Recent content by rugapark

how did you get the x, y and z to equal those three? and where did the t's come from? thanks for the help!

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?

[edit] - there should be 'dt' s on the RHS in the 2nd and 3rd line of work

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 into...

is \int\frac{dx}{1+x^{2}} the same as \int\frac{1}{1+x^{2}}dx ?

brilliant, thanks for that guys.

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 doesn't 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?