1. Determine the maximum angle a uniform ladder can make with a wall without sli

Question

1. Determine the maximum angle a uniform ladder can make with a wall without slipping if its coefficient of static friction with the ground and the wall are 0.4 and 0.3 respectively.(figure 4)

2. A 2 kg hangs from the bottom of a 40 cm string fixed at its top end to the ceiling. The mass is then set to move in a horizontal circle at 2m/s under the action of gravity and the tension of the string only. Determine the angle made between the string and the vertical. (figure 2)

3. The same mass and string in (2) are configured so that the mass can move in a vertical circle, again under the influence of gravity and tension only. If the tension of the string is

40N at point A, determine the tension at the bottom. (figure 3)

Thank you so much!!!

Explanation / Answer

At the point where the ladder is just about to slide, the two forces,the component of the weight pushing away from the wall and the friction,would become equal.
So,
0.3*mg*sin(theta) = mg*cos(theta)
=> theta = Tan inverse(1/0.3) = 73.3 degree.

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