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Problem 56 Easy Difficulty

Three seconds after a polisher is started from rest, small tufts of fleece from along the circumference of the 225 -mm-diameter polishing pad are observed to fly free of the pad. If the polisher is started so that the fleece along the circumference undergoes a constant tangential acceleration of $4 \mathrm{m} / \mathrm{s}^{2},$ determine $(a)$ the speed $v$ of a tuft as it leaves the pad, $(b)$ the magnitude of the force required to free a tuft if the average mass of a tuft is $1.6 \mathrm{mg}$


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Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

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Video Transcript

the free body diagram for the human problem is in following way the tough Here's the tangential force acting in this direction, which we call it F D, where we have ah mass times. Tangential exploration is in this direction. If in is a downward, so is the motion is uniformly accelerated. Weaken right b is equal. Teoh being on unusual lost E plus 80 times t then at tees equal to authorities equal to he's equal to three seconds we get there. We physical to four times three. Since we know zero, this will give us a 12 meter for a second. This is for about a off the problem for ah be off the problem where, um, some off forces efty is a quote the mass times 80 we can write ah f t is equal to mass times Ah, the T which is 1.6 times 10 to the ball minus six times four. This will give us f d o foe 6.4 times 10 to the power minus six Newton. Then we can write some off the FN forces is you call the mass Times. Yeah, which is downward here most times in this will be cool. Teoh m we squared, divided by r Then substituting your values, we get to your offend to be 2.0 for eight times 10 to the power minus three Newton. Then therefore sewn tuft will be four. Soon tuft will be simply square Ruto for lefty Ah square plus half in square which we found earlier will pluck those values and look 10 foursome tough to be 2.5 time center The ball were minus three Newton.

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Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

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