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Physics includes charged object in electric and examining changes in internal energy with changes in Big Idea 6 Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena Enduring Understanding 6 A A wave is a traveling disturbance that transfers energy and momentum Essential Knowledge 6 A 1 Waves can propagate via different oscillation modes such as transverse and longitudinal Essential Knowledge 6 A 2 For propagation mechanical waves require a medium while electromagnetic waves do not require a physical medium | [
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Examples should include light traveling through a vacuum and sound not traveling through a vacuum Essential Knowledge 6 A 3 The amplitude is the maximum displacement of a wave from its equilibrium value Essential Knowledge 6 A 4 Classically the energy carried by a wave depends on and increases with amplitude | [
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] | 8,851 |
Examples should include sound waves Enduring Understanding 6 B A periodic wave is one that repeats as a function of both time and position and can be described by its amplitude frequency wavelength speed and energy Essential Knowledge 6 B 1 The period is the repeat time of the wave | [
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] | 8,852 |
The frequency is the number of repetitions over a period of time Essential Knowledge 6 B 2 The wavelength is the repeat distance of the wave Essential Knowledge 6 B 3 A simple wave can be described by an equation involving one sine or cosine function involving the wavelength amplitude and frequency of the wave Essential Knowledge 6 B 4 The wavelength is the ratio of speed over frequency Enduring Understanding 6 C Only waves exhibit interference and dif fraction Essential Knowledge 6 C 1 When two waves cross they travel through each they do not bounce of f each other | [
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] | 8,854 |
This is called superposition Enduring Understanding 6 D Interference and superposition lead to standing waves and beats Essential Knowledge 6 D 1 Two or more wave pulses can interact in such a way as to produce amplitude variations in the resultant wave | [
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] | 8,855 |
When two pulses cross they travel through each they do not bounce of f each other | [
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] | 8,856 |
Where the pulses overlap the resulting displacement can be determined by adding the displacements of the two pulses | [
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] | 8,857 |
This is called superposition Essential Knowledge 6 D 2 Two or more traveling waves can interact in such a way as to produce amplitude variations in the resultant wave Essential Knowledge 6 D 3 Standing waves are the result of the addition of incident and waves that are to a region and have nodes and antinodes | [
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Examples should include waves on a length of string and sound waves in both closed and open tubes Essential Knowledge 6 D 4 The possible wavelengths of a standing wave are determined by the size of the region to which it is Essential Knowledge 6 D 5 Beats arise from the addition of waves of slightly dif ferent frequency 682 Chapter 16 Oscillatory Motion and Waves This OpenStax book is available for free at 1416 Stress and Strain Revisited Learning Objectives By the end of this section you will be able Explain third law of motion with respect to stress and deformation Describe the restoring force and displacement Use law of deformation and calculate stored energy in a spring The information presented in this section supports the following learning objectives and science B 3 3 The student can analyze data to identify qualitative or quantitative relationships between given values and variables e force displacement acceleration velocity period of motion frequency spring constant string length associated with objects in oscillatory motion to use that data to determine the value of an unknown P 2 2 5 B 3 4 The student is able to construct a qualitative a quantitative explanation of oscillatory behavior given evidence of a restoring force P 2 2 6 Figure 16 2 When displaced from its vertical equilibrium position this plastic ruler oscillates back and forth because of the restoring force opposing displacement | [
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] | 8,859 |
When the ruler is on the left there is a force to the right and vice versa first law implies that an object oscillating back and forth is experiencing forces | [
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] | 8,860 |
Without force the object would move in a straight line at a constant speed rather than oscillate | [
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Consider for example plucking a plastic ruler to the left as shown in Figure 16 2 | [
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] | 8,862 |
The deformation of the ruler creates a force in the opposite direction known as a restoring force | [
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] | 8,863 |
Once released the restoring force causes the ruler to move back toward its stable equilibrium position where the net force on it is zero However by the time the ruler gets there it gains momentum and continues to move to the right producing the opposite deformation | [
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It is then forced to the left back through equilibrium and the process is repeated until dissipative forces dampen the motion | [
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] | 8,865 |
These forces remove mechanical energy from the system gradually reducing the motion until the ruler comes to rest The simplest oscillations occur when the restoring force is directly proportional to displacement | [
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] | 8,866 |
When stress and strain were covered in Third Law of Motion the name was given to this relationship between force and displacement was Here Fis the restoring force xis the displacement from equilibrium or deformation and kis a constant related to the difficulty in deforming the system | [
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] | 8,867 |
The minus sign indicates the restoring force is in the direction opposite to the displacement Figure 16 3 The plastic ruler has been released and the restoring force is returning the ruler to its equilibrium position The net force is zero at the equilibrium position but the ruler has momentum and continues to move to the right The restoring force is in the opposite direction | [
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] | 8,868 |
