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Understanding Force, Pressure, Energy, Power and Intensity: Concepts in Physics - Prof. Ro, Study notes of Physics

Belmont UniversityPhysics
Prof. Robert H. Magruder

Operational definitions and explanations of various physical concepts including velocity, force, pressure, work, energy, and power. It discusses the importance of these concepts in the context of sound and music, and explores how instruments generate specific pressure changes to produce music. The document also covers the concepts of kinetic and potential energy, and the ability of energy to switch forms and be transferred between systems.

Typology: Study notes

Pre 2010

Uploaded on 12/12/2009

absentvirtue
absentvirtue 🇺🇸

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Force, Pressure, Energy, Power and Intensity
There some operational definitions of quantities we need to consider first. First is
distance. We are of course familiar with this as it is simply the displacement of a an
object from a reference point. Here we will use the metric system or the MKS system
and the unit for distance is the meter. The second is velocity(or speed) which is the rate
of change with distance or how fast displacement from a reference position changes with
time. Here we will sue the terms velocity and speed interchangeably.
The average velocity is the distance traveled divided by time of travel.
v
ave
distan ce
time
The units of velocity are meter/second or m/s.
We are familiar with this term from driving. For example if you travel 200 miles in four
hours your average velocity or speed is 50 miles per hour. Conversely, if we want to
know how far something traveled given the speed and time of travel we can find the
distance.
distan ce velocity x time
While at first glance not related to sound we must consider that waves move or travel. As
a result waves travel with a velocity v. We will find this to be an important consideration
in due time.
Force
The concept of force is our way of describing the reality of objects behaving
in a particular manner. We do not see forces but infer their presence from the behavior
of objects. Force is that which causes a change in motion. The tension in a rope pulling
a wagon furnishes the force but what we observe is the behavior of the rope due to the
presence of the force in the rope and we observe the effect of the force on the wagon.
The force causes the wagon to move. It affects a change. The rope itself is not the force
but merely the conduit for the force. As another example we do not see the force due to
gravity as it pulls an object dropped from a height to the ground, yet we can observe the
1.
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Force, Pressure, Energy, Power and Intensity There some operational definitions of quantities we need to consider first. First is distance. We are of course familiar with this as it is simply the displacement of a an object from a reference point. Here we will use the metric system or the MKS system and the unit for distance is the meter. The second is velocity(or speed) which is the rate of change with distance or how fast displacement from a reference position changes with time. Here we will sue the terms velocity and speed interchangeably. The average velocity is the distance traveled divided by time of travel.  vavedis tan ce time The units of velocity are meter/second or m/s. We are familiar with this term from driving. For example if you travel 200 miles in four hours your average velocity or speed is 50 miles per hour. Conversely, if we want to know how far something traveled given the speed and time of travel we can find the distance.  dis tan cevelocity x time While at first glance not related to sound we must consider that waves move or travel. As a result waves travel with a velocity v. We will find this to be an important consideration in due time. Force The concept of force is our way of describing the reality of objects behaving in a particular manner. We do not see forces but infer their presence from the behavior of objects. Force is that which causes a change in motion. The tension in a rope pulling a wagon furnishes the force but what we observe is the behavior of the rope due to the presence of the force in the rope and we observe the effect of the force on the wagon. The force causes the wagon to move. It affects a change. The rope itself is not the force but merely the conduit for the force. As another example we do not see the force due to gravity as it pulls an object dropped from a height to the ground, yet we can observe the

