One of the problems posed by the Marquis de I’Hospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C by a rope of length r . At another point B on the ceiling, at a distance d from C (where d > r ), a rope of length ℓ is attached and passed through the pulley at F and connected to a weight W . The weight is released and comes to rest at its equilibrium position D . (See the figure.) As I’Hospital argued, this happens when the distance | ED | is maximized. Show that when the system reaches equilibrium, the value of x is r 4 d ( r + r 2 + 8 d 2 )
One of the problems posed by the Marquis de I’Hospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C by a rope of length r . At another point B on the ceiling, at a distance d from C (where d > r ), a rope of length ℓ is attached and passed through the pulley at F and connected to a weight W . The weight is released and comes to rest at its equilibrium position D . (See the figure.) As I’Hospital argued, this happens when the distance | ED | is maximized. Show that when the system reaches equilibrium, the value of x is r 4 d ( r + r 2 + 8 d 2 )
Solution Summary: The author explains how Marquis de L'Hospital's model reaches equilibrium when the value of x is underset_r4d(r+sq
One of the problems posed by the Marquis de I’Hospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C by a rope of length r. At another point B on the ceiling, at a distance d from C (where d > r), a rope of length ℓ is attached and passed through the pulley at F and connected to a weight W. The weight is released and comes to rest at its equilibrium position D. (See the figure.) As I’Hospital argued, this happens when the distance | ED | is maximized. Show that when the system reaches equilibrium, the value of x is
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