A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Zenmo

  • one year ago

Find the angle between the forces given the magnitude of their resultant. (Hint: Write force 1 as a vector in the direction of the positive x-axis and force 2 as a vector at an angle theta with the positive x-axis. Force 1=45 pounds, Force 2=60 pounds, Resultant Force= 90 pounds.

  • This Question is Closed
  1. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you attempt to make a force diagram?

  2. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433812186168:dw|

  3. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, that is what I have so far.

  4. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This involves the section of "Vectors in a plane."

  5. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    correct so far

  6. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433819768895:dw|

  7. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ops, forgot to put a 60 in there. Now, I'm not sure what to do next.

  8. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The directions state that the magnitude of the resultant is 90 pounds.

  9. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If we call the resultant vector R then magnitude of R= sqrt( Rx^2 + Ry^2)

  10. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What is the magnitude of R= sqrt(Rx^2+Ry^2) formula/name called?

  11. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that comes from pythagorean theorem

  12. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the length of a vector is the length of the hypotenuse

  13. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433820260557:dw|

  14. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just to check, R= sqrt (Rx^2+Ry^2) is the same as C= sqrt (Ax^2+By^2) ?

  15. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  16. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433813159626:dw|

  17. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433820470702:dw|

  18. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433820609869:dw|

  19. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    =\[2025+3600\cos^2t+5400cost+3600\sin^2=8100\]

  20. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is that the correct next step?

  21. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ops forgot to put the t for 3600sin^2t.

  22. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  23. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    we can simplify this by factoring out 3600 from sin^2 t and cos^2 t

  24. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    $$\large {2025+3600\cos^2t+5400\cos t+3600\sin^2 t=8100 \\ 2025+3600( \cos^2t +\sin^2 t ) +5400\cos t=8100 \\2025+3600( 1) +5400\cos t=8100 } $$

  25. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[5625+5400\cos t = 8100. ->5400\cos t =2475. ->\cos t =2475/5400. -> \cos t = .4583 -> arc \cos t = 62.7 degrees.\]

  26. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now solve for t, the angle

  27. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\cos t = 0.4583 -> \arccos t (0.4583)\]

  28. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    = 62.7 degrees?

  29. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, that is the answer. Thanks! One small question, so dealing with these type of problems, this will always involve the Pythagorean Theorem of R=sqrt(Rx^2+Ry^2)?

  30. perl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if you need to find magnitude of a vector, then yes :)

  31. Zenmo
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, thanks again. :D

  32. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.