http://prntscr.com/88757l Im mainly stuck on b.

- anonymous

http://prntscr.com/88757l Im mainly stuck on b.

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- anonymous

@dan815 @Hero

- anonymous

@ganeshie8

- anonymous

hahaah okay.

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## More answers

- dan815

|dw:1440395793167:dw|

- dan815

okay lets do AB first,
a vector can be written in terms of its change in x and y
AB=
or xi + yj

- dan815

AB=<15,12> or 15i+12j are you okay with this

- anonymous

yeah so the vector of F is < -180cosx, -180 sinx>

- anonymous

im with you.

- dan815

yep

- dan815

now for B take the cross product and its magnitude

- dan815

thsi is actually going to tell you the torqure experiences at joint A

- anonymous

i did the cross product of AB x F and got <-2700 cosx, -2160sinx>

- dan815

experienced*

- dan815

take the magnitude of it now

- dan815

ill check ur cross product in the mean time

- anonymous

actually cross product is -2700sinx, 2160cosx

- anonymous

my bad, typed it in incorrectly

- dan815

|dw:1440396026100:dw|

- anonymous

since there is a variable, i cant take the actual magnitude, im left with \[\sqrt{7290000\sin^2x+4665600^2x}\]

- dan815

ya the cross results in
<0,0,(15*-180sinx - 12*-180*cosx)>
so the magnitude
=(15*-180sinx - 12*-180*cosx)

- anonymous

there is suppse to be a sin after4665600

- dan815

be careful with the cross product you arent doing it properly

- anonymous

sin^2

- anonymous

what did i do wrong?

- dan815

the cross product will result in a vector that is perpendicular to both of these vectors which has to be only in the k or z direction, as both of these vectors are in the x,y plane

- anonymous

i thought since we are 2d, we assume there is no k. is that my mistake? i should place a 0 in k?

- dan815

wait what formula for cross product did u learn theres 2, one with the matrices and the other one is
ABXF = |AB| |F| * sin theta

- anonymous

how does finding the magnitude of a mean i find the orthogonal vector?

- dan815

|ABXF| = |AB| |F| * sin theta

- dan815

im a little lost right now lets do b over

- dan815

you have AB and F right

- anonymous

so lets take the cross product.

- dan815

|AB X F| = |AB| * |F| sin theta

- dan815

what did u get for the angle between these fectors

- anonymous

you arent suppose to get an angle. the answer is left in terms of theta

- dan815

yes that is fine give it to me interms of the angle

- anonymous

what do you mean interms?

- dan815

|dw:1440396551765:dw|

- anonymous

btw, the answer to b is 225sinx+180cosx

- anonymous

theta 2 is 38.7 degrees

- dan815

okay

- anonymous

theta 1 is not given yet.

- dan815

it will be interms of that theta

- dan815

put these 2 vectors together and using that cross product formula

- dan815

|dw:1440396697687:dw|

- dan815

|dw:1440396725482:dw|

- anonymous

okay, AB x F
that means we get 15*(-180sinx) - 12(-180cosx)
which simplifies to -2700sinx+2160cosx
agree?

- dan815

|dw:1440396763984:dw|

- dan815

yea u can do it that way too

- anonymous

yeah can we do it my way, because that is how the teacher taught us in class.

- dan815

both these expresison are equivalent

- dan815

okay

- anonymous

so now that i have my cross product vector, how do i find the magnitude?

- dan815

u already have hte magnitude

- dan815

becaause there is only a z direction component

- dan815

your vector from the cross product was
<0,0,-2700sinx+2160cosx>

- anonymous

so how do i go from my cross product answer to 225sinx+180cosx?

- anonymous

because that is the answer, apparently from the back of the book

- dan815

its wrong

- anonymous

really? okay. sp i guess ive had the answer the whole time, lmao. thanks for assuring me i had the right answer.

- dan815

okay no problem

- dan815

wait i want to check something

- dan815

what are the units for lb

- anonymous

im not sure, i dont think the units are relevant

- dan815

there a feet in there though right

- dan815

u might have to rewrite 12 and 15 in feet see what that givesu

- anonymous

google it, im not sure.

- dan815

oh hehe the answer at the book is right :)

- anonymous

i have to convert in to feet?

- dan815

ya so the 12 is 1 and the 15 = 15/12

- anonymous

why is it that the answer does not have any i or j or k?

- dan815

gives u the asnwer of book

- dan815

remember the cross was only in the z direction

- dan815

and we took the magnitude of it , so no more directions

- dan815

http://www.wolframalpha.com/input/?i=%3C180cosx%2C180sinx%3E+cross+%3C15%2F12%2C1%3E check ur answer

- anonymous

so the answer is a scalar quantity?

- anonymous

all i did was do cross product, which is a vector, not a scalar quantity.

- dan815

magnitude of any vector is always scalar

- dan815

okay look umm

- anonymous

i havent taken the norm of anything yet.

- dan815

what is the length of this vector?

- anonymous

a.

- dan815

right.. now the cross product resulted in a vector with
<0,0,a>

- dan815

where a was that expression..

- anonymous

ahhhh i see what you mean.

- dan815

ok good

- anonymous

okay thanks for your help and the great idea of converting to feet!

- dan815

sure np

- anonymous

was this question interesting like how you asked? ;)

- dan815

well lol maybe part d is better

- anonymous

i havent gotten there yet, so ill let you know.

- dan815

i kind dont know lb is actually, we use the metric system here

- dan815

u know how newtoms is m*a so for us its kg*m/s^2

- dan815

you guys use lb instead of newtons

- dan815

F=m*a
for you i guess its
pounds * f/s^2
remember that from now on

- anonymous

yeah haha thanks for the advice!

- anonymous

yeah im not really sure how to approach part d. im assuming we have to somehow make a 90 degree because thats what maximizes torque.

- dan815

yep but they want u to prove with optimization

- dan815

so do it with derivatives first

- dan815

to check u will see that the angle theta makes is 90 degrees with AB

- dan815

|dw:1440398825441:dw|

- dan815

do with with derivatives and then do it with geometry and see if they are equal

- dan815

Moment = 180 cos(x)-225 sin(x)
max moment happens when??
solve for 0

- dan815

remember what happens at maxs??

- dan815

the derivative goes to 0

- dan815

make sure you have the max and not min though

- dan815

|dw:1440399048233:dw|

- dan815

180 cos(x)-225 sin(x) = another sinusoid so u will have to solve your angle with in the bounds of 0 to 360 degrees or 0 to 2pi radians

- dan815

ill leave u to that

- dan815

remember this form, it might be better to use that here now |dw:1440399289233:dw|

- dan815

just giving u alternatives both of them are jut as viable

- Jhannybean

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