Homework Statement
A flat rigid body is rotating with angular velocity 3 rads-1 about an axis in the
direction of the vector (i + 2 j + 3 k) and passing through the point (1, 1, 0) on
the body. Find the linear velocity of the point P = (1, 0, 1) on the body.
(You may use the result v =...
Homework Statement
A ball of mass 1 kg is acted upon by three forces:
Fl = (2i + 4j - 3k) N, F2 = (-3i - j + 2k) Nand F3 = (i - 5j - k) N.
Determine a vector expression for the acceleration of the particle.
If, at time t = 0, it has position r = (i +j) m and velocity u = (i +3j)m/s...
Q. In a particular spectrometer, doubly ionised \stackrel{12}{6}C and singly ionised \stackrel{6}{3}Li atoms are detected. The ratio of the path radii is 1.00252, the Li having the larger value. The fields are constant. Find the mass of of the lithium atom.
I can only think of the equation...
I'm trying to integrate a function which is given as
F(u)= \int f(x)e^{-2}^{\pi} ^{i} ^{x} ^{u} dx
with limits of +ve and -ve infinity
integrating by parts gives me
\frac{1}{2} f(x)^{2}e^{-2}^{\pi}^{i}^{x}^{u}-\frac{1}{2} \int f(x)^{2}xe^{-2}^{\pi}^{i}^{x}^{u}dx
fisrt off, is the...
oh right, my mistake lol
so, the last line should be
ln(3x+4)=\frac{1}{2}ln(t^{\frac{1}{2}})
I have no idea where to go from here with the initial value that I was given x(0)=2! would I sub in x=2 into the equation?
I'm trying to solve this firrst order diff. equation, where I'm given the initial value, x(0)=2
\frac{dx}{dt}=\frac{3x+4}{\sqrt{t}}
\frac{dx}{3x+4}=\frac{1}{\sqrt{t}}dt
\int\frac{1}{3x+4}dx=\int\frac{1}{\sqrt{t}}dt
ln(3x+4)=ln(t^{\frac{1}{2}})
this is as far as I got, do I sub in x(0)=2...
I am given F=(3i + 2j + 4k) N and mass = 2kg
I need to calculate acceleration, so I plugged it into F=ma,
am I right in saying
(3i + 2j + 4k) = 2 a
\frac{(3i + 2j + 4k)}{2} = a
therefore a = 1.5i + 1j + 2k ?
cheers.
y=A sin (wt\pmkx) is the formula where
A = amplitude
w = angular freq.
t = time
k = wave vector
wave vector doesnt have units as it's a vector quantity.. right?
I needed to write an equation for a wave with:
amplitude : 2cm
wave vector : 502.7
angular frequency : 125.7 Hz
time : 0 sec
and I used the general equation for waves to come up with:
y = 0.02 sin (125.7 - 502.7x)
is that alright?
I ended up discussing something with friends when we were going through this question - why is it that we don't see wave like properties in larger bodies i.e. in macroscopic levels? is it because the larger the mass, the smaller the de Broglie wavelength, and so the wave like properties are just...
brilliant - just another quicky, some of the answer guides ignored the whole square root part of the equation.. is that because that part of the equation is always roughly equal to 1?
I had a go at 2 Q's and wanted to make sure I'm doing this right.
so here's the first one, and maybe if i went wrong with it I was going to redo the 2nd Q on my own.
\lambda = h/p = h/mv (\sqrt{1-((v^2)/(c^2))})
so, an Alpha Particle travelling @ 2x106m/s (mass = 6.645x10-27 kg)...
the question is \int 2x sec^2 (x^2) dx
do i sub u= sec (x^2) ?
I so far have got to trying to sub u= sec(x^2) and getting du= 2 (sec x^2 tan x^2)... i have a strong feeling i fudged the "du" part. hmm.
intergrating "e"
I'm doing some intergration q's and I'm stuck on one which involves e
[x^2 e^(x^3) ]dx
I know to integrate you "add one to the power and divide by the new power.. would that make the solution
((x^3)/3) ((e^(x^4))/(x^4)? hope that makes a bit of sense..
so would i be right in saying,
"If the collision between the two bodies is an elastic collision, all momentum, kinetic energy and total energy will be conserved as elastic collisions do not convert any original energy forms into another."
I am struggling to understand this, but I really...
I am going through some questions for resits in August, and I have no idea what this question is wanting me to explain :
"Briefly discuss the circumstances under which (i) momentum, (ii) kinetic energy and (iii) total energy are conserved in collisions between two bodies. [3]"
it's only a...