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Unformatted text preview: 7 Energy of a System CHAPTER OUTLINE 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 Potential Energy of a System 7.7 Conservative and Nonconservative Forces 7.8 Relationship Between Conserva- tive Forces and Potential Energy 7.9 Energy Diagrams and the Equilibrium of a System ANSWERS TO QUESTIONS Q7.1 (a) Positive work is done by the chicken on the dirt. (b) The person does no work on anything in the environ- ment. Perhaps some extra chemical energy goes through being energy transmitted electrically and is converted into internal energy in his brain; but it would be very hard to quantify extra. (c) Positive work is done on the bucket. (d) Negative work is done on the bucket. (e) Negative work is done on the persons torso. Q7.2 Force of tension on a ball moving in a circle on the end of a string. Normal force and gravitational force on an object at rest or moving across a level oor. Q7.3 (a) Tension (b) Air resistance (c) The gravitational force does positive work in increasing speed on the downswing. It does negative work in decreasing speed on the upswing. *Q7.4 Each dot product has magnitude 1 1 cos where is the angle between the two factors. Thus for (a) and (f ) we have cos 0 = 1. For (b) and (g), cos 45 = 0.707. For (c) and (h), cos 180 = 1. For (d) and (e), cos 90 = 0. The assembled answer is a = f > b = g > d = e > c = h. Q7.5 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 < < . *Q7.6 (i) The force of block on spring is equal in magnitude and opposite to the force of spring on block. The answers are (c) and (e). (ii) The spring tension exerts equal-magnitude forces toward the center of the spring on objects at both ends. The answers are (c) and (e). Q7.7 = 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. Q7.8 No. 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. 153 13794_07_ch07_p153-174.indd 153 13794_07_ch07_p153-174.indd 153 12/2/06 1:46:44 PM 12/2/06 1:46:44 PM Q7.9 Work is only done in accelerating the ball from rest. The work is done over the effective length of the pitchers armthe distance his hand moves through windup and until release. He extends this distance by taking a step forward....
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