1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statics: two unknown angles and resultant force

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Two forces P and Q with respective magnitudes 100N and 200N are applied to the upper corner of a crate. The sum of the two forces is to the right (+x direction) with a magnitude of 250N. Find the angles that P and Q make with their sum - that is, with the horizontal line through +x axis.


    2. Relevant equations

    R = P + Q where R is the resultant vector and P and Q are vectors given in the problem

    Rx = Px + Qx = 250

    Ry = Py + Qy = 0

    3. The attempt at a solution

    All the information is given except the two angles. Plugging in the given values gives me the equation:

    [tex]\Sigma[/tex]Rx = 100cos([tex]\theta[/tex]) + 200cos([tex]\phi[/tex]) = 250N

    [tex]\Sigma[/tex]Ry = 100sin([tex]\theta[/tex]) - 200sin([tex]\phi[/tex]) = 0

    where theta is the angle between P and R and phi is the angle between Q and R.

    Basically this comes down to confusion on algebra for me. I attempted substitution and that got me nowhere. I know there is some kind of trick to solving this, but I cannot figure it out. There are two equations and two unknowns so there must be a way to do it. I have worked a similar problem where one of the angles is known and the other was supposed to be at a maximum and calculus could be used there. Is that a possibility in this problem or is there just a little trick that I am missing?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 10, 2009 #2

    djeitnstine

    User Avatar
    Gold Member

    How about [tex]tan(\theta)[/tex] does that equal anything?
     
  4. Feb 10, 2009 #3
    I tried that, but still had phi in the expression.

    Rx: sin([tex]\theta[/tex]) = 2sin([tex]\phi[/tex])

    Ry: 2.5 - 2cos([tex]\phi[/tex])


    I thought that since magnitude of R is sqrt[Rx^2 + Ry^2] = 250 things might cancel out. Well all the angles canceled out so i just got an incorrect expression.

    I tried Ry/Rx just for fun, to get a tan expression and that was not beneficial because nothing canceled out there either. I just thought about this though: if you take tan inverse of Ry/Rx the resultant angle will be 0 since the resultant is about the x-axis. However, that means little as I don't know if you can evaluate arctan[0.8sin[tex]\phi[/tex]) - tan([tex]\phi[/tex])]
     
  5. Feb 10, 2009 #4
    Since vectors add head-to-tail, could you maybe draw a force triangle with P, Q, and R and find the angles that way?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Statics: two unknown angles and resultant force
Loading...