anonymous
  • anonymous
http://prntscr.com/88757l Im mainly stuck on b.
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
hahaah okay.

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dan815
  • dan815
|dw:1440395793167:dw|
dan815
  • 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
  • dan815
AB=<15,12> or 15i+12j are you okay with this
anonymous
  • anonymous
yeah so the vector of F is < -180cosx, -180 sinx>
anonymous
  • anonymous
im with you.
dan815
  • dan815
yep
dan815
  • dan815
now for B take the cross product and its magnitude
dan815
  • dan815
thsi is actually going to tell you the torqure experiences at joint A
anonymous
  • anonymous
i did the cross product of AB x F and got <-2700 cosx, -2160sinx>
dan815
  • dan815
experienced*
dan815
  • dan815
take the magnitude of it now
dan815
  • dan815
ill check ur cross product in the mean time
anonymous
  • anonymous
actually cross product is -2700sinx, 2160cosx
anonymous
  • anonymous
my bad, typed it in incorrectly
dan815
  • dan815
|dw:1440396026100:dw|
anonymous
  • anonymous
since there is a variable, i cant take the actual magnitude, im left with \[\sqrt{7290000\sin^2x+4665600^2x}\]
dan815
  • dan815
ya the cross results in <0,0,(15*-180sinx - 12*-180*cosx)> so the magnitude =(15*-180sinx - 12*-180*cosx)
anonymous
  • anonymous
there is suppse to be a sin after4665600
dan815
  • dan815
be careful with the cross product you arent doing it properly
anonymous
  • anonymous
sin^2
anonymous
  • anonymous
what did i do wrong?
dan815
  • 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
  • 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
  • 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
  • anonymous
how does finding the magnitude of a mean i find the orthogonal vector?
dan815
  • dan815
|ABXF| = |AB| |F| * sin theta
dan815
  • dan815
im a little lost right now lets do b over
dan815
  • dan815
you have AB and F right
anonymous
  • anonymous
so lets take the cross product.
dan815
  • dan815
|AB X F| = |AB| * |F| sin theta
dan815
  • dan815
what did u get for the angle between these fectors
anonymous
  • anonymous
you arent suppose to get an angle. the answer is left in terms of theta
dan815
  • dan815
yes that is fine give it to me interms of the angle
anonymous
  • anonymous
what do you mean interms?
dan815
  • dan815
|dw:1440396551765:dw|
anonymous
  • anonymous
btw, the answer to b is 225sinx+180cosx
anonymous
  • anonymous
theta 2 is 38.7 degrees
dan815
  • dan815
okay
anonymous
  • anonymous
theta 1 is not given yet.
dan815
  • dan815
it will be interms of that theta
dan815
  • dan815
put these 2 vectors together and using that cross product formula
dan815
  • dan815
|dw:1440396697687:dw|
dan815
  • dan815
|dw:1440396725482:dw|
anonymous
  • anonymous
okay, AB x F that means we get 15*(-180sinx) - 12(-180cosx) which simplifies to -2700sinx+2160cosx agree?
dan815
  • dan815
|dw:1440396763984:dw|
dan815
  • dan815
yea u can do it that way too
anonymous
  • anonymous
yeah can we do it my way, because that is how the teacher taught us in class.
dan815
  • dan815
both these expresison are equivalent
dan815
  • dan815
okay
anonymous
  • anonymous
so now that i have my cross product vector, how do i find the magnitude?
dan815
  • dan815
u already have hte magnitude
dan815
  • dan815
becaause there is only a z direction component
dan815
  • dan815
your vector from the cross product was <0,0,-2700sinx+2160cosx>
anonymous
  • anonymous
so how do i go from my cross product answer to 225sinx+180cosx?
anonymous
  • anonymous
because that is the answer, apparently from the back of the book
dan815
  • dan815
its wrong
anonymous
  • anonymous
really? okay. sp i guess ive had the answer the whole time, lmao. thanks for assuring me i had the right answer.
dan815
  • dan815
okay no problem
dan815
  • dan815
wait i want to check something
dan815
  • dan815
what are the units for lb
anonymous
  • anonymous
im not sure, i dont think the units are relevant
dan815
  • dan815
there a feet in there though right
dan815
  • dan815
u might have to rewrite 12 and 15 in feet see what that givesu
anonymous
  • anonymous
google it, im not sure.
dan815
  • dan815
oh hehe the answer at the book is right :)
anonymous
  • anonymous
i have to convert in to feet?
dan815
  • dan815
ya so the 12 is 1 and the 15 = 15/12
anonymous
  • anonymous
why is it that the answer does not have any i or j or k?
dan815
  • dan815
gives u the asnwer of book
dan815
  • dan815
remember the cross was only in the z direction
dan815
  • dan815
and we took the magnitude of it , so no more directions
dan815
  • dan815
http://www.wolframalpha.com/input/?i=%3C180cosx%2C180sinx%3E+cross+%3C15%2F12%2C1%3E check ur answer
anonymous
  • anonymous
so the answer is a scalar quantity?
anonymous
  • anonymous
all i did was do cross product, which is a vector, not a scalar quantity.
dan815
  • dan815
magnitude of any vector is always scalar
dan815
  • dan815
okay look umm
anonymous
  • anonymous
i havent taken the norm of anything yet.
dan815
  • dan815
lets say i give u a vecotr
dan815
  • dan815
what is the length of this vector?
anonymous
  • anonymous
a.
dan815
  • dan815
right.. now the cross product resulted in a vector with <0,0,a>
dan815
  • dan815
where a was that expression..
anonymous
  • anonymous
ahhhh i see what you mean.
dan815
  • dan815
ok good
anonymous
  • anonymous
okay thanks for your help and the great idea of converting to feet!
dan815
  • dan815
sure np
anonymous
  • anonymous
was this question interesting like how you asked? ;)
dan815
  • dan815
well lol maybe part d is better
anonymous
  • anonymous
i havent gotten there yet, so ill let you know.
dan815
  • dan815
i kind dont know lb is actually, we use the metric system here
dan815
  • dan815
u know how newtoms is m*a so for us its kg*m/s^2
dan815
  • dan815
you guys use lb instead of newtons
dan815
  • dan815
F=m*a for you i guess its pounds * f/s^2 remember that from now on
anonymous
  • anonymous
yeah haha thanks for the advice!
anonymous
  • 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
  • dan815
yep but they want u to prove with optimization
dan815
  • dan815
so do it with derivatives first
dan815
  • dan815
to check u will see that the angle theta makes is 90 degrees with AB
dan815
  • dan815
|dw:1440398825441:dw|
dan815
  • dan815
do with with derivatives and then do it with geometry and see if they are equal
dan815
  • dan815
Moment = 180 cos(x)-225 sin(x) max moment happens when?? solve for 0
dan815
  • dan815
remember what happens at maxs??
dan815
  • dan815
the derivative goes to 0
dan815
  • dan815
make sure you have the max and not min though
dan815
  • dan815
|dw:1440399048233:dw|
dan815
  • 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
  • dan815
ill leave u to that
dan815
  • dan815
remember this form, it might be better to use that here now |dw:1440399289233:dw|
dan815
  • dan815
just giving u alternatives both of them are jut as viable
Jhannybean
  • Jhannybean
.

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