01-04-2020-Дедушенко И.С.Обучение чтению и устной речи на английском языке (1171845), страница 5
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The usual physics terminology for motionthat repeats itself over and over is periodic motion, and the timerequired for one repetition is called the period, T. (The symbol P28is not used because of the possible confusion with momentum.)One complete repetition of the motion is called a cycle.We are used to referring to short-period sound vibrations as“high” in pitch, and it sounds odd to have to say that high pitcheshave low periods. It is therefore more common to discuss therapidity of a vibration in terms of the number of vibrations persecond, a quantity called the frequency, f.Since the period is the number of seconds per cycle and thefrequency is the number of cycles per second, they are reciprocalsof each other, f = 1/T.(1328)Text 3C. Simple Harmonic MotionRead the text and give a short summary.Why are sine-wave vibrations so common? If we actuallyconstruct the mass-on-a-spring system and measure its motionaccurately, we will find that its x–t graph is nearly a perfect sinewave shape.
(We call it a “sine wave” or “sinusoidal” even if it isa cosine, or a sine or cosine shifted by some arbitrary horizontalamount.) It may not be surprising that it is a wiggle of thisgeneral sort, but why is it a specific mathematically perfectshape? Why is it not a sawtooth shape or some other shape?The mystery deepens as we find that a vast number ofapparently unrelated vibrating systems show the samemathematical feature. A tuning fork, a sapling pulled to one sideand released, a car bouncing on its shock absorbers, all thesesystems will exhibit sine-wave motion under one condition: theamplitude of the motion must be small.It is not hard to see intuitively why extremes of amplitudewould act differently.
For example, a car that is bouncing lightlyon its shock absorbers may behave smoothly, but if we try todouble the amplitude of the vibrations the bottom of the car maybegin hitting the ground. (Although we are assuming forsimplicity that energy is never dissipated, this is clearly not a very29realistic assumption in this example. Each time the car hits theground it will convert quite a bit of its potential and kineticenergy into heat and sound, so the vibrations would actually dieout quite quickly, rather than repeating for many cycles as shownin the figure.)The key to understanding how an object vibrates is to knowhow the force on the object depends on the object’s position.
If anobject is vibrating to the right and left, then it must have aleftward force on it when it is on the right side and a rightwardforce when it is on the left side.(1467)Tasks to perform1. Find an equation for the frequency of simple harmonicmotion in terms of k and m.2. Many single-celled organisms propel themselves throughwater with long tails, which they wiggle back and forth. (Themost obvious example is the sperm cell.) The frequency of thetail’s vibration is typically about 10–15 Hz. To what range ofperiods does this range of frequencies correspond?3. (a) Pendulum 2 has a string twice as long as pendulum 1. Ifwe define x as the distance traveled by the bob along a circleaway from the bottom, how does the k of pendulum 2 comparewith the k of pendulum 1? Give a numerical ratio.
(Hint: the totalforce on the bob is the same if the angles away from the bottomare the same, but equal angles do not correspond to equal valuesof x.)(b) Based on your answer from part (a), how does the periodof pendulum 2 compare with the period of pendulum 1? Give anumerical ratio.30Grammar and vocabulary revisionEx. 1. Translate the following sentences into Russian,paying attention to “following” and “followed”.1. The calculations following the experiment gave accurateresults.2. The lecture followed by the demonstration of experimentswas a success.3. The practical studies following the theoretical ones were ofgreat use.4.
Following this new method they achieved good results.5. 108 is a number expressed by one followed by eight zeroes.6. Experiments of many other scientists followingRutherford’s research proved his predictions.Ex. 2. Insert the right preposition: “at”, “under”.1.
This assumption holds true … certain conditions.2. The experiment has been carried our … normal pressure.3. The rate … which the speed of an object changes is calledacceleration.4. The body is kept … normal pressure.5. A state of equilibrium is achieved … certain circumstances.6. The collision of molecules become violent … hightemperatures.7. The Hall electric current increases … the action of amagnetic field.8. Gases … normal conditions are poor conductors ofelectricity.Ex. 3. Translate these sentences into Russian payingattention to the Gerund forms and functions.1. Solving physical problems is a difficult job.2. They spoke of the results having been achieved.3. Their having obtained the data is very important.314.
His knowing physics well did not surprise us.5. On measuring the current they put down the results.6. Besides putting forward a new theory he succeeded inproving it experimentally.Ex. 4. Translate these sentences into English payingattention to the Gerund forms and functions.1. Стоит обсудить проблему субатомных частицподробно.2. Мы не можем не попытаться дать определение этимпонятиям.3.
