P2(10pts): A mass of 3.0 kg is connected to an ideal spring with spring constant k =and free to move on a frictionless horizontal surface as shown in the figure below. The equation1.0 N/m,of the ideal (un-damped) oscillator has the form:x(t) = Acos(wt + 0)ma. Using Newton's second law, set up the equation of motion, and prove that the solutionabove is indeed a valid solution.b. What is the natural frequency and period of oscillation T, w in SI units?c. If at time t = 0 the position and velocity are given by x(0) = 0.20 m and v(0) =0.10 m/s, find both A and .d. What is the total energy of the system?e. BONUS: Prove that the total mechanical energy of the system is a constant in time.

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Answered: P2(10pts): A mass of 3.0 kg is…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Suppose that S is regarded as a function of T and p, show that TdS= C,dT- T(dP/aT)y dV.
4) Consider an adyabatic expansion of the ideal single-atom gas. (a) Find dT/dV differential equality by obtaining dQ = 0 in the first law. (b) Resolve the dT/dV differential equality for the adyabatic condition. ( V Ta =constant SHOW IT). (c)Using the ideal gas law,, p Vg =constant Show it and find g
Q9 + Show that, for a perfect gas, (US)y= T and (@U/V)₁=-p.
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R = 0.08205 L atm mol-1 K-1 T(K)= T (°C) + 273.15 1 atm = 101,325 Pa = 1.01325 bar The experimentally determined density of N₂ (MW = 28.0134) at 180 bar and 150 K is 544 g L-¹. Calculate z from this information. 3 sig figs
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Given ab = Q/r and R = 2T, solve for T in terms of A, B, and Q
nRT (c) Consider the following differential: dq = nC, dT +“A dV, where n and R are constants. V (i) Is the above differential dq, an exact or inexact differential? [Show how you arrived to your conclusion by evaluating the appropriate partial differentials!!]
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Suppose we put an object with temperature T0 in a room with constant temperature K.We know that the heating/cooling speed of the object is proportional to the temperature differencebetween the object and the environment with ratio r a positive constant. If we write the temperature of the object T as a function of time t, write out the differentialequation it has to satisfy.
P1B.1 A rotating slotted-disc apparatus consists of five coaxial 5.0 cm diameter discs separated by 1.0 cm, the radial slots being displaced by 2.0° between neighbours. The relative intensities, I, of the detected beam of Kr atoms for two different temperatures and at a series of rotation rates were as follows: v/Hz 20 40 80 100 120 I (40 K) 0.846 0.513 0.069 0.015 0.002 I (100 K) 0.592 0.485 0.217 0.119 0.057 Find the distributions of molecular velocities, f(v,), at these temperatures, and check that they conform to the theoretical prediction for a one-dimensional system for this low-pressure, collision-free system.

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