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Challenge Problem Solutions: Static Equilibrium

Static Equilibrium Challenge Problem solutions Problem 1: Static Equilibrium : Steel Beam and Cable A uniform steel beam of mass m1= !10 2 kg is held up by a steel cable that is connected to the beam a distance L = m from the wall, at an angle ! = 30 ! as shown ! in the sketch. The beam is bolted to the wall with an unknown force F exerted by the 1wall on the beam. An object of mass m2 = !10 kg, resting on top of the beam, is placed a distance d = m from the wall. Use g = m s "!2for the gravitational acceleration. a) Draw a free-body diagram for the beam.

-coordinate axes respectively, the . x-direction being to the right in Figure 1 and the . y-direction being vertically upward. (b) Equations for Static Equilibrium for the beam: The equations for force equilibrium are: ˆi : F. x " T. cos! = 0 (1.1) ˆ. j: F " m g " m g + T. sin! = 0. y. 2 1. The equations for torque equilibrium are (taking ...

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