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Unformatted text preview: Solution for Practice Test 8 for Test 4 Solution to Practice Test Problem 8.1(careful three laws) Problem: There are three qualitatively different statements of the second law of thermodynamics. In your own words, cafefully explain each of the three. Solution (a) Thermal energy flows spontaneously from a higher temperature object to a lower temperature object, but not the other way. (b) It is impossible for any cyclic process to occur whose sole value is the extraction of heat from a reservoir and the performance of an equivalent amount of work. (In other words, heat engines are always less than 100% efficient.) (c) The total entropy of all participants in any physical process cannot decrease, but it can increase. 3 point(s) (3 times) : for correct idea: flow, efficiency or work, entropy or number of states. 2 point(s) (3 times) : correctly conveys the idea, 1 out of 2 if only partly right, like saying entropy always increases instead of it can never decrease (since it can stay the same). Total Points for Problem: 15 Points Solution to Practice Test Problem 8.2(Calibrate then oscillate) Problem: Consider a spring hung vertically from the ceiling. (a)When . 5kg object is attached to the spring, the spring stretches 2 . 5cm . What is the force constant of the spring? (b)The spring is then placed horizontally along an air track, connected to a . 5kg-glider that is free to oscillate nearly frictionlessly on the airtrack. You compress the spring by pushing the glider to the left. It then undergoes simple harmonic motion along the track. What is the period of the motion? (c)You compressed the spring in part (b) so that the glider undergoes simple harmonic motion with an amplitude of 10 cm . What is its maximum acceleration and velocity? (d)Taking toward the right to be positive, at what position (and when travelling in what direction, if more than one is possible) in the motion do the maximum position, velocity and acceleration occur? Remember these are all vectors. (e)If we call the time where you release it from its leftmost position t = 0 , (still taking to the right to be positive) write an equation of motion for the oscillation, x ( t ) = ?, identifying the values of all constants that you use. Solution to Part (a) Using Hooke’s law, F = k Δ x (0 . 5kg)(9 . 8 m s 2 ) = k(0 . 025m) k = 196 N m Grading Key: Part (a) 6 Points 2 point(s) : correct relation for spring force 1 point(s) : correct number and units 2 point(s) : correctly sets | F spring | = | mg | 1 point(s) : correct substitutions Solution to Part (b) The frequency is the inverse of the period, f = 1 T . The angular frequency is related to the frequency as ω = 2 πf = 2 π T . Use these and the relation ω = radicalBig k m to solve for the period....
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