Hi,
So I used the formula ##\nabla \times(\mathbf{c}\times\mathbf{r}) = (\nabla \cdot \mathbf{r})\mathbf{c}+(\mathbf{r}\cdot\nabla)\mathbf{c}-(\nabla\cdot\mathbf{c})\mathbf{r}-(\mathbf{c}\cdot\nabla)\mathbf{r}##. Then the terms where ##\nabla## acts on ##\mathbf{c}## will be zero since...
Homework Statement
Without explicit calculation, argue why the following expression cannot be correct: $$\nabla \times (\mathbf{c} \times \mathbf{r}) = c_{2}\mathbf{e_{1}}+c_{1}\mathbf{e_{2}}+c_{3}\mathbf{e_{3}}$$ where ##\mathbf{c}## is a constant vector and ##\mathbf{r}## is the position...
Sorry that's a typo it should read ##\frac{\pi}{8}## in the question not ##\frac{\pi}{2}##.
Ah yeah of course that makes perfect sense. Thank you so much!
Homework Statement
Let:
##I=\int _{-1} ^{1}{\frac{dx}{\sqrt{1+x}+\sqrt{1-x}+2}}##
Show that ##I=\int_{0}^{\frac{ \pi}{8}}{\frac{2cos4t}{cos^{2}t}}## using ##x=sin4t##.
Hence show that ##I=2\sqrt{2}-1- \pi##
Homework EquationsThe Attempt at a Solution
The substitution is ##x=sin4t## which...
Homework Statement
Show that the real solution ##x## of $$tanhx=cosechx$$ can be written in the form ##x=ln(a \pm \sqrt{a})## and find an explicit value for ##a##.
Homework Equations
$$cosh^{2}x-sinh^{2}x=1$$
$$coshx=\frac{e^{x}+e^{-x}}{2}$$
The Attempt at a Solution
I reduced the original...
Homework Statement
3 towns are located at D,F & E; the vertices of an scalene triangle. The bearing of F from D is 48 degrees. D to E=640m and E to F=430m. Point G is located at the end of a south line at F.
a)i)Find angle DFG
ii) Find angle GFE
iii) Find angle DFE
b) Calculate angle...
In Scotland St Andrews has one of the best reputations for physics but on their website they only list astrophysics, condensed matter and photonics as research fields. Edinburgh also has a good reputation and it does do research in particle physics. I've also heard that Strathclyde has a very...
I have been going through my equations and writing them up on the computer so I can refer to that when needed and have go to angular acceleration, velocity and displacement equations yet I don't have very many equations for those topics and I wondered if anyone had some equations for finding...
I was wondering what would g equal on Jupiter if you could stand on its surface? I wrote a computer programme (my 1st one) to work g out anywhere and when i plugged in the numbers for Earth it gave me 9.799 which is correct and for Jupiter it gave me 24.778 but when I looked it up I kept finding...
Would I be right in saying the following:
Potential energy arises from the conservation of energy. To lift a mass you must exert a force counteracting the force of gravity. As it moved and a force was exerted work was done on it. As it is not moving it has no kinetic energy. Due to the...