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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    @dan815 @Hero

  2. anonymous
    • one year ago
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    @ganeshie8

  3. anonymous
    • one year ago
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    hahaah okay.

  4. dan815
    • one year ago
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    |dw:1440395793167:dw|

  5. dan815
    • one year ago
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    okay lets do AB first, a vector can be written in terms of its change in x and y AB=<x,y> or xi + yj

  6. dan815
    • one year ago
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    AB=<15,12> or 15i+12j are you okay with this

  7. anonymous
    • one year ago
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    yeah so the vector of F is < -180cosx, -180 sinx>

  8. anonymous
    • one year ago
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    im with you.

  9. dan815
    • one year ago
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    yep

  10. dan815
    • one year ago
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    now for B take the cross product and its magnitude

  11. dan815
    • one year ago
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    thsi is actually going to tell you the torqure experiences at joint A

  12. anonymous
    • one year ago
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    i did the cross product of AB x F and got <-2700 cosx, -2160sinx>

  13. dan815
    • one year ago
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    experienced*

  14. dan815
    • one year ago
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    take the magnitude of it now

  15. dan815
    • one year ago
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    ill check ur cross product in the mean time

  16. anonymous
    • one year ago
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    actually cross product is -2700sinx, 2160cosx

  17. anonymous
    • one year ago
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    my bad, typed it in incorrectly

  18. dan815
    • one year ago
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    |dw:1440396026100:dw|

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

  20. dan815
    • one year ago
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    ya the cross results in <0,0,(15*-180sinx - 12*-180*cosx)> so the magnitude =(15*-180sinx - 12*-180*cosx)

  21. anonymous
    • one year ago
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    there is suppse to be a sin after4665600

  22. dan815
    • one year ago
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    be careful with the cross product you arent doing it properly

  23. anonymous
    • one year ago
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    sin^2

  24. anonymous
    • one year ago
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    what did i do wrong?

  25. dan815
    • one year ago
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    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

  26. anonymous
    • one year ago
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    i thought since we are 2d, we assume there is no k. is that my mistake? i should place a 0 in k?

  27. dan815
    • one year ago
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    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

  28. anonymous
    • one year ago
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    how does finding the magnitude of a mean i find the orthogonal vector?

  29. dan815
    • one year ago
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    |ABXF| = |AB| |F| * sin theta

  30. dan815
    • one year ago
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    im a little lost right now lets do b over

  31. dan815
    • one year ago
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    you have AB and F right

  32. anonymous
    • one year ago
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    so lets take the cross product.

  33. dan815
    • one year ago
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    |AB X F| = |AB| * |F| sin theta

  34. dan815
    • one year ago
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    what did u get for the angle between these fectors

  35. anonymous
    • one year ago
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    you arent suppose to get an angle. the answer is left in terms of theta

  36. dan815
    • one year ago
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    yes that is fine give it to me interms of the angle

  37. anonymous
    • one year ago
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    what do you mean interms?

  38. dan815
    • one year ago
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    |dw:1440396551765:dw|

  39. anonymous
    • one year ago
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    btw, the answer to b is 225sinx+180cosx

  40. anonymous
    • one year ago
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    theta 2 is 38.7 degrees

  41. dan815
    • one year ago
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    okay

  42. anonymous
    • one year ago
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    theta 1 is not given yet.

  43. dan815
    • one year ago
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    it will be interms of that theta

  44. dan815
    • one year ago
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    put these 2 vectors together and using that cross product formula

  45. dan815
    • one year ago
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    |dw:1440396697687:dw|

  46. dan815
    • one year ago
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    |dw:1440396725482:dw|

  47. anonymous
    • one year ago
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    okay, AB x F that means we get 15*(-180sinx) - 12(-180cosx) which simplifies to -2700sinx+2160cosx agree?

  48. dan815
    • one year ago
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    |dw:1440396763984:dw|

  49. dan815
    • one year ago
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    yea u can do it that way too

  50. anonymous
    • one year ago
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    yeah can we do it my way, because that is how the teacher taught us in class.

  51. dan815
    • one year ago
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    both these expresison are equivalent

  52. dan815
    • one year ago
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    okay

  53. anonymous
    • one year ago
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    so now that i have my cross product vector, how do i find the magnitude?

  54. dan815
    • one year ago
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    u already have hte magnitude

  55. dan815
    • one year ago
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    becaause there is only a z direction component

  56. dan815
    • one year ago
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    your vector from the cross product was <0,0,-2700sinx+2160cosx>

  57. anonymous
    • one year ago
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    so how do i go from my cross product answer to 225sinx+180cosx?

