Question $15$ Take $d1=5\mathrm{.}5cm,d2=3\mathrm{.}85cm,d3=2\mathrm{.}58cm,d4=1\mathrm{.}71cm,=81\mathrm{.}6$deg,$=27\mathrm{.}7$

deg,$=31\mathrm{.}4$ deg, and $F=95\mathrm{.}6$hat$()-81\mathrm{.}5$hat$()+61\mathrm{.}2$hat$(k)N.$

The vector $AD=|AD{|}^{*}$hat$()+|AD{|}_{{?}^{?}}^{*}(*)hat()+|AD{|}^{*},{?}^{*}$hat$(k).$ What goes in that first blank? That

is$,$ what is the $x$ coordinate of $AD$ divided by its magnitude?

$($You may assume that $|AD|$ includes the units for the force; that is$,$ your answers below

for the vectors in Cartesian$-$component form do not need units.$)$

Answer:

The vector $AD=|AD|,$hat$()+|AD{|}^{\text{'}},$hat$()+|AD{|}^{*}$

$*$k$.$ What goes in that second blank?

That is$,$ what is the $y$ coordinate of AD divided by its magnitude?

Answer:

The vector $AD=|AD|,$hat$()+|AD|,i+|AD{|}^{*}$

$*$k$.$ What goes in that third blank? That

is$,$ what is the $z$ coordinate of AD divided by its magnitude?

Answer: The vector $CD=|CD{|}^{*}dot{s}^{**}$hat$()+|CD{|}^{*}dot{s}^{*}$hat$()+|CD{|}^{*}$dots$*k.$ What goes in that first blank? That

is$,$ what is the $x$ coordinate of $CD$ divided by its magnitude?

Answer:

The vector $CD=|CD|,$hat$()+|CD{|}^{*},{?}^{*}$hat$()+|CD{|}^{*},*hat(k).$ What goes in that second blank?

That is$,$ what is the y coordinate of CD divided by its magnitude?

Answer:

That is$,$ what is the $z$ coordinate of CD divided by its magnitude?

Answer: The vector $BD=|BBD{|}^{*}dot{s}_{{?}^{?}}(*)hat()+|BD{|}^{\text{'}},$hat$()+|BD{|}^{*}$dots$*hat(k).$ What goes in that first blank? That

is$,$ what is the $x$ coordinate of BD divided by its magnitude?

Answer:

The vector $BD=|BD{|}^{*},{?}^{**}$hat$()+|BD{|}^{\text{'}},$hat$()+|BD{|}^{*},{?}^{*}$hat$(k).$ What goes in that second blank?

That is$,$ what is the $y$ coordinate of BD divided by its magnitude?

Answer:

The vector $BD=|BD{|}^{*},{?}^{*}$hat$()+|BD|,$hat$()+|BD{|}^{*},{?}^{*}$hat$(k).$ What goes in that third blank?

That is$,$ what is the $z$ coordinate of BD divided by its magnitude?

Answer:Writing the equations of equilibrium amounts to adding up all the $$ components and setting it equal to zero. $($And then repeating

for hat$()$ and hat$(k).)$ We reviewed this week how one could put this into a matrix form to solve the system using a computer.

Drag the terms from the list below to create the matrix equation.

$\left[\begin{array}{ccc}M11& M12& M13\\ M21& M22& M23\\ M31& M32& M33\end{array}\right]\left[\begin{array}{c}|AD|\\ |CD|\\ |BD|\end{array}\right]=\left[\begin{array}{c}constant1\\ constant2\\ constant3\end{array}\right]$

matrix

$*$Note that the word "coordinate" is abbreviated as coord below for space$-$savings.

$z$ coord of $F$ times $(-1)$

$x$ coord of CD over $|CD|$

z coord of BD over $|$BD$|$

y coord of BD over $|$BD$|$

z coord of CD over $|CD|$

$x$ coord of BD over $|BD|$

y coord of AD over $|$AD$|$

$z$ coord of AD over $|$AD$|$

$x$ coord of AD over $|AD|$

y coord of F times $(-1)$

y coord of CD over $|CD|$

Answer saved

Points out of

$3\mathrm{.}00$

P Flag

question

$7$

that the rod is

in tension. Draw a FBD to be graded and submit it to Gradescope. $($Remember BREAD.$)$ Which of these reaction forces exist at your FBD$?$

$?$