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lecture7 - Lecture 7 Introducing a Model of a Solid 1...

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Unformatted text preview: Lecture 7 Introducing a Model of a Solid 1 Review from Last Time • Hook’s Law: F=-kx - this force depends on position (compression of the spring). • Last time we derived the equations of motion for a mass on a spring using this expression for the force and Newton’s 2nd Law. We found: x ( t ) = Acos ( ωt ) where ω = radicalBigg k m We can differentiate the position versus time function to get the velocity and acceleration versus time. v ( t ) =- ωAsin ( ωt ) a ( t ) =- ω 2 Acos ( ωt ) • DRAW • EXAMPLE problem 2 More about springs • Springs in parallel ⇒ stiffer spring (larger spring constant) • Springs in series ⇒ less stiff (smaller spring constant) • DEMOS 3 Application: A Model of a Solid • It turns out that this mass-spring oscillation is incredibly useful for more than just designing rocket launchers or shooting our monkey. • As we’ll see, we can understand a lot about solids by building a simple model of a solid. – Tension forces - how does a rope hold something, what determines how much it will stretch or whether it will break? – Compression forces: How does a table exert a normal force on an object sitting on it? – What happens if you hit a solid with a hammer? How and at what speed does the “disturbance” (sound wave) propogate through the solid? 25 • As you’ll see, this is a great example of how physicists and engineers build simple models to try to understand how something behaves. We might not capture all the complexity with just our simple model, but we can do surprisingly well at understanding an awful lot! 3.1 The Model: Balls connected by springs • A solid is of course made of atoms arranged in a lattice structure. (PICTURE). We know this from X-ray scattering experiments and STM images....
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