Presentation on theme: "Simple Harmonic Motion and Elasticity"— Presentation transcript:
1Simple Harmonic Motion and Elasticity Chapter 10Simple Harmonic Motion and Elasticity
210.1 The Ideal Spring and Simple Harmonic Motion spring constantUnits: N/m
310.1 The Ideal Spring and Simple Harmonic Motion Example 1 A Tire Pressure GaugeThe spring constant of the springis 320 N/m and the bar indicatorextends 2.0 cm. What force does theair in the tire apply to the spring?
510.1 The Ideal Spring and Simple Harmonic Motion Conceptual Example 2 Are Shorter Springs Stiffer?A 10-coil spring has a spring constant k. If the spring iscut in half, so there are two 5-coil springs, what is the springconstant of each of the smaller springs?
610.1 The Ideal Spring and Simple Harmonic Motion HOOKE’S LAW: RESTORING FORCE OF AN IDEAL SPRINGThe restoring force of an ideal spring is
710.2 Simple Harmonic Motion and the Reference Circle DISPLACEMENT
810.2 Simple Harmonic Motion and the Reference Circle
910.2 Simple Harmonic Motion and the Reference Circle amplitude A: the maximum displacementperiod T: the time required to complete one cyclefrequency f: the number of cycles per second (measured in Hz)
1010.2 Simple Harmonic Motion and the Reference Circle VELOCITY
1110.2 Simple Harmonic Motion and the Reference Circle Example 3 The Maximum Speed of a Loudspeaker DiaphragmThe frequency of motion is 1.0 KHz and the amplitude is 0.20 mm.What is the maximum speed of the diaphragm?Where in the motion does this maximum speed occur?
1210.2 Simple Harmonic Motion and the Reference Circle The maximum speedoccurs midway betweenthe ends of its motion.
1310.2 Simple Harmonic Motion and the Reference Circle ACCELERATION
1410.2 Simple Harmonic Motion and the Reference Circle FREQUENCY OF VIBRATION
1510.2 Simple Harmonic Motion and the Reference Circle
1610.3 Energy and Simple Harmonic Motion A compressed spring can do work.
1710.2 Simple Harmonic Motion and the Reference Circle Example 6 A Body Mass Measurement DeviceThe device consists of a spring-mounted chair in which the astronautsits. The spring has a spring constant of 606 N/m and the mass ofthe chair is 12.0 kg. The measuredperiod is 2.41 s. Find the mass of theastronaut.
1910.3 Energy and Simple Harmonic Motion DEFINITION OF ELASTIC POTENTIAL ENERGYThe elastic potential energy is the energy that a springhas by virtue of being stretched or compressed. For anideal spring, the elastic potential energy isSI Unit of Elastic Potential Energy: joule (J)
2010.3 Energy and Simple Harmonic Motion Conceptual Example 8 Changing the Mass of a SimpleHarmonic OscilatorThe box rests on a horizontal, frictionlesssurface. The spring is stretched to x=Aand released. When the box is passingthrough x=0, a second box of the samemass is attached to it. Discuss whathappens to the (a) maximum speed,(b) amplitude, and (c) angular frequency.
2110.3 Energy and Simple Harmonic Motion Example 8 Adding a Mass to a Simple Harmonic OscillatorA 0.20-kg ball is attached to a vertical spring. The spring constantis 28 N/m. When released from rest, how far does the ball fallbefore being brought to a momentary stop by the spring?
23A simple pendulum consists of a particle attached to a frictionless 10.4 The PendulumA simple pendulum consists ofa particle attached to a frictionlesspivot by a cable of negligible mass.
24Determine the length of a simple pendulum that will 10.4 The PendulumExample 10 Keeping TimeDetermine the length of a simple pendulum that willswing back and forth in simple harmonic motion witha period of 1.00 s.
2510.5 Damped Harmonic Motion In simple harmonic motion, an object oscillateswith a constant amplitude.In reality, friction or some other energydissipating mechanism is always presentand the amplitude decreases as timepasses.This is referred to as damped harmonicmotion.
2710.6 Driven Harmonic Motion and Resonance When a force is applied to an oscillating system at all times,the result is driven harmonic motion.Here, the driving force has the same frequency as thespring system and always points in the direction of theobject’s velocity.
2810.6 Driven Harmonic Motion and Resonance Resonance is the condition in which a time-dependent applied force cantransmit large amounts of energy to an oscillating object, leading to alarge amplitude motion.Resonance occurs when the frequency of the applied force matches anatural frequency at which the object will oscillate.
29Because of these atomic-level “springs”, a material tends to 10.7 Elastic DeformationBecause of these atomic-level “springs”, a material tends toreturn to its initial shape once forces have been removed.ATOMSFORCES
30STRETCHING, COMPRESSION, AND YOUNG’S MODULUS 10.7 Elastic DeformationSTRETCHING, COMPRESSION, AND YOUNG’S MODULUSYoung’s modulus has the units of pressure: N/m2
32Example 12 Bone Compression 10.7 Elastic DeformationExample 12 Bone CompressionIn a circus act, a performer supports the combined weight (1080 N) ofa number of colleagues. Each thighbone of this performer has a lengthof 0.55 m and an effective cross sectional area of 7.7×10-4 m2. Determinethe amount that each thighbone compresses under the extra weight.
36You push tangentially across the top 10.7 Elastic DeformationExample 14 J-E-L-L-OYou push tangentially across the topsurface with a force of 0.45 N. Thetop surface moves a distance of 6.0 mmrelative to the bottom surface. What isthe shear modulus of Jell-O?
4010.8 Stress, Strain, and Hooke’s Law In general the quantity F/A is called the stress.The change in the quantity divided by that quantity is called thestrain:HOOKE’S LAW FOR STRESS AND STRAINStress is directly proportional to strain.Strain is a unitless quantity.SI Unit of Stress: N/m2