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!

Equilibrium. How to solve for four variables?

  1. Oct 27, 2009 #1
    1. The problem statement, all variables and given/known data
    One end of a uniform beam weighing 288 N and 3.12 feet long is attached to a wall with a hinge. The other end is supported by a wire making equal angles of 30° with the beam and wall.

    (a) Find the tension in the wire.

    (b) What is the horizontal component of the force of the hinge on the beam?

    (c)What is the vertical component of the force of the hinge on the beam?

    2. Relevant equations
    [tex]\Sigma[/tex]F=0
    [tex]\Sigma[/tex][tex]Torque[/tex]=0

    3. The attempt at a solution
    I drew a free body diagram of the beam and the components of the forces from tension and the hinge. From this I got four equations:
    [tex]\Sigma[/tex]Fx = Fx-Tx = 0
    [tex]\Sigma[/tex]Fy = Fy+Ty-mg = 0
    [tex]\Sigma[/tex] Torque = 118.5+.4754Tx-.823Ty=0 (T is tension, this torque is with the hinge as the origin.)
    Fy=Fxtan(30)
    I'm not sure how to solve for each variable with these equations.
     
  2. jcsd
  3. Oct 27, 2009 #2
    The easiest way to think about this is to break it into parts. Instead of solving for multiple unknowns just solve for part a.

    The vertical component of tension must be perfectly balanced by the vertical component of the torque of the beam. Same goes for the horizontal tension.

    You can calculate the torque in the x and y directions and then you have two equations with two unknowns.
     
  4. Oct 27, 2009 #3

    rl.bhat

    User Avatar
    Homework Helper

    Take the components of tension T along and perpendicular to the beam. Similarly take the components of the weight of the beam, which acts at the center of the beam.
    The perpendicular components contribute to the torque, while components along the beam does not contribute to the torque.
    Apply the condition for equilibrium and solve for T.
    Convert the unit of length from ft to m.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Equilibrium. How to solve for four variables?
  1. Solving for variables (Replies: 1)

  2. Solving for a variable (Replies: 2)

  3. Solving for variables (Replies: 8)

Loading...