behavior of the falling object. Forces can also be balanced. While you are sitting in a chair reading these written words gravity is pulling you down. At the same time the floor is holding you up. The forces in this example are balanced. Forces are not a property of an object but are applied to an object. The presence of forces can be ascertained and measured by observing their effect on objects. This ability to measure forces and predict the results of the presence of forces makes the abstract concept of forces useful. Forces have both magnitude and direction. Both of these descriptions of magnitude and direction are important. Consider the case of two students pushing a chair across the floor in a dorm room. If both students push with equal force but in exactly opposite directions, what happens? The chair remains motionless. Note that this does not mean the forces do not exist but only the sum of the forces is zero due to the fact that each is trying to move the object in opposite directions with the same magnitude. Again an example of balanced forces. On the other hand if the students push in the same direction then the chair will move. How fast the chair is moved will depend on the magnitude of the forces and any retarding force like the force of friction or drag of the chair moving across the floor. The motion is described by Newton’s Laws. While they are very important to how our world works we will not discuss them here. Forces are used to effect changes in musical instruments for us to hear sound. A guitarist strings the string with a force or flutist blows into a flute. In both cases a mechanical force is sued to cause something to vibrate. In the mks system of units the unit of force is the Newton. Pressure Pressure is force acting perpendicular to an area divided by the area over which the force is applied or force per unit area.  pressureforce area The units of force are newtons/m^2. A N/m^2 is a pascal or Pa. For example lets find the pressure on the floor of a person whose mass is 80 kg (approximately a 176 lb person). This mass corresponds to a weight of 784 N. If each foot of our example person is ~0.3 m by 0.10 m or approximately a size 11 shoe, then the

 workforce x dis tan ce The units for work are newtons times meters or Nm. The newton-meter is called a joule (J). In the mks system of measurements the joule is the unit of energy and work. While at first glance just as with pressure, energy does not appear to be not important to our study, consider how a musician plays a guitar. The musician exerts a force on string causing the string to move thereby doing work on the string and putting energy into the string. The motion of the string is the starting point of a note. The string can then in turn do work on the body of the guitar transferring energy to the guitar body. The body of the guitar can do work on the air and put energy into the air. This energy can propagate out in the form of sound waves. Clearly we have simplified the steps at this point to paint a bigger picture. We will wait and fill in those the details later. We can note here though that work is done on a system and that the energy put into the system transfers to other systems. This is a very important property of energy, i.e. its ability to exist and interchange between various forms. One can make a simple analogy with money. Money allows its bearer to effect certain changes in society. Money (or the concept of money) can exist in several forms. You can use the money you have to make things happen and you have to work to get money. You can have cash in your pocket, you can put the money in a checking account, or you can put the money in a savings account, which can not be readily accessed. Money like energy can be readily interchanged between these various forms. The money in your pocket can be put into the bank or money can be removed from the bank. Either way the money is changing forms as you move it around. There several forms energy can take but there are two we need to have some knowledge of for this class. Kinetic energy is the energy associated with motion, while potential energy is stored energy that can be released at arbitrary times when needed. An example of potential energy is energy stored in a battery. An example of kinetic energy is a baseball that has been thrown. The baseball has energy based on the fact that it is moving and can cause something to happen. The battery may sit there and do nothing until a switch is

turned and then the battery supplies energy to make something happen like a current flow. One very important aspect of energy is its ability to switch forms. In particular, for this class, energy can be stored in a simple harmonic oscillator. A useful model of a simple harmonic oscillator system is a mass attached to a spring. When the spring is displaced but not released, work is done on the system and the energy resulting from the work is stored as potential energy. (For example when you stretch a rubber band you but potential energy into the rubber band by doing work.) When the spring is released the potential energy stored is converted to kinetic energy as the mass moves. In fact the oscillating motion of a mass on a spring is due to the interchange of energy between kinetic and potential. If it were not for friction removing energy from the system the mass would oscillate indefinitely. A second very important aspect of energy is the ability to be passed from one system to another. Returning to our money analogy, if you perform some useful task for your employer they give you money, i.e., work was done and your energy was increased from by an outside source. On the other hand when you pay a bill negative work is done by your system and your energy as measured by the amount of money you have decreases. In either case, work has been done and the energy of the system is changed, in one case you the energy is increased and in one case the energy is decreased. Money was transferred from one system to another. This ability to transfer energy is important for this course. For example energy is put into the string on a guitar by the guitarist when they apply a force on the string by striking (plucking, strumming, etc.) it. This string must somehow do work to create sound energy using the body of the guitar. The string does this by executing small pushes on the guitar top therefore doing work on the guitar top and passing energy from the string to the guitar top. The guitar top in turn does work on the air and puts energy in to the air. The energy transferred to air does work on our eardrums and the energy is passed to our ears. We in turn interpret this energy as sound. We will discuss in greater detail these topics during throughout the semester.

