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Chapter 07 - 7 Energy and Energy Transfer CHAPTER OUTLINE...

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7 CHAPTER OUTLINE 7.1 Systems and Environments 7.2 Work Done by a Constant Force 7.3 The Scalar Product of Two Vectors 7.4 Work Done by a Varying Force 7.5 Kinetic Energy and the Work-Kinetic Energy Theorem 7.6 The Non-Isolated System—Conservation of 7.7 Situations Involving Kinetic Energy Friction 7.8 Power 7.9 Energy and the Automobile Energy and Energy Transfer ANSWERS TO QUESTIONS Q7.1 The force is perpendicular to every increment of displacement. Therefore, F r = 0 . Q7.2 (a) Positive work is done by the chicken on the dirt. (b) No work is done, although it may seem like there is. (c) Positive work is done on the bucket. (d) Negative work is done on the bucket. (e) Negative work is done on the person’s torso. Q7.3 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. Q7.4 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. Q7.5 (a) Tension (b) Air resistance (c) Positive in increasing velocity on the downswing. Negative in decreasing velocity on the upswing. Q7.6 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. Q7.7 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 . Q7.8 If the coils of the spring are initially in contact with one another, as the load increases from zero, the graph would be an upwardly curved arc. After the load increases sufficiently, the graph will be linear, described by Hooke’s Law. This linear region will be quite large compared to the first region. The graph will then be a downward curved arc as the coiled spring becomes a completely straight wire. As the load increases with a straight wire, the graph will become a straight line again, with a significantly smaller slope. Eventually, the wire would break. Q7.9 ′ = 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. 191
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192 Energy and Energy Transfer Q7.10 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. Q7.11 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. Q7.12 Kinetic energy is proportional to mass. The first bullet has twice as much kinetic energy.
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