Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Textbook Question

Chapter 8.5, Problem 1TFR

For Questions (a)—(i), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

The spring force on a mass acts in a direction opposite to the displacement of the mass from equilibrium.

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Chapter 8.3, Problem 48P

Chapter 8.5, Problem 2TFR

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On a sunny day, your friend Issac was daydreaming under an apple tree. All of a sudden, an apple dropped from the tree and hit Issac's head. From there Issac had the idea that the apple was dragged down from the tree by a "force". He contemplated an equation to describe this "force": F = m*g Where F is the force exerted onto the apple (in unit N), m is the mass of the apple (in unit kg), and g is a fundamental constant of nature, Issac named it the gravitational constant. Issac was intrigued by this idea and he wanted to measure the gravitational constant. He designed a simple experiment to do this: 1. Collect 5 apples 2. Measure the mass of each of them and put them into a dataset M 3. Put each apple onto the tree branch, and let 4. Measure the force exerted on each apple F = it drop from the tree [6.9, 7.3, 9.8, 9.0, 10} = {0.7, 0.7, 0.9, 0.8, 1.0} Issac carefully prepared his dataset so that there is one-to-one correspondence between each element in M and F. (i.e., the 1st apple…

A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.

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Chapter 8 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - Prob. 5TFR Ch. 8.1 - Prob. 6TFR Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - Prob. 8TFR Ch. 8.1 - Prob. 9TFR Ch. 8.1 - True-False Review For Questions a-j, decide if the...

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Solution Summary: The author analyzes how Hooke's Law states that, for relatively small deformations of an object, the displacement or size is directly proportional to the deforming force or load.

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Chapter 8 Solutions