SM_PDF_chapter6

# SM_PDF_chapter6 - Energy and Energy Transfer CHAPTER...

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143 Energy and Energy Transfer CHAPTER OUTLINE 6.1 Systems and Environments 6.2 Work Done by a Constant Force 6.3 The Scalar Product of Two Vectors 6.4 Work Done by a Varying Force 6.5 Kinetic Energy and the Work-Kinetic Energy Theorem 6.6 The Nonisolated System 6.7 Situations Involving Kinetic Friction 6.8 Power 6.9 Context Connection Horsepower Ratings of Automobiles ANSWERS TO QUESTIONS Q6.1 The force is perpendicular to every increment of displacement. Therefore, r r F r = 0 . Q6.2 Yes. Force times distance over which the toe is in contact with the ball. No, he is no longer applying a force. Yes, both air friction and gravity do work. Q6.3 Force of tension on a ball rotating on the end of a string. Normal force and gravitational force on an object at rest or moving across a level floor. Q6.4 Work is only done in accelerating the ball from rest. The work is done over the effective length of the pitcher’s arm—the distance his hand moves through windup and until release. Q6.5 (a) Tension (b) Air resistance (c) Positive in increasing velocity on the downswing. Negative in decreasing velocity on the upswing. Q6.6 No. The vectors might be in the third and fourth quadrants, but if the angle between them is less than 90 ° their dot product is positive. Q6.7 The scalar product of two vectors is positive if the angle between them is between 0 and 90°. The scalar product is negative when 90 180 °< < ° θ . Q6.8 ′ = k k 2 . To stretch the smaller piece one meter, each coil would have to stretch twice as much as one coil in the original long spring, since there would be half as many coils. Assuming that the spring is ideal, twice the stretch requires twice the force. Q6.9 Kinetic energy is always positive. Mass and squared speed are both positive. A moving object can always do positive work in striking another object and causing it to move along the same direction of motion. Q6.10 The longer barrel will have the higher muzzle speed. Since the accelerating force acts over a longer distance, the change in kinetic energy will be larger.

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144 Energy and Energy Transfer Q6.11 Kinetic energy is proportional to mass. The first bullet has twice as much kinetic energy. Q6.12 No violation. Choose the book as the system. You did work and the earth did work on the book. The average force you exerted just counterbalanced the weight of the book. The total work on the book is zero, and is equal to its overall change in kinetic energy. Q6.13 (a) Kinetic energy is proportional to squared speed. Doubling the speed makes an object’s kinetic energy four times larger. (b) If the total work on an object is zero in some process, its speed must be the same at the final point as it was at the initial point. Q6.14 The larger engine is unnecessary. Consider a 30-minute commute. If you travel the same speed in each car, it will take the same amount of time, expending the same amount of energy. The extra power available from the larger engine isn’t used.
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• Fall '07
• MahaAshour-Abdalla

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