You take on a research assistantship with a molecular physicist. She is studying the vibrations of diatomic molecules. In these vibrations, the two atoms in the molecule move back and forth along the line connecting them (see Figure 20.5c). As an introduction to her research, she asks you to familiarize yourself with the Lennard–Jones potential (see Example 7.9), which describes the potential energy function for a diatomic molecule. She asks you to determine the effective spring constant, in terms of the parameters σ and ϵ , for the bond holding the atoms together in the molecule for small vibrations around the equilibrium separation r eq . After being stumped for a while, you ask her for a hint. She responds, “Example 7.9 provides the derivative of the potential energy function. Compare that to Equation 7.29 to find the force between the atoms. You want to show that F is of the form − kx , and find k . Let the separation distance r = r eq + x , where x is small and take advantage of the series approximations in Appendix Section B.5.” Wow, that’s several hints! You sit down and get to work.

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Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
BuyFind

Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

Solutions

Chapter
Section
Chapter 15, Problem 30P
Textbook Problem

You take on a research assistantship with a molecular physicist. She is studying the vibrations of diatomic molecules. In these vibrations, the two atoms in the molecule move back and forth along the line connecting them (see Figure 20.5c). As an introduction to her research, she asks you to familiarize yourself with the Lennard–Jones potential (see Example 7.9), which describes the potential energy function for a diatomic molecule. She asks you to determine the effective spring constant, in terms of the parameters σ and ϵ, for the bond holding the atoms together in the molecule for small vibrations around the equilibrium separation req. After being stumped for a while, you ask her for a hint. She responds, “Example 7.9 provides the derivative of the potential energy function. Compare that to Equation 7.29 to find the force between the atoms. You want to show that F is of the form −kx, and find k. Let the separation distance r = req + x, where x is small and take advantage of the series approximations in Appendix Section B.5.” Wow, that’s several hints! You sit down and get to work.

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Chapter 15 Solutions

Physics for Scientists and Engineers
Ch. 15 - Review. A particle moves along the x axis. It is...Ch. 15 - A ball dropped from a height of 4.00 m makes an...Ch. 15 - A particle moving along the x axis in simple...Ch. 15 - The initial position, velocity, and acceleration...Ch. 15 - You attach an object to the bottom end of a...Ch. 15 - To test the resiliency of its bumper during...Ch. 15 - A particle executes simple harmonic motion with an...Ch. 15 - The amplitude of a system moving in simple...Ch. 15 - A simple harmonic oscillator of amplitude A has a...Ch. 15 - Review. A 65.0-kg bungee jumper steps off a bridge...Ch. 15 - Review. A 0.250-kg block resting on a...Ch. 15 - While driving behind a car traveling at 3.00 m/s,...Ch. 15 - A simple pendulum makes 120 complete oscillations...Ch. 15 - A particle of mass m slides without friction...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - A physical pendulum in the form of a planar object...Ch. 15 - A simple pendulum has a mass of 0.250 kg and a...Ch. 15 - Consider the physical pendulum of Figure 15.16....Ch. 15 - A watch balance wheel (Fig. P15.25) has a period...Ch. 15 - Show that the time rate of change of mechanical...Ch. 15 - Show that Equation 15.32 is a solution of Equation...Ch. 15 - As you enter a fine restaurant, you realize that...Ch. 15 - A 2.00-kg object attached to a spring moves...Ch. 15 - Considering an undamped, forced oscillator (b =...Ch. 15 - You have scored a part-time job at a company that...Ch. 15 - You take on a research assistantship with a...Ch. 15 - An object of mass m moves in simple harmonic...Ch. 15 - Review. This problem extends the reasoning of...Ch. 15 - An object attached to a spring vibrates with...Ch. 15 - Review. A rock rests on a concrete sidewalk. An...Ch. 15 - A pendulum of length L and mass M has a spring of...Ch. 15 - To account for the walking speed of a bipedal or...Ch. 15 - Review. A particle of mass 4.00 kg is attached to...Ch. 15 - People who ride motorcycles and bicycles learn to...Ch. 15 - A ball of mass m is connected to two rubber bands...Ch. 15 - Consider the damped oscillator illustrated in...Ch. 15 - Review. A lobstermans buoy is a solid wooden...Ch. 15 - Your thumb squeaks on a plate you have just...Ch. 15 - Your father is preparing the backyard for the...Ch. 15 - Why is the following situation impossible? Your...Ch. 15 - A block of mass m is connected to two springs of...Ch. 15 - Review. A light balloon filled with helium of...Ch. 15 - A particle with a mass of 0.500 kg is attached to...Ch. 15 - A smaller disk of radius r and mass m is attached...Ch. 15 - Review. A system consists of a spring with force...Ch. 15 - Review. Why is the following situation impassible?...Ch. 15 - A light, cubical container of volume a3 is...

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