22. Infinite Pulleys. An infinite pulley system's masses follow M, = M/3"-1 where n runs from topto bottom, starting from n = 1, as shown in the figure. Assume that the pulleys are massless. Find themagnitude of the acceleration of the topmost mass.MM23. Devil's Coin Trick. Eustass, Luffy, and Law were having a casual drink together, when Luffy eagerlyasks Eustass to show him a trick using his devil fruit power. Eustass, drunk from the sake, happily obliges,and proceeds to take out some coins. He lays 23 coins on the ground, forming the vertices of a convex regular23-gon with side length 2.3 m. He then sets up the coins such that the Ist coin is always moving towards the3rd coin, the 3rd coin is always moving towards the 5th coin, and so on. (The 23rd coin moves towards the2nd coin, and the 22nd coin moves towards the 1st coin). After some time, the coins all converge together,completing the coin trick. If the coins all move with constant velocity 0.23 m/s, find how much time it takesfor the coins to converge. Answer in s and 3 Significant Figures.

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22. Infinite Pulleys. An infinite pulley system's masses follow M, = M/3"-1 where n runs from top to bottom, starting from n = 1, as shown in the figure. Assume that the pulleys are massless. Find the magnitude of the acceleration of the topmost mass. M M

22. Infinite Pulleys. An infinite pulley system's masses follow M, = M/3"-1 where n runs from top to bottom, starting from n = 1, as shown in the figure. Assume that the pulleys are massless. Find the magnitude of the acceleration of the topmost mass. M M

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Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter6: Applications Of Newton's Laws

Section: Chapter Questions

Problem 18CQ: In one amusement park ride, riders enter a large vertical barrel and stand against the wall on its...

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Concept explainers

Newton's First Law of Motion

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!

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Question

22. Infinite Pulleys. An infinite pulley system's masses follow M, = M/3"-1 where n runs from top
to bottom, starting from n = 1, as shown in the figure. Assume that the pulleys are massless. Find the
magnitude of the acceleration of the topmost mass.
M
M
23. Devil's Coin Trick. Eustass, Luffy, and Law were having a casual drink together, when Luffy eagerly
asks Eustass to show him a trick using his devil fruit power. Eustass, drunk from the sake, happily obliges,
and proceeds to take out some coins. He lays 23 coins on the ground, forming the vertices of a convex regular
23-gon with side length 2.3 m. He then sets up the coins such that the Ist coin is always moving towards the
3rd coin, the 3rd coin is always moving towards the 5th coin, and so on. (The 23rd coin moves towards the
2nd coin, and the 22nd coin moves towards the 1st coin). After some time, the coins all converge together,
completing the coin trick. If the coins all move with constant velocity 0.23 m/s, find how much time it takes
for the coins to converge. Answer in s and 3 Significant Figures.

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