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Chapter 3 Review Exercises

Chapter 3 Review Exercises
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  • 17. Universal Gravity

    Use the excerpt.

    "Why should that apple always descend perpendicularly to the ground, thought [Newton] to himself; occasioned by the fall of an apple, as he sat in a contemplative mood. Why should it not go sideways, or upwards? But constantly to the earth's center? Assuredly, the reason is, that the earth draws it. There must be a drawing power in matter. . . . If matter thus draws matter; it must be in proportion of its quantity. Therefore, the apple draws the earth, as well as the earth draws the apple."

    Memoirs of Sir Isacc Newton's Life, William Stukely

    How does Newton conclude that there is a drawing power in matter? What type of reasoning is this? Explain.

    • Worked-Out Solution

      Newton's reasoning was based on observation of a pattern. In all cases in which he observed something falling, he noticed that it fell in a path that is perpendicular to the ground. From this he concluded that Earth must be drawing the falling object. This is an example in inductive reasoning.

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                 ___      ____       ___              
        ___     / _ \\   |  _ \\    / _ \\    ____    
       /   ||  / //\ \\  | |_| ||  / //\ \\  |    \\  
      | [] || |  ___  || | .  //  |  ___  || | [] ||  
       \__ || |_||  |_|| |_|\_\\  |_||  |_|| |  __//  
        -|_|| `-`   `-`  `-` --`  `-`   `-`  |_|`-`   
         `-`                                 `-`      
    
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  • 18. Universal Gravity

    Use the excerpt.

    "Why should that apple always descend perpendicularly to the ground, thought [Newton] to himself; occasioned by the fall of an apple, as he sat in a contemplative mood. Why should it not go sideways, or upwards? But constantly to the earth's center? Assuredly, the reason is, that the earth draws it. There must be a drawing power in matter. . . . If matter thus draws matter; it must be in proportion of its quantity. Therefore, the apple draws the earth, as well as the earth draws the apple."

    Memoirs of Sir Isacc Newton's Life, William Stukely

    How does Newton conclude that, in addition to Earth pulling on the apple, the apple is pulling on the earth? What type of reasoning is this?

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                ______               ___      _  _   
        ___    /_   _//   ____      / _ \\   | \| || 
       /   ||   -| ||-   |    \\   | / \ ||  |  ' || 
      | [] ||   _| ||_   | [] ||   | \_/ ||  | .  || 
       \__ ||  /_____//  |  __//    \___//   |_|\_|| 
        -|_||  `-----`   |_|`-`     `---`    `-` -`  
         `-`             `-`                         
    
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  • 19. Laws of Motion

    Use Newton's Laws of Motion.

    Law 1: Every object in uniform motion will remain in uniform motion unless an external force acts on it.
    Law 2: Force equals mass times acceleration.
    Law 3: For every action, there is an equal and opposite reaction.

    What type of reasoning do you think Newton used to arrive at his three laws of motion? Explain.

    • Worked-Out Solution

      As is true of almost all scientific laws, Newton based his laws of motion on observed patterns and inductive reasoning. This process has been summarized in what is called the scientific method.

      The scientific method has 5 steps identified by the letters POHEC.

      1. State the Problem.
      2. Make Observations.
      3. Use inductive reasoning to form a Hypothesis.
      4. Do the Experiment.
      5. Draw a Conclusion.
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      ______    _____    _    _      ___      _  _   
     /_   _//  |  ___|| | \  / ||   / _ \\   | \| || 
     `-| |,-   | ||__   |  \/  ||  / //\ \\  |  ' || 
       | ||    | ||__   | .  . || |  ___  || | .  || 
       |_||    |_____|| |_|\/|_|| |_||  |_|| |_|\_|| 
       `-`'    `-----`  `-`  `-`  `-`   `-`  `-` -`  
                                                     
    
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  • 20. Laws of Motion

    Use Newton's Laws of Motion.

    Law 1: Every object in uniform motion will remain in uniform motion unless an external force acts on it.
    Law 2: Force equals mass times acceleration.
    Law 3: For every action, there is an equal and opposite reaction.

    What type of reasoning do you think Newton used to apply his three laws of motion? Explain.

