# 12.13.1. Equilibrium of an Original Body

A uniform ladder of weight N is resting with its upper end against a smooth vertical wall and with its lower end against a rough horizontal ground, where the coefficient of friction between the ladder and the ground is . If a force of magnitude N acts on the lower end of the ladder trying to move it away from the wall, where the force makes an angle of with the horizontal, the ladder is about to slide. Determine the tangent of the angle that the ladder makes with the horizontal ground.

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A uniform ladder weighing is resting with its upper end against a smooth vertical wall and its lower one on a rough horizontal ground, where it lies in a plane perpendicular to the wall, and it is inclined to the horizontal at an angle of . When a man, whose weight is , tried to go up the ladder reached the point of the length of the ladder, it became about to slide. If the man wanted to go all the way up to the top of the ladder, find the minimum horizontal force required to act on the lower end of the ladder so it does not slide.

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is a uniform ladder having a weight of N that is resting at its end on a rough horizontal ground, where its end is against a smooth vertical wall. If the ladder is inclined to the horizontal at an angle of , and the coefficient of friction between the ground and the ladder is , find the magnitude of the maximum weight that can be suspended at without breaking the equilibrium.

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A uniform ladder having a length of and weighing is resting at its upper end against a rough vertical wall, where its lower end is resting on a rough horizontal ground of the same coefficient of friction that is . If the ladder is inclined to the horizontal at an angle whose tangent is , find the maximum distance that a man weighing can ascend the ladder.

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