As a side note the more power applied to the speaker in general the louder the sound. However speakers are not all the same and as we shall se loudness level is not the same for all people. The amount of acoustical power emitted by the speaker is related to the power used to drive the speaker but is not linear and various speakers have different efficiencies of conversion of applied electrical power to acoustical power. The range of efficiencies of speakers can be quite large. Here we need to note that efficiency of a speaker is not like the normal use of the word efficiency. Low efficiency speakers can be quite good and expensive and so can high efficiency speakers. It has to do with their way of converting electrical energy into acoustical energy not how good or bad they are. Example of power : A 100 watt light bulb uses 100 joules per second of electrical power. In 20 seconds it uses 2000 joules of energy. Note the 100 watts is the electrical power not the optical power emitted by the source. Sound is emitted by speakers in the form of waves of pressure changes. These sound waves spread out as they move away from the source. This means the energy does not stay in one place but because it is a wave it spreads out uniformly in all directions in general. Later we will see that waves can be made spread in specified ways as opposed to all directions. However the key point is that the energy is spread uniformly across the wavefront and as the wavefront spreads so does the energy. One can draw an analogy with blowing up a balloon. The wavefront would be represented by the surface of the balloon. If we measure the thickness of the balloon before we blow it up and compare it to the thickness of the balloon as we blow it up, we would observe the balloon spreads out in more or less all directions and that the thickness of the balloon decreases as the balloon becomes larger or spreads out. The exact same thing happens with the energy. As the wave spreads out, the energy available at any point on the wavefront decreases. As the balloon is blown up the surface area of the balloon increases and the thickness (or energy in the analogy) decreases. So we come to perhaps the most important quantity and that is intensity.

Intensity is a measure of how much energy per unit time is available at a specific point. Area Power IntensityWhere the power is the power of the source and the area is the area the power is spread over. It is intensity that determines our ability to hear and see. What this means is that for use to hear or see we need to have a certain amount of energy in a given time impinge the sensor region of the ear or eye. As we move away from a source the waves it is emitting spread and the energy at any point of the wavefront decreases. Again this is analogous to the balloon material decreasing in thickness as we blow up the balloon. In general we expect the spread of energy to be uniform or evenly distributed over the entire wave front. The ability of the wave to do something at any particular point is related to how much energy there is at that point, not how much energy the total wave has because the total wave is not at that point. Only the part of the wave that is present at a point at a given time will influence what happens at that point. Intensity measures the energy per unit area per unit time. Lets take our money analogy a little farther. Suppose we have $100 total and we spend at $10 per hour spend rate. Now lets divide our spend rate equally between 5 people. This means each person can spend $2 per hour. As the people spread out and we are assuming that they do, each one can only purchase $2 per hour worth of goods where they are because that is all the energy per unit time they have. So while there is $10 per hour at the source as the people spread out each person has only $2 per hour to spend to cause something to happen. We can put this example into a table to help see what the results are: Quantity Amount Result energy 100 dollars Total amount of energy we have power 10 dollars per hour This is how much energy we have at a particular time

Sound energy spreads out evenly. As the surface over which the energy is spread increases then the intensity decreases. For waves there is wave property called the inverse square law that describes mathematically this process. This property will be discussed in more detail later. Summary In summary the energy of a source tells us what the source is capable of producing. What it does not tell us is how long that it will take to produce the amount of work. Power tells us how fast the source can produce the energy to effect a change and in that sense is amore important measure to ascertain the effect a source will have. The intensity tells us how much power is available where we need it. Because energy transmitted as waves like sound and light the ability to effect change not only depends on the power of the source but also on how much the energy has spread out. It is only the energy at a specific point and at a specific time that will affect the change. Power is the energy being used or supplied per unit time. Time Energy Power  Where the energy is the energy being emitted or received and the time the source is time of emission or reception of the energy. Intensity is a measure of how much energy per unit time is available at a specific point. Area Power Intensity  Where the power is the power of the source and the area is the area the power is spread over.