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Solids

Solids. A simple model of elasticity. Objectives. Describe the deformation of a solid in response to a tension or compression. What’s the point?. How do solids react when deformed?. compression. tension. Structure of Solids. Atoms and molecules connected by chemical bonds

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Solids

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  1. Solids A simple model of elasticity

  2. Objectives • Describe the deformation of a solid in response to a tension or compression.

  3. What’s the point? • How do solids react when deformed?

  4. compression tension Structure of Solids • Atoms and molecules connected by chemical bonds • Considerable force needed to deform

  5. Structure of Solids Atoms are always “attracting each other when they are a little distance apart, but repelling upon being squeezed into one another” apart force 0 toward equil equil apart distance

  6. apart force 0 toward equil distance Structure of Solids Atoms are always “attracting each other when they are a little distance apart, but repelling upon being squeezed into one another”

  7. apart force 0 toward equil distance Force and Distance

  8. small stretch larger stretch Elasticity of Solids Small deformations are proportional to force Hooke’s Law: ut tensio, sic vis (as the pull, so the stretch) Robert Hooke, 1635–1703

  9. slope < 0 forward backward backward forward Hooke’s Law Graph Force exerted by the spring 0 0 Displacement from equilibrium position

  10. Hooke’s Law Formula F = force exerted by the spring k = spring constant; units: N/m; k > 0 x = displacement from equilibrium position negative sign: force opposes distortion F = –kx

  11. backward forward What direction of force is needed to hold the object (against the spring) at its plotted displacement? forward backward • Forward (right). • Backward (left). • No force (zero). • Can’t tell. Poll Question Spring’s Force Displacement

  12. 0 N 10 N 0 N 10 N Group Work A spring stretches 4 cm when a load of 10 N is suspended from it. How much will the combined springs stretch if another identical spring also supports the load as in a and b? Hint: what is the load on each spring? Another hint: draw force diagrams for each load.

  13. slope = k kx area = W force x displacement F = kx • Work = F·x ; • Work = = 1 1 kx·x 1 2 2 kx2 2 Work to Deform a Spring • To pull a distance x from equilibrium

  14. Potential Energy of a Spring The potential energy of a stretched or compressed spring is equal to the work needed to stretch or compress it from its rest length. PE = 1/2 kx2 The PE is positive for both positive and negative x.

  15. Group Poll Question Two springs are gradually stretched to the same final tension. One spring is twice as stiff as the other: k2 = 2k1.Which spring has the most work done on it? • The stiffer spring (k = 2k1). • The softer spring (k = k1). • Equal for both.

  16. Reading for Next Time Vibrations Big ideas: Interplay between Hooke’s force law and Newton’s laws of motion New vocabulary that will also apply to waves

  17. A Word

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