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                ______   _    _     ______    ____    
        ___    /_   _// | |  | ||  /_   _//  |  _ \\  
       /   ||   -| ||-  | |/\| ||   -| ||-   | |_| || 
      | [] ||   _| ||_  |  /\  ||   _| ||_   | .  //  
       \__ ||  /_____// |_// \_||  /_____//  |_|\_\\  
        -|_||  `-----`  `-`   `-`  `-----`   `-` --`  
         `-`                                          
    
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  • 21. Laws of Motion

    Use Newton's Laws of Motion.

    Law 1: Every object in uniform motion will remain in uniform motion unless an external force acts on it.
    Law 2: Force equals mass times acceleration.
    Law 3: For every action, there is an equal and opposite reaction.

    Write a syllogism that involves Newton's first law.

    • Worked-Out Solution

      Here is one possible syllogism involving Newton's first law of motion.

      Premise: If an object is in uniform motion and no external force acts on it, then it will remain in uniform motion.
      Premise: An object is in uniform motion and no external force is acting on it.
      Conclusion: The object will remain in uniform motion.
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      _  __    ______    _____     ______            
     | |/ //  /_   _//  /  ___||  /_   _//     ___   
     | ' //    -| ||-  | // __     -| ||-     /   || 
     | . \\    _| ||_  | \\_\ ||   _| ||_    | [] || 
     |_|\_\\  /_____//  \____//   /_____//    \__ || 
     `-` --`  `-----`    `---`    `-----`      -|_|| 
                                                `-`  
    
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  • 22. Laws of Motion

    Use Newton's Laws of Motion.

    Law 1: Every object in uniform motion will remain in uniform motion unless an external force acts on it.
    Law 2: Force equals mass times acceleration.
    Law 3: For every action, there is an equal and opposite reaction.

    Write a syllogism that involves Newton's third law.

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      ______     ___     _    _    _    _    _    _   
     /_   _//   / _ \\  | \  / || | || | || | \  / || 
       | ||    / //\ \\ |  \/  || | || | || |  \/  || 
      _| ||   |  ___  ||| .  . || | \\_/ || | .  . || 
     /__//    |_||  |_|||_|\/|_||  \____//  |_|\/|_|| 
     `--`     `-`   `-` `-`  `-`    `---`   `-`  `-`  
                                                      
    
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  • 23. Laws of Motion

    Use Newton's Laws of Motion.

    Law 1: Every object in uniform motion will remain in uniform motion unless an external force acts on it.
    Law 2: Force equals mass times acceleration.
    Law 3: For every action, there is an equal and opposite reaction.

    In the twentieth century, it was discovered that Newton's second law does not hold at high velocities. Explain this revelation in the context of inductive reasoning.

    • Worked-Out Solution

      All of Newton's obervations were based on objects moving at low velocities, nowhere near the speed of light. In the 20th century, it was discovered that as the speed of an object approaches the speed of light, unusal things can be observed. At this point, Newton's laws started to be called "Newtonian physics." The laws are still valid, but only for certain conditions.

      This is an example in which you can reach a false conclusion using inductive reasoning because the reasoning was not based on a large enough and diverse enough sample.

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     _____      _____              _    _      _____  
    |  __ \\   |  ___||   ____    | || | ||   / ___// 
    | |  \ ||  | ||__    |    \\  | || | ||   \___ \\ 
    | |__/ ||  | ||__    | [] ||  | \\_/ ||   /    // 
    |_____//   |_____||  |  __//   \____//   /____//  
     -----`    `-----`   |_|`-`     `---`   `-----`   
                         `-`                          
    
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  • 24. Scientific Method

    Explain the relationship between inductive and deductive reasoning in science.

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      ______    _____     _  _      ___     _    _   
     /_   _//  |  ___||  | \| ||   / _ \\  | || | || 
       | ||    | ||__    |  ' ||  / //\ \\ | || | || 
      _| ||    | ||__    | .  || |  ___  ||| \\_/ || 
     /__//     |_____||  |_|\_|| |_||  |_|| \____//  
     `--`      `-----`   `-` -`  `-`   `-`   `---`   
                                                     
    
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