In Galileo's final book, Discorsi e dimostrazioni matematiche, intorno à due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences), published in 1683, he described the inclined experiments he'd conducted years earlier, and by which he'd demonstrated that all objects released from rest near the earth's surface fall with the same acceleration, regardless of mass. Since there were -- at the time -- no timepieces which could measure intervals less than a second, he used an inclined plane to decrease the acceleration of the falling object (a rolling ball), so that he could measure the interval between the rinaina of bells equally spaced along the track. use Newtonian dynamics to show that -- for solid spherical balls of uniform mass density -- neither the mass nor the radius of the ball will affect the acceleration of the ball on a particular incline. State your assumptions clearly. Hint: ALGEBRA

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Chapter1: Units, Trigonometry. And Vectors
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In Galileo's final book, Discorsi e dimostrazioni matematiche, intorno à due nuove scienze
(Discourses and Mathematical Demonstrations Relating to Two New
Sciences), published in 1683, he described the inclined experiments he'd
conducted years earlier, and by which he'd demonstrated that all objects
released from rest near the earth's surface fall with the same
acceleration, regardless of mass. Since there were -- at the time --
no timepieces which could measure intervals less than a
second, he used an inclined plane to decrease the
acceleration of the falling object (a rolling ball), so that he
could measure the interval between the rinaina of bells
equally spaced along the track.
use Newtonian dynamics to show that -
for solid spherical balls of uniform mass
density -- neither the mass nor the radius of
the ball will affect the acceleration of the
ball on a particular incline. State your
assumptions clearly.
Hint: ALGEBRA
Transcribed Image Text:In Galileo's final book, Discorsi e dimostrazioni matematiche, intorno à due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences), published in 1683, he described the inclined experiments he'd conducted years earlier, and by which he'd demonstrated that all objects released from rest near the earth's surface fall with the same acceleration, regardless of mass. Since there were -- at the time -- no timepieces which could measure intervals less than a second, he used an inclined plane to decrease the acceleration of the falling object (a rolling ball), so that he could measure the interval between the rinaina of bells equally spaced along the track. use Newtonian dynamics to show that - for solid spherical balls of uniform mass density -- neither the mass nor the radius of the ball will affect the acceleration of the ball on a particular incline. State your assumptions clearly. Hint: ALGEBRA
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