It stops the ruler and moves it back toward equilibrium again Now the ruler has momentum to the left In the absence of damping by frictional the ruler reaches its original position | [
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] | 8,869 |
From there the motion will repeat itself Theforce constant kis related to the rigidity of a larger the force constant the greater the restoringChapter 16 Oscillatory Motion and Waves 683force and the stiffer the system | [
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] | 8,870 |
The units of kare newtons per meter | [
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] | 8,871 |
For example kis directly related to modulus when we stretch a string | [
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] | 8,872 |
Figure 16 4 shows a graph of the absolute value of the restoring force versus the displacement for a system that can be described by simple spring in this case | [
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] | 8,873 |
The slope of the graph equals the force constant kin newtons per meter | [
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A common physics laboratory exercise is to measure restoring forces created by springs determine if they follow law and calculate their force constants if they do Figure 16 4 A graph of absolute value of the restoring force versus displacement is displayed | [
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] | 8,875 |
The fact that the graph is a straight line means that the system obeys law | [
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The restoring force equals the weight supported if the mass is stationary Example 16 1 How Stiff Are Car Figure 16 5 The mass of a car increases due to the introduction of a passenger | [
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This affects the displacement of the car on its suspension system exfordy on What is the force constant for the suspension system of a car that settles 1 20 cm when an 80 person gets Chapter 16 Oscillatory Motion and Waves This OpenStax book is available for free at 14Strategy Consider the car to be in its equilibrium position 0 before the person gets in | [
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] | 8,879 |
The car then settles down 1 20 cm which means it is displaced to a position | [
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] | 8,880 |
At that point the springs supply a restoring force Fequal to the weight 0 80 784 N | [
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0.04648476839065552,
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0.011049017310142517,
0.0696047767996788,
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0.017216932028532028,
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0.046396635472774506,
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0.03830735757946968,
0.057558443397283554,
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0.04118179529905319,
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-0.04788828641176224,
0.06974872201681137,
-0.030856186524033546
] | 8,882 |
Knowing Fand x we can then solve the force constant k Solution 1 | [
-0.0048966496251523495,
0.023265624418854713,
0.03947236388921738,
0.009289939887821674,
0.025783810764551163,
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0.07722187787294388,
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0.018819235265254974,
0.12364731729030609,
0.014022784307599068,
0.07423907518386841,
-1.7848557449381838e-33,
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0.0416112020611763,
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0.0682966336607933,
0.02666439488530159,
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0.03952536731958389,
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0.03406520187854767,
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0.01837657019495964,
0.0979899913072586,
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0.0524054653942585,
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0.10558655858039856,
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0.035561755299568176,
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0.0025145590770989656,
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0.0010693318909034133,
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0.033013757318258286,
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0.014822286553680897,
0.017625872045755386,
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0.010387584567070007,
0.049441978335380554,
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0.004428573418408632,
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0.02509314753115177,
0.007887007668614388,
-0.023011770099401474,
0.06506379693746567
] | 8,883 |
Solve law Substitute known values and solve N 6 Discussion Note that Fandxhave opposite signs because they are in opposite restoring force is up and the displacement is down | [
-0.0421455055475235,
0.08531245589256287,
0.13915471732616425,
0.017619820311665535,
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] | 8,884 |
Also note that the car would oscillate up and down when the person got in if it were not for damping to frictional provided by shock absorbers | [
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] | 8,885 |
Bouncing cars are a sure sign of bad shock absorbers Energy in Law of Deformation In order to produce a deformation work must be done | [
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] | 8,886 |
That is a force must be exerted through a distance whether you pluck a guitar string or compress a car spring | [
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] | 8,887 |
If the only result is deformation and no work goes into thermal sound or kinetic energy then all the work is initially stored in the deformed object as some form of potential energy | [
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] | 8,888 |
The potential energy stored in a spring 2kx2 | [
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] | 8,889 |
Here we generalize the idea to elastic potential energy for a deformation of any system that can be described by law | [
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] | 8,890 |
Hence 2kx2 wherePEelis theelastic potential energy stored in any deformed system that obeys law and has a displacement x from equilibrium and a force constant k It is possible to find the work done in deforming a system in order to find the energy stored | [
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] | 8,891 |
This work is performed by an applied forceFapp | [
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] | 8,892 |
The applied force is exactly opposite to the restoring force and so Figure 16 6 shows a graph of the applied force versus deformation xfor a system that can be described by law | [
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] | 8,893 |
Subsets and Splits