8 Elasticity of Solids Small deformations are proportional to force small stretchlarger stretchHooke’s Law: ut tensio, sic vis (as the pull, so the stretch)Robert Hooke, 1635–1703
9 Hooke’s Law Graph slope < 0 Force exerted by the spring forwardslope < 0Force exerted by the springbackwardbackwardforwardDisplacement from equilibrium position
10 Hooke’s Law Formula F = –kx F = force exerted by the spring k = spring constant; units: N/m; k > 0x = displacement from equilibrium positionnegative sign: force opposes distortionrestoring force.
11 Poll QuestionforwardbackwardWhat direction of force is needed to hold the object (against the spring) at its plotted displacement?Forward (right).Backward (left).No force (zero).Can’t tell.forwardbackwardSpring’s ForceDisplacement
12 Group WorkA 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?0 N10 N10 N0 NHint: what is the load on each spring?Another hint: draw force diagrams for each load.
13 Work to Deform a Spring To pull a distance x from equilibrium kx2 slope = kxkxforcedisplacementarea = WWork =F·x ;12F = kxWork =kx·x12kx212=
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.Just as the work is always positive, so is the potential energy. This follows automatically from the x2 term.PE = 1/2 kx2The PE is positive for both positive and negative x.
15 Group Poll QuestionTwo 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 motionNew vocabulary that will also apply to waves