Results 1 to 4 of 4

Math Help - Resultant Force Problem

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    12

    Resultant Force Problem

    Hello, I have a trig/physics problem from my foundations of engineering class. If this is in the wrong forum please let me know. Here it is.

    Two forces P and Q with respective magnitudes 100N and 200N are are applied to the upper right corner of a crate. The sum of the two forces is a horizontal force with magnitude 250N. The the angles that P and Q make with their sum. In the picture force P is on top and force Q is below the resultant horizontal force.

    So far I have taken the scalar form of the two forces and summed them to their resultant. Im calling the angles p, and q for their respective forces.

    100N*COS(p)i + 100N*SIN(p)j

    +200N*COS(q)i - 200N*SIN(q)j

    = 250Ni

    From here I am not sure where to proceed. I tried summing the individual components but I did not make any progress. Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,160
    Thanks
    348
    You have two equation in two unknowns:

    100 \cos(p) + 200 \cos(q) = 250
    100 \sin(p) - 200 \sin(q) = 0

    From the 2nd equaton:

    \sin(p) = 2 \sin(q), so
    <br />
\cos(p) = \sqrt{1 - \sin^2p} = \sqrt{1 - 4 \sin^2q}

    Put that back into the first, and solve for cos(q):

     100 \sqrt {1-4 \sin^2q} = 250- 200 \cos (q)

    Square both sides, and rearrange:

     1-4 \sin^2q = 2.5^2 - 10 \cos(q) + 4 \cos^2q
     0 = 5.25 - 10 \cos(q) + 4(cos^2q + sin^2q) = 9.25 - 10 \cos(q)
     q = Arccos (0.925)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    12
    Thank You!! That was very helpful. I thought there may have been a identity lurking in there. Your a life saver!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, repete!

    \text{Two forces }P\text{ and }Q\text{ with respective magnitudes 100N and 200N}
    . . \text{are applied to a point.}

    \text{The sum of the two forces is a horizontal force with magnitude 250N.}

    \text}Find the angles that }P\text{ and }Q\text{ make with their sum.}

    \text{(In the diagram, force }P\text{ is over and force }Q\text{ is under}
    . . \text{the resultant horizontal force.)}
    Code:
                      P
                      o
                    *    *
             100  *         *   200
                *              *
              *                   *
            *  p                     *
        O o - - - - - - - - - - - - - - o R
             *  q      250            *
                *                   *
                   *              *
                200   *         *  100
                         *    *
                            o
                            Q

    We have: . \begin{array}{cccccccccc}<br />
|\overrightarrow{OP}| \;=\;100 && p \:=\:\angle POR \\ \\[-4mm]<br />
|\overrightarrow{OQ}| \;=\;200 && q \;=\;\angle QOR \\ \\[-4mm]<br />
|\overrightarrow{OR}| \;=\;250 \end{array}




    \text{In }\Delta OPR\!:\;\; \cos p \:=\:\dfrac{100^2 + 250^2 - 200^2}{2(100)(250)} \;=\;<br />
0.65

    Hence: . \angle p \;\approx\;49.46^o


    \text{In }\Delta OQR\!:\;\;\cos q \:=\:\dfrac{200^2 + 250^2 - 100^2}{2(200)(250)} \;=\;0.925

    Hence:. . \anglen q \;\approx\;22.33^o
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Resultant Force
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 25th 2009, 05:33 PM
  2. Need help with resultant force
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 16th 2009, 04:03 PM
  3. Resultant force
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: January 21st 2009, 08:37 AM
  4. Resultant Force
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: November 5th 2008, 02:01 AM
  5. resultant force problem
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: May 14th 2008, 11:28 PM

Search Tags


/mathhelpforum @mathhelpforum