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# A cylindrical barrel s feet in diameter of weight w lb is

ISBN: 9781111827052 44

## Solution for problem 18E Chapter 1.3

A First Course in Differential Equations with Modeling Applications | 10th Edition

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A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 18E

A cylindrical barrel s feet in diameter of weight w lb is floating in water as shown in Figure 1.3.16(a). After an initial depression the barrel exhibits an up-anddown bobbing motion along a vertical line. Using Figure 1.3.16(b), determine a differential equation for the vertical displacement y(t) if the origin is taken to be on the vertical axis at the surface of the water when the barrel is at rest. Use Archimedes’ principle: Buoyancy, or upward force of the water on the barrel, is equal to the weight of the water displaced. Assume that the downward direction is positive, that the weight density of water is 62.4 lb/ft3, and that there is no resistance between the barrel and the water.

Step-by-Step Solution:

Solution:Step 1:In the given figure, we have to determine a differential equation for the vertical displacement y(t) where A cylindrical barrel s/2 feet in radius of weight w lb is floating in water as shown in Figure

Step 2 of 3

Step 3 of 3

##### ISBN: 9781111827052

This full solution covers the following key subjects: Water, barrel, vertical, weight, figure. This expansive textbook survival guide covers 109 chapters, and 4053 solutions. Since the solution to 18E from 1.3 chapter was answered, more than 776 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. The answer to “A cylindrical barrel s feet in diameter of weight w lb is floating in water as shown in Figure 1.3.16(a). After an initial depression the barrel exhibits an up-anddown bobbing motion along a vertical line. Using Figure 1.3.16(b), determine a differential equation for the vertical displacement y(t) if the origin is taken to be on the vertical axis at the surface of the water when the barrel is at rest. Use Archimedes’ principle: Buoyancy, or upward force of the water on the barrel, is equal to the weight of the water displaced. Assume that the downward direction is positive, that the weight density of water is 62.4 lb/ft3, and that there is no resistance between the barrel and the water.” is broken down into a number of easy to follow steps, and 120 words. The full step-by-step solution to problem: 18E from chapter: 1.3 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM.

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A cylindrical barrel s feet in diameter of weight w lb is