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katherinekc

  • 2 years ago

Two forces with magnitudes of 200 and 100 pounds act on an object at angles of 60° and 170° respectively. Find the direction and magnitude of these forces. Round to two decimal places in all intermediate steps and in your final answer. show work

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  1. youarestupid
    • 2 years ago
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    write something down if YOU want a medal

  2. katherinekc
    • 2 years ago
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    i just need help on the problem please!

  3. youarestupid
    • 2 years ago
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    plus I am sorry but I do not know the answer

  4. Tushara
    • 2 years ago
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    calculate the vertical and horizontal components of each force, and then all the vertical forces together, then add horizontal forces together... after that u can combine the vertical and horizontal vector using pythagaros theorem to get the resulting force

  5. katherinekc
    • 2 years ago
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    im not sure how to do all that .. im horrible in math and im just trying to pass so i can be done:(

  6. katherinekc
    • 2 years ago
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    I know i have to resolve each vector into horizontal and vertical components using sin and cos but im not sure how to actually begin

  7. geerky42
    • 2 years ago
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    Always try to sketch. It may help you.|dw:1359302063400:dw|

  8. geerky42
    • 2 years ago
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    Just do what @Tushara told you to do.

  9. katherinekc
    • 2 years ago
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    i just dont know where or how to really do it :/

  10. mathstudent55
    • 2 years ago
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    |dw:1359302350812:dw|

  11. geerky42
    • 2 years ago
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    |dw:1359302341604:dw|\[\Large \sin \theta = \dfrac{y}{r} \Rightarrow r \sin \theta = y\]\[\Large \cos \theta = \dfrac{x}{r} \Rightarrow r \cos \theta = x\]

  12. katherinekc
    • 2 years ago
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    but how would i put this all into writing to show my work? like in step form?

  13. mathstudent55
    • 2 years ago
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    |dw:1359302475063:dw|

  14. katherinekc
    • 2 years ago
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    i began with this.. is this a good start; f1x= 200cos(60) f1x= 100 cos (170) rx= 200 cos(60) + 100 cos(170)

  15. mathstudent55
    • 2 years ago
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    F1 = 200, F2 = 100 F1x = F1 cos 60 F1y = F1 sin 60 F2x = f2 cos 170 F2x =F2 sin 170 Rx = F1x + F2x Ry = F1y + F2y R(theta) = tan^1(Ry/Rx)

  16. mathstudent55
    • 2 years ago
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    On the second line, you mean f2x, but that's good.

  17. katherinekc
    • 2 years ago
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    but now where do i go ?

  18. mathstudent55
    • 2 years ago
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    Now do the same for the force components in the y direction.

  19. katherinekc
    • 2 years ago
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    whhat do u mean?

  20. mathstudent55
    • 2 years ago
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    Do this: f1x= 200cos(60) f2x= 100 cos (170) rx= 200 cos(60) + 100 cos(170) For F1y, F2y, and Ry

  21. mathstudent55
    • 2 years ago
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    F1y = F1 sin 170 F2y = ... Ry = F1y + F2y = ...

  22. katherinekc
    • 2 years ago
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    f1y = 100 sin (170) f2y = 200 sin ( ) ?? hmm

  23. mathstudent55
    • 2 years ago
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    F1 = 200, F2 = 100. You switched them.

  24. katherinekc
    • 2 years ago
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    f1 = 200 sin (170) f2 = 100 sin (60) ??

  25. katherinekc
    • 2 years ago
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    okay the it would be ..

  26. mathstudent55
    • 2 years ago
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    You got the x-components above and you did it correctly. Now you need the y-components. f1y = 200 sin (60) f2y = 100 sin (170) Ry = f1y + f2y = 200 sin 60 + 100 sin 170

  27. katherinekc
    • 2 years ago
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    ok i got the 70 and 170 mixed around

  28. mathstudent55
    • 2 years ago
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    There is no 70.

  29. katherinekc
    • 2 years ago
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    i mean 60*

  30. katherinekc
    • 2 years ago
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    sorry!

  31. mathstudent55
    • 2 years ago
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    Remember the first force, F1, is 200 lb at 60 deg The x component is F1x = 200 cos 60 The y component is F1y = 200 sin 60 The second force, F2, is 100 lb at 170 deg The x component is F2x = 100 cos 170 The y component is F2y = 100 sin 170 The resultant's x-component is Rx = F1x + F2x = 200 cos 60 + 100 cos 170 The resultant's y-component is Ry = F1y + F2y = 200 sin 60 + 100 sin 170

  32. mathstudent55
    • 2 years ago
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    Now you need to do the actual calculations with a calculator of what Rx and Ry are, and round off to 2 decimal places.

  33. katherinekc
    • 2 years ago
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    so all i have to do is put the equation in the calculator for rx and ry and thatll give me the answers?

  34. katherinekc
    • 2 years ago
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    i need to complete the problem?

  35. mathstudent55
    • 2 years ago
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    For now, yes. That will give you the x- and y-components of the resultant.

  36. katherinekc
    • 2 years ago
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    okay .. and thats all i do then right

  37. katherinekc
    • 2 years ago
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    but i have to find the direction and magnitude?

  38. katherinekc
    • 2 years ago
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    ??

  39. mathstudent55
    • 2 years ago
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    Once you have the x- and y-components of the resultant, you need two more steps. 1. You need to find the magnitude of the resultant. 2. You need to find the direction of the resultant.

  40. katherinekc
    • 2 years ago
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    how do i do that?

  41. mathstudent55
    • 2 years ago
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    For the magnitude of the resultant, you use the Pythagoras theorem. For the direction of the resultant, you use the inverse tangent to get the angle. See figure below: |dw:1359304507660:dw|

  42. mathstudent55
    • 2 years ago
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    yes

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