Explanation Given information: The function v 2 = 2 g h 1 + I * where I * = I m r 2 . Formula used: Conservation of energy: m g h = 1 2 m v 2 + 1 2 I ω 2 . Calculation: Consider the following conservation of energy: m g h = 1 2 m v 2 + 1 2 I ω 2 Where m is the mass, r is the radius and moment of inertia / (about the axis of rotation). The potential energy at the top is m g h . There are two components to the bottom-up kinetic energy: 1 2 m v 2 from translation (moving down the slope) and 1 2 I ω 2 from rotation. m g h = 1 2 m v 2 + 1 2 I ω 2 m g h − 1 2 I ω 2 = 1 2 m v 2 m g h − 1 2 I ω 2 1 2 m = v 2 … … ( 1 ) Assume the item descends with velocity v and angular velocity ω , resulting in v = ω r . Substitute v = ω r ⇒ v r = ω in ( 1 ) equation

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Author: Stewart

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Chapter 15.8, Problem 1AP

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To show: that v2=2gh1+I* .

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Chapter 15 Solutions

CALCULUS:EARLY TRANS W/WEB ASSIGN CARD

Ch. 15.1 - (a) Estimate the volume of the solid that lies...Ch. 15.1 - If R = [0, 4] [1, 2], use a Riemann sum with m =...Ch. 15.1 - (a) Use a Riemann sum with m = n = 2 to estimate...Ch. 15.1 - (a) Estimate the volume of the solid that lies...Ch. 15.1 - Let V be the volume of the solid that lies under...Ch. 15.1 - A 20-ft-by-30-ft swimming pool is filled with...Ch. 15.1 - A contour map is shown for a function f on the...Ch. 15.1 - Evaluate the double integral by first identifying...Ch. 15.1 - Evaluate the double integral by first identifying...Ch. 15.1 - Evaluate the double integral by first identifying...

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that v 2 = 2 g h 1 + I * .

Solution Summary: The author explains that v2= 2gh1+I*. The potential energy at the top is mgh

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To show: that v2=2gh1+I* .

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Chapter 15 Solutions