## anonymous one year ago http://prntscr.com/88757l Im mainly stuck on b.

1. anonymous

@dan815 @Hero

2. anonymous

@ganeshie8

3. anonymous

hahaah okay.

4. dan815

|dw:1440395793167:dw|

5. dan815

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

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

7. anonymous

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

8. anonymous

im with you.

9. dan815

yep

10. dan815

now for B take the cross product and its magnitude

11. dan815

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

12. anonymous

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

13. dan815

experienced*

14. dan815

take the magnitude of it now

15. dan815

ill check ur cross product in the mean time

16. anonymous

actually cross product is -2700sinx, 2160cosx

17. anonymous

my bad, typed it in incorrectly

18. dan815

|dw:1440396026100:dw|

19. anonymous

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

20. dan815

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

21. anonymous

there is suppse to be a sin after4665600

22. dan815

be careful with the cross product you arent doing it properly

23. anonymous

sin^2

24. anonymous

what did i do wrong?

25. 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

26. anonymous

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

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

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

29. dan815

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

30. dan815

im a little lost right now lets do b over

31. dan815

you have AB and F right

32. anonymous

so lets take the cross product.

33. dan815

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

34. dan815

what did u get for the angle between these fectors

35. anonymous

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

36. dan815

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

37. anonymous

what do you mean interms?

38. dan815

|dw:1440396551765:dw|

39. anonymous

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

40. anonymous

theta 2 is 38.7 degrees

41. dan815

okay

42. anonymous

theta 1 is not given yet.

43. dan815

it will be interms of that theta

44. dan815

put these 2 vectors together and using that cross product formula

45. dan815

|dw:1440396697687:dw|

46. dan815

|dw:1440396725482:dw|

47. anonymous

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

48. dan815

|dw:1440396763984:dw|

49. dan815

yea u can do it that way too

50. anonymous

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

51. dan815

both these expresison are equivalent

52. dan815

okay

53. anonymous

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

54. dan815

55. dan815

becaause there is only a z direction component

56. dan815

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

57. anonymous

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

58. anonymous

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

59. dan815

its wrong

60. anonymous

61. dan815

okay no problem

62. dan815

wait i want to check something

63. dan815

what are the units for lb

64. anonymous

im not sure, i dont think the units are relevant

65. dan815

there a feet in there though right

66. dan815

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

67. anonymous

68. dan815

oh hehe the answer at the book is right :)

69. anonymous

i have to convert in to feet?

70. dan815

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

71. anonymous

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

72. dan815

gives u the asnwer of book

73. dan815

remember the cross was only in the z direction

74. dan815

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

75. dan815
76. anonymous

so the answer is a scalar quantity?

77. anonymous

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

78. dan815

magnitude of any vector is always scalar

79. dan815

okay look umm

80. anonymous

i havent taken the norm of anything yet.

81. dan815

lets say i give u a vecotr <a,0,0>

82. dan815

what is the length of this vector?

83. anonymous

a.

84. dan815

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

85. dan815

where a was that expression..

86. anonymous

ahhhh i see what you mean.

87. dan815

ok good

88. anonymous

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

89. dan815

sure np

90. anonymous

91. dan815

well lol maybe part d is better

92. anonymous

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

93. dan815

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

94. dan815

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

95. dan815

you guys use lb instead of newtons

96. dan815

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

97. anonymous

yeah haha thanks for the advice!

98. 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.

99. dan815

yep but they want u to prove with optimization

100. dan815

so do it with derivatives first

101. dan815

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

102. dan815

|dw:1440398825441:dw|

103. dan815

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

104. dan815

Moment = 180 cos(x)-225 sin(x) max moment happens when?? solve for 0 <x<2pi radians

105. dan815

remember what happens at maxs??

106. dan815

the derivative goes to 0

107. dan815

make sure you have the max and not min though

108. dan815

|dw:1440399048233:dw|

109. 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

110. dan815

ill leave u to that

111. dan815

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

112. dan815

just giving u alternatives both of them are jut as viable

113. anonymous

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