/sci/ - Science & Math

>>11669373
>Problem 13.5
Use ropes with loops connected to other ropes, so that ropes can slide along each other.

>gee bill two threads?
>>11554687
Total reluctance in the circuit is [math] \mathfrak{R}=\mathfrak{R}_\text{core}+\mathfrak{R}_\text{gap}=L_c/(\mu A)+L_g/(\mu_0 A) [/math]. Then [math] B=\Phi/A=NI/\mathfrak{R}A=...=1.118\text{ tesla} [/math]. Let [math] u=B^2/(2\mu_0) [/math]. Energy stored is just u*volume*relative permeability. So for gap and core we got [math] E_g=Axu [/math] and [math] E_c=A\ell u\mu [/math] with ell being the corrected length of the core.
>force
>Nm
[math] F=Au=...=1792\ \text{N} [/math] with less rounding.
>ii
I'm getting a different number for a) but I think the idea is to find the impedance of the wire at 60 Hz.
>>11555196
>write down a 2 by 4 augmented matrix, with the LHS being the matrix you want to invert and the RHS being identity
>take row 2 and add to row 1
>add row 1 to row 2
>multiply row two by 1/9
>you should now have identity on the LHS and
you get [math] \begin{pmatrix} 4/9 & -1/9 \\ 1/9 & 2/9 \end{pmatrix} [/math] as the inverse on the RHS
>is it just trial and error
not really