Не стоит повторять эти измерения без высокочувствительного прибора.4. Нельзя не признать ценность этих исследований.5. Не имеет смысла перечислять достоинства этой работы.6. Стоит учесть все недостатки этой работы.32SUPPLEMENTARY READING TO UNIT 1Read the following texts with a dictionary and answer thequestions.Text 1. Forces Have No Perpendicular EffectsSuppose you could shoot a rifle and arrange for a secondbullet to be dropped from the same height at the exact momentwhen the first left the barrel. Which would hit the ground first?Nearly everyone expects that the dropped bullet will reach thedirt first, and Aristotle would have agreed. Aristotle would havedescribed it like this.
The shot bullet receives some forced motionfrom the gun. It travels forward for a split second, slowing downrapidly because there is no longer any force to make it continue inmotion. Once it is done with its forced motion, it changes tonatural motion, i.e. falling straight down. While the shot bullet isslowing down, the dropped bullet gets on with the business offalling, so according to Aristotle it will hit the ground first.A bullet is shot from a gun, and another bullet issimultaneously dropped from the same height. 1.
Aristotelianphysics says that the horizontal motion of the shot bullet delaysthe onset of falling, so the dropped bullet hits the ground first.2. Newtonian physics says the two bullets have the same verticalmotion, regardless of their different horizontal motions.Luckily, nature isn’t as complicated as Aristotle thought! Toconvince yourself that Aristotle’s ideas were wrong andneedlessly complex, stand up now and try this experiment. Takeyour keys out of your pocket, and begin walking briskly forward.33Without speeding up or slowing down, release your keys and letthem fall while you continue walking at the same pace.
You havefound that your keys hit the ground right next to your feet. Theirhorizontal motion never slowed down at all, and the whole timethey were dropping, they were right next to you. The horizontalmotion and the vertical motion happen at the same time, and theyare independent of each other.
Your experiment proves that thehorizontal motion is unaffected by the vertical motion, but it’salso true that the vertical motion is not changed in any way by thehorizontal motion. The keys take exactly the same amount oftime to get to the ground as they would have if you simplydropped them, and the same is true of the bullets: both bullets hitthe ground simultaneously.These have been our first examples of motion in more than onedimension, and they illustrate the most important new idea that isrequired to understand the three-dimensional generalization ofNewtonian physics: Forces have no perpendicular effects.
When aforce acts on an object, it has no effect on the part of the object’smotion that is perpendicular to the force.In the examples above, the vertical force of gravity had noeffect on the horizontal motions of the objects. These wereexamples of projectile motion, which interested people likeGalileo because of its military applications.
The principle is moregeneral than that, however. For instance, if a rolling ball isinitially heading straight for a wall, but a steady wind beginsblowing from the side, the ball does not take any longer to get tothe wall. In the case of projectile motion, the force involved isgravity, so we can say more specifically that the verticalacceleration is 9.8 m/s2, regardless of the horizontal motion.(2641)Text 2. Relationship to Relative MotionThese concepts are directly related to the idea that motion isrelative. Galileo’s opponents argued that the earth could not34possibly be rotating as he claimed, because then if you jumpedstraight up in the air you wouldn’t be able to come down in thesame place.
Their argument was based on their incorrectAristotelian assumption that once the force of gravity began toact on you and bring you back down, your horizontal motionwould stop. In the correct Newtonian theory, the earth’sdownward gravitational force is acting before, during, and afteryour jump, but has no effect on your motion in theperpendicular (horizontal) direction. If Aristotle had beencorrect, then we would have a handy way to determine absolutemotion and absolute rest: jump straight up in the air, and if youland back where you started, the surface from which youjumped must have been in a state of rest. In reality, this testgives the same result as long as the surface under you is aninertial frame.
If you try this in a jet plane, you land back on thesame spot on the deck from which you started, regardless ofwhether the plane is flying at 500 miles per hour or parked onthe runway. The method would in fact only be good fordetecting whether the plane was accelerating.(1038)Text 3. Newton’s Laws in Three DimensionsIt is now fairly straightforward to extend Newton’s laws tothree dimensions: Newton’s first law: If all three components ofthe total force on an object are zero, then it will continue in thesame state of motion.Newton’s second law: The components of an object’sacceleration are predicted by the equations ax = Fx,total/m, ay == Fy,total /m, and az = Fz,total /m.Newton’s third law: If two objects A and B interact via forces,then the components of their forces on each other are equal andopposite.For example: An object is initially at rest.
Two constant forcesbegin acting on it, and continue acting on it for a while. As35suggested by the two arrows, the forces are perpendicular, and therightward force is stronger. What happens?Aristotle believed, and many students still do, that only oneforce can “give orders” to an object at one time. They thereforethink that the object will begin speeding up and moving in thedirection of the stronger force. In fact the object will move alonga diagonal. In the example the object will respond to the largerightward force with a large acceleration component to the right,and the small upward force will give it a small accelerationcomponent upward.
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