  58. anonymous
    • one year ago
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    because that is the answer, apparently from the back of the book

  59. dan815
    • one year ago
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    its wrong

  60. anonymous
    • one year ago
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    really? okay. sp i guess ive had the answer the whole time, lmao. thanks for assuring me i had the right answer.

  61. dan815
    • one year ago
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    okay no problem

  62. dan815
    • one year ago
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    wait i want to check something

  63. dan815
    • one year ago
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    what are the units for lb

  64. anonymous
    • one year ago
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    im not sure, i dont think the units are relevant

  65. dan815
    • one year ago
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    there a feet in there though right

  66. dan815
    • one year ago
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    u might have to rewrite 12 and 15 in feet see what that givesu

  67. anonymous
    • one year ago
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    google it, im not sure.

  68. dan815
    • one year ago
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    oh hehe the answer at the book is right :)

  69. anonymous
    • one year ago
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    i have to convert in to feet?

  70. dan815
    • one year ago
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    ya so the 12 is 1 and the 15 = 15/12

  71. anonymous
    • one year ago
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    why is it that the answer does not have any i or j or k?

  72. dan815
    • one year ago
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    gives u the asnwer of book

  73. dan815
    • one year ago
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    remember the cross was only in the z direction

  74. dan815
    • one year ago
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    and we took the magnitude of it , so no more directions

  75. dan815
    • one year ago
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    http://www.wolframalpha.com/input/?i=%3C180cosx%2C180sinx%3E+cross+%3C15%2F12%2C1%3E check ur answer

  76. anonymous
    • one year ago
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    so the answer is a scalar quantity?

  77. anonymous
    • one year ago
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    all i did was do cross product, which is a vector, not a scalar quantity.

  78. dan815
    • one year ago
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    magnitude of any vector is always scalar

  79. dan815
    • one year ago
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    okay look umm

  80. anonymous
    • one year ago
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    i havent taken the norm of anything yet.

  81. dan815
    • one year ago
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    lets say i give u a vecotr <a,0,0>

  82. dan815
    • one year ago
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    what is the length of this vector?

  83. anonymous
    • one year ago
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    a.

  84. dan815
    • one year ago
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    right.. now the cross product resulted in a vector with <0,0,a>

  85. dan815
    • one year ago
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    where a was that expression..

  86. anonymous
    • one year ago
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    ahhhh i see what you mean.

  87. dan815
    • one year ago
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    ok good

  88. anonymous
    • one year ago
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    okay thanks for your help and the great idea of converting to feet!

  89. dan815
    • one year ago
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    sure np

  90. anonymous
    • one year ago
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    was this question interesting like how you asked? ;)

  91. dan815
    • one year ago
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    well lol maybe part d is better

  92. anonymous
    • one year ago
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    i havent gotten there yet, so ill let you know.

  93. dan815
    • one year ago
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    i kind dont know lb is actually, we use the metric system here

  94. dan815
    • one year ago
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    u know how newtoms is m*a so for us its kg*m/s^2

  95. dan815
    • one year ago
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    you guys use lb instead of newtons

  96. dan815
    • one year ago
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    F=m*a for you i guess its pounds * f/s^2 remember that from now on

  97. anonymous
    • one year ago
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    yeah haha thanks for the advice!

  98. anonymous
    • one year ago
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    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.

  99. dan815
    • one year ago
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    yep but they want u to prove with optimization

  100. dan815
    • one year ago
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    so do it with derivatives first

  101. dan815
    • one year ago
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    to check u will see that the angle theta makes is 90 degrees with AB

  102. dan815
    • one year ago
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    |dw:1440398825441:dw|

  103. dan815
    • one year ago
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    do with with derivatives and then do it with geometry and see if they are equal

  104. dan815
    • one year ago
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    Moment = 180 cos(x)-225 sin(x) max moment happens when?? solve for 0 <x<2pi radians

  105. dan815
    • one year ago
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    remember what happens at maxs??

  106. dan815
    • one year ago
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    the derivative goes to 0

  107. dan815
    • one year ago
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    make sure you have the max and not min though

  108. dan815
    • one year ago
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    |dw:1440399048233:dw|

  109. dan815
    • one year ago
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    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

  110. dan815
    • one year ago
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    ill leave u to that

  111. dan815
    • one year ago
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    remember this form, it might be better to use that here now |dw:1440399289233:dw|

  112. dan815
    • one year ago
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    just giving u alternatives both of them are jut as viable

  113. Jhannybean
    • one year ago
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    .

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