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Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 3.4 - Problem 19e
Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 3.4 - Problem 19e

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# otherwise stated, in the following problems we | Ch 3.4 - 19E

ISBN: 9780321747730 43

## Solution for problem 19E Chapter 3.4

Fundamentals of Differential Equations | 8th Edition

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Problem 19E

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.An object of mass 60 kg starts from rest at the top of a 45º inclined plane. Assume that the coefficient of kinetic friction is 0.05 (see 18). If the force due to air resistance is proportional to the velocity of the object, say, -3y, find the equation of motion of the object. How long will it take the object to reach the bottom of the inclined plane if the incline is 10 m long?

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Solution:Step-1:In this problem we need to find the equation of motion of the object and we have to find how long will it take the object to reach the bottom of the inclined plane if the incline is 10m long.step-2:Given: The mass of an object (m)= 60kg . Inclination .Gravitational force is constant with and b = 3.Assume that , the coefficient of kinetic friction We know that, Step-3:Therefore, the force of gravity in the direction is Normal force Now,we have to find the value of .Clearly, is a differential equation .Step-4:Now , find the general solution of the equation.We know that,is the integrating factor.Multiply the above equation both sides with . Integrating both sides we get:, since Therefore,step-5:We know that at initial point v = t= 0 , then becomes., since .Therefore, C = (-131.78)Hence,We know that, Integrating on both sides we get:, since . step-6:We know that at initial point x = t= 0.So, Therefore, By using method of newton’s law:Consider, differentiate both sides with respect to t we get. Step-7:Therefore, If , then = 2- (0.2187) = 1.7814Similarly, =1.7814-0.0117 = 1.7697Therefore, t at x= 10 is 1.7697 seconds

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##### ISBN: 9780321747730

The answer to “Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.An object of mass 60 kg starts from rest at the top of a 45º inclined plane. Assume that the coefficient of kinetic friction is 0.05 (see 18). If the force due to air resistance is proportional to the velocity of the object, say, -3y, find the equation of motion of the object. How long will it take the object to reach the bottom of the inclined plane if the incline is 10 m long?” is broken down into a number of easy to follow steps, and 108 words. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This full solution covers the following key subjects: Object, assume, SEC, Plane, system. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. The full step-by-step solution to problem: 19E from chapter: 3.4 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since the solution to 19E from 3.4 chapter was answered, more than 281 students have viewed the full step-by-step answer.

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