A hungry bear weighing 745 N walks out on a beam in an attempt to retrieve a bas

Question

A hungry bear weighing 745 N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam (see figure below). The beam is uniform, weighs 200 N, and is 5.50 m long, and it is supported by a wire at an angle of θ = 60.0 °. The basket weighs 80.0 N.

http://www.webassign.net/serpse8/12-p-043.gif

When the bear is at x = 0.90 m, find the tension in the wire supporting the beam and the components of the force exerted by the wall on the left end of the beam.

Explanation / Answer

Draw a free body diagram of the beam. From this, you can get the following three equations:

Fx = Tcos(60)
Fy + Tsin(60) = 745 + 200 + 80
Tsin(60)*5.5 = 750*.95 + 200*2.75 + 80*5.5 (sum of the moments about the left end of beam)

solving these three equations for T,Fx, and Fy (in that order) you get
T=357.43 Fx=178.71, Fy=720.45
to find the max distance, solve the moment equation again substituting 775 for T and x for .95
x=3.602 m

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