relates to the length of the cylinder, not it's radius.
I think I need to find an equation for r at a specific point in the bar in terms of x (which ranges from 0 to L)
Would this be...
The equations I would think would be useful are ρ=F/A, ρ=m/V, P=mv
ρ= air density, P=momentum
as m=ρV then I can substitute it into momentum giving p=ρVv.
I just don't know what to do. It's most probably frustration blocking something simple.
I'm not even sure how to describe the mass...
Ah thank you very much.
I probably wouldn't have noticed that I got the sign wrong :(
If f(x)=x2 then f(2x)=4x2
So the ratio of the power at frequencies ω and 2ω would be 4
Homework Statement
I have to find the ratio of RB/RA where R is electrical resistance.
Both objects A and B have circular cross section and length L, and are made of the same material.
A has radius r0. B has radius r0/2 at the bottom and increases linearly to 2r0.
Homework Equations...
Sorry to ask another question :/
Homework Statement
Consider the change of momentum.
A wind (of speed v) acts perpendicularly to a wall. Show that the pressure do to this wind acting of the wall is v2ρ, where ρ is air density.
Hence show by suitable integration that the torque about the...
I always seem to forget the simple things :(
Thanks for the help
So by converting everything to SI units I got A=-4, B=2, C=-3, D=-1
I got this from:
kgm2s-3 = (s-1)A (Asm)B (ms-1)C (s4A2m-3kg-1)D
D is the only one dealing with kg, so that must equal -1.
Then B must equal 2 so that A is...
Homework Statement
The total power radiated by an oscillating electric dipole is a function of the oscillation frequency ω, the dipole moment p(=Qd, where ±Q is the charge at each end of the dipole and d is the distance between charges), the speed of light c and the permittivity of free space...