I'm going over the photoelectric effect and have run into a conceptual problem, and was hoping for some help in resolving it. In particular, I am looking at the frequencies below the threshold frequency of whatever metal is being examined.
So, because of the lower frequency, there will be no...
Homework Statement
I'm given two equations for coordinates of a certain particle in the xy plane, \dot{x}+ωy=0
and \dot{y}-ωx=0.
Then using the complex variable z=x+iy, find the differential for z, and solve it. Hence give x and y as functions of time.
Homework Equations
The...
Homework Statement
I'm trying to define a vector space over Q. Does this make any sense?
Homework Equations
The properties of a vector space
The Attempt at a Solution
Let V=Q^2 over Q. It seems to me that everything would be defined and I shouldn't be able to do anything to a...
Homework Statement
Let D be the triangular domain given by 0\leq y \leq3, (y/3)-1 \leq 1-(y/3). Then
\int\int (e-x^{5}e^(sqrt(1+y^2))
Homework Equations
The Attempt at a Solution
There is a quick way to solve it by breaking apart the double integral and then, apparently the x^5...
Homework Statement
Let a_n be defined recursively by
a_{1}=1, a_{n+1}=sqrt(6+a_{n}) (n=1,2,3,...).
Show that lim n->infinity a_{n} exists and find its value
The Attempt at a Solution
Observe that a_{2}=\sqrt{6+1}=\sqrt{7} > a_{1}. If a_{k+1} > a_{k}, then a_{k+2} = \sqrt{6+a_{k+1}} >...
Homework Statement
y''+25y=cot(5x)
Find one possible solution
The Attempt at a Solution
I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed).
Ok, so I take...
Homework Statement
y''-49y=7cos(7x)+7+e^(7x)
The Attempt at a Solution
I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one.
First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the...
Homework Statement
\frac{dy}{dx} = \frac{3xy}{3x^2+7y^2}, y(1)=1
Express it in the form F(x,y)=0
The Attempt at a Solution
I'm not sure where I'm going wrong. I let v=y/x,
v+x\frac{dv}{dx} = \frac{3x^2v}{3x^2+7x^2v^2}=\frac{x^2(3v)}{x^2(3+7v^2)}= \frac{3v}{3+7v^2}
\Rightarrow...
Homework Statement
Determine if the following is improper and convergent, improper and divergent, or proper
\int \frac{dx}{\sqrt[3]{x^2 - 7}}
from 8 to infinity
The Attempt at a Solution
Since I don't know how to...
Homework Statement
I'm confused about integrating something like \int\frac{1}{u}
Sometimes the answer seems to be ln|u| and sometimes just ln(u), and I wasn't sure why it is different from problem to problem. (after subbing u back in; I'm using the u-sub method)
It looks like the answer should...
Homework Statement
A magic stalk starts growing at a spot 10 metres from a 4 metre lamppost. The stalk grows 1 metre per hour. Find the rate at which the length 's' of the stalk's shadow is increasing at the instant when the height h of the stalk is 3 metres.
The Attempt at a Solution...
Homework Statement If f(x)=\frac{2x+1}{x+2}, the equation for y=f^-1(x) is?
So I switch x, x=\frac{2y+1}{y+2}
The Attempt at a Solution
I've tried many ways, but I must be going wrong somewhere, here's what I think to be my nearest:
x(y+2)=2y+1
x(y)+2x=2y+1
x(y)+2x-2x=2y+1-2x...
Homework Statement
I have two graphs (Radiant Power vs wavelength) and I have to choose which one would be the best for a shop -- the one with the least yellowing. (fluorescent bulbs)
I wasn't sure how to tell. The emission spectrums are very similar. The continuous spectrums are different...
Homework Statement
A photon enters an atom in the ground state. I have the energies to get to the next level.
My question is, does the photon have to be the exact energy to get to the next level before it is absorbed, or can the atom absorb it and go up those few levels and.. sort of store the...
Homework Statement
In an experiment similar to J. J. Thomson's, charged particles are observed to travel through a magnetic field of 0.040 T with a radius of curvature of 0.20 m. The path of these particles is made straight again when an electric field is introduced by two parallel plates...
Homework Statement
I'm doing an assignment involving a current balance, and the one thing I don't understand is the currents.
I have two separate currents, one labeled "Current in Solenoid" and another labeled "Current in Loop".
Now, I know the current in the loop is the part that causes...
[SOLVED] Wording Question Regarding Angles
If it says "to the horizontal", such as 30 degrees to the horizontal, would the angle be measured from Y or X? I measured it from the horizontal, but reading it over, it sounds like it's measured towards the horizontal, so I was thinking it may be from...
[SOLVED] Force Calculations
If an object is being pushed horizontally, does Fnormal always equal Fg? And Ffriction only equals Fapplied if it's at a constant velocity? I think that's how it goes, but I'm a little unsure.
Thanks!
[SOLVED] Significant Digits
I know how to do significant digits, but was wondering about answers involving multiple equations. If I find acceleration first, then find net force, should I wait to round the answer until the end?
a=vf-vi/t and then fnet=ma
To reiterate, should I keep...
[SOLVED] Question On Displacement -- Velocity-Time Graph
When calculating displacement, if you have a graph that starts with a non zero velocity, do you calculate the area from zero still, or do you calculate only from where it starts?
For instance, a linear problem with a velocity starting...
[SOLVED] Independence of Motion
I have a problem with a diagram that goes along with independence of motion. When air resistance is negligible, objects are supposed to fall at the same rate. In the diagram (a flash photograph), it shows 2 balls falling, one straight down, and the other...
[SOLVED] Instantaneous Acceleration on a Velocity-Time Graph
I need to find the acceleration at a specific time (for example, 6s). I know how to do the acceleration between time intervals, slope=rise/run, a=vf-vi/t2-t1, but what do I do when I need the acceleration at a specific time?
I've...
[SOLVED] Simple Acceleration Equation Help
g=-9.80 m/s^2
t= 3.85
vi= 0.00 m/s
d=?
d=vi(t) + (1/2)gt^2
d=0 + (1/2)(-9.80m/s^2)((3.85s)^2)
=-72.6
I'm trying to find the distance. So, this d represents displacement. Since in this case, this is also the distance, would there be any...