Equilibrium Applications of Newton's Laws of Rotation

AI Thread Summary
The discussion focuses on calculating the additional displacement needed for the Leaning Tower of Pisa to reach the verge of toppling, given its height and current lean. It emphasizes treating the tower as a uniform circular cylinder to find the center of mass (c.m.) and the conditions under which it becomes unstable. The key points include determining the angle with the vertical at the point of toppling and the relationship between the tower's weight and the ground support force. The current rate of movement of the top is noted as 1 mm/year, which may impact future stability. Understanding these dynamics is crucial for assessing the tower's structural integrity.
SUchica10
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Hi, I am stuck on this problem, any feedback would be greatly appreciated. Thank you...

The leaning Tower of Pisa is 55 m high and 7.0 m in diameter. The top of the tower is displaced 4.5 m from the vertical. Treating the tower as a uniform, circular cylinder, (a) what additional displacement, measured at the top, will bring the tower to the verge of toppling? (b) What angle with the vertical with the tower make at that moment? (The current rate of movement of the top is 1 mm/year.)
 
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SUchica10 said:
Hi, I am stuck on this problem, any feedback would be greatly appreciated. Thank you...

The leaning Tower of Pisa is 55 m high and 7.0 m in diameter. The top of the tower is displaced 4.5 m from the vertical. Treating the tower as a uniform, circular cylinder, (a) what additional displacement, measured at the top, will bring the tower to the verge of toppling? (b) What angle with the vertical with the tower make at that moment? (The current rate of movement of the top is 1 mm/year.)
Find the c.m. of the tower. At what point will the c.m. be directly above the lower right corner of the tower (at the 7 m mark)? This is where it will become unstable due to the overturning torque from the tower's weight not being able to countered by the ground support force and torque that will no longer exist.
 
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