1.         Elasticity and Harmonic Motion

2.         Elastic

            a.         The ability to return to original shape when deformed

            b.         Characteristic of solids and gels

3.         Source of Elasticity

            a.         Interatomic forces hold atoms in place

            b.         Spring is good model

                        i.         Compressed or stretched force returns it to normal

            c.         External force deforms object, internal force returns it to normal

4.         Stretching and Compression

            a.         Force applied perpendicular to center of end

            b.         Force needed depends on:

                        i.         Fractional change in length

                        ii.        Cross section area

                        iii.       Type of material (Young’s Modulus)

5.         Formula

            a.         

            b.         L_O º Original Length

            c.         Y º Young’s Modulus

6.         Shear Deformation

            a.         Shape change due to net sideways force

            b.         Opposite forces on top and bottom

7.         Variables Affecting Shear Force

            a.         Cross section area

            b.         Type of material (Shear Modulus)

            c.         Ratio of shear to height

8.         Formula

            a.         

            b.         DX º shear

            c.         L_O º height

            d.         S º Shear Modulus

9.         Difference in S and Y

            a.         S applies when shape changed by shearing forces

            b.         Y applies when only length changes

10.       Volume Deformation

            a.         Forces act on all sides of object

            b.         Volume changes

            c.         Normally refer to pressure (F/A)

11.       Variables Affecting Pressure

            a.         Fractional change in volume

            b.         Type of material (Bulk Modulus)

12.       Formula

            a.         

            b.         B º Bulk Modulus

            c.         V_O º original Volume

            d.         DP and DV inversely realted

13.       Definitions

            a.         Stress º ratio of force to area

            b.         Strain º fractional change of dimension

14.       Hooke’s Law

            a.         Developed by Hooke from analysis of experimental results

            b.         

            c.         Stress is directly proportional to strain

            d.         

15.       General Form of Equation

            a.         k has form

            b.         x is dimension that changes (DL)

16.       Definitions

            a.         Proportionality Limit º point where relationship is no longer linear

            b.         Elastic Limit º point where deformation becomes permanent

17.       Effect of 3rd Law

            a.         Force on spring produces restoring force

            b.         Given by Hooke’s Law

            c.         Returns spring to starting length

18.       Effect of Spring and Oject’s Inertia

            a.         Object begins at rest

            b.         F moves object and spring, -F created in spring

            c.         -F returns spring to rest position, inertia takes object beyond rest

            d.         F created in spring, process repeats

19.       Simple Harmonic Motion

            a.         Motion created when the restoring force is given by F = -kx

            b.         Max “x” is amplitude (A)

            c.         Graph of x is sine wave

20.       SHM and the Reference Circle

            a.         Shadow of object mounted on turntable shows SHM

                        i.         Oscillates between -A and +A

            b.         Circular motion can be used to analyze SHM

21.       Variables Used

            a.         q º angle measured in radians

            b.         T º time to move from A to -A to A

            c.         w º angular speed (q/t)

22.       Displacement

            a.         

23.       Frequency of SHM

            a.         

24.       Velocity

            a.         

            b.         Velocity (v) is horizontal component of V_T

25.       Velocity

            a.         w and A are constants, thus V varies with t

            b.         V = 0 at max displacement

            c.         V_max = Aw = at x=0

26.       Acceleration

            a.         “a” is present because “v” changes

            b.         “a” is horizontal component of a_c

            c.         

27.       Frequency of Vibration

            a.         From the 2nd law we can derive:

            b.         From earlier we know:

28.       Elastic PE

            a.         Work used to distort spring is stored as PE

            b.         This is one component of conservation of energy

29.       Motion of a Pendulum

            a.         Pendulum moves through part of a circle

            b.         Produces SHM

30.       Damped Harmonic Motion

            a.         Normal harmonic motion has no way to dissipate energy

            b.         Addition of dissipating mechanism creates damped harmonic motion

            c.         Damping produces a decrease in amplitude

31.       Definitions

            a.         Critical Damping: eliminates SHM

            b.         Overdamping: exceeds critical value

            c.         Underdamping: less than critical value

                        i.         Slowly stops SHM

                        ii.        Vehicle shock absorbers