1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Force, Find the Angle Given 2 Forces of Equal Magnitude, but Different Direction

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Two horses pull horizontally on ropes attached to a tree stump. Each horse pulls with a force of magnitude F. If the resultant force (vector R) has the magnitude R = 1.51 F, what is the angle (in degrees) between the two ropes?

    2. Relevant equations

    3. The attempt at a solution
    Ry= 0+cos
    Rx= 1+ sin

    R= 1.51

    tan= 1/1.54
    angle= 33 degrees

    33 * 2 = total angle for both of 66 degrees
  2. jcsd
  3. Sep 14, 2011 #2
    I'm on my 5th hour for this problem and still can't get it. I realize it's necessary to assign an arbitrary value of say 1 to F. That gives F=1 and R=1.51, but everything I've tried to do with that information has failed.
  4. Sep 14, 2011 #3
    Using vector addition... We don't know whether the three vectors make a right triangle (when putting the two F's nose to tail), so it's easier to divide them into 2 triangles. We'll call the new segment G.

    So now F becomes the Hypotenuse, G is Opposite, and 1.51/2 F is the adjacent (divided in half because it's now the adjacent on 2 triangles instead of just 1).

    F sin(angle) = 1.51/2 F => divide out the F => arcsin(1.51/2) = angle = 49.025 degrees

    That's just half of your angle though since you split it into two triangles
    49.025*2 = 98.05 degrees
    Last edited: Sep 14, 2011
  5. Sep 14, 2011 #4
    The professor gave an answer of 81.9 degrees.
  6. Sep 14, 2011 #5
    Hmmmm maybe someone else will chime in... I don't see anything wrong with what I did, maybe I'm overlooking something.
  7. Sep 14, 2011 #6
    I really appreciate the response, I initially did what you did and was told to rethink it and that it was 81.9. That's what's been making me go insane. I don't know why this method is wrong.
  8. Sep 14, 2011 #7
    You had it right and explained it right, but used arcsin instead of arccos. I get how to do this now, thank you so much for helping me finally understand this.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook