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F.6 Statics

發問:

A uniform ladder 5.0m long and having mass 40kg with its upper end against a smooth vertical wall and with its lower end 3.0m from the wall on rough ground. Find the magnitude and direction of the force exerted at the bottom of the ladder.

最佳解答:

From the given, we have the height of the ladder top is 4 m from the ground. Then with reference to the diagram below: 圖片參考：http://i388.photobucket.com/albums/oo325/loyitak1990/Oct09/Crazymech2.jpg The force from the wall should be horizontal since it is smooth and hence no friction. In translational, we have F = f and R = W in magnitude Therefore R = 400 N Then taking moment about the bottom of the ladder: 4F = 1.5W F = 150 N f = 150 N So by Pyth. theorem, the amgnitude of the force exerted at the bottom of the ladder should be √(R2 + f2) = 427 N With inclination at tan-1 (R/f) = 69.4 deg.

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