Horizontal bar Physics Problem?

1.A uniform horizontal bar of length L = 5.0 m and weight 106 N is pinned to a vertical wall and supported by a thin wire that makes an angle of 胃 = 29掳 with the horizontal. A mass M, with a weight of 322 N, can be moved anywhere along the bar. The wire can withstand a maximum tension of 557 N. What is the maximum possible distance from the wall at which mass M can be placed before the wire breaks?


2.With M placed at this maximum distance what is the horizontal component of the force exerted on the bar by the pin at A?


3.With M placed at this maximum distance what is the vertical component of the force exerted on the bar by the pin at A?|||1. Place the mass M at a distance x from the pin. Now sum the moments about the pin:


The mass of the bar (106N) is acting at a distance 2.5m; the mass M (322 N) is acting at the distance x; the horizontal component of the tension in the wire is acting at a distance of 2.77m (5m*tan29). This horizontal component of the wire's tension is 487.2 N at the wire's maximum tension.





Solving for x gives 3.4m.





2. The horizontal component at the pin must equal the horizontal component of the tension in the wire. This is 487.2 N.





3. The vertical component of the wire's tension at 557 N is 557*sin 29 = 270 N.


Summing all the forces in the vertical direction yields a vertical force at the pin of 158 N.