01-04-2020-Дедушенко И.С.Обучение чтению и устной речи на английском языке (1171845), страница 7
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Mass into EnergyEinstein showed that mass itself could be converted to andfrom energy, according to his celebrated equation E = mc2, inwhich c is the speed of light. So mass is spoken of as simplyanother form of energy, and it is valid to measure it in units ofjoules. The mass of a 15-gram pencil corresponds to about 1.3 ×× 1015 J. The issue is largely academic in the case of the pencil,because very violent processes such as nuclear reactions arerequired in order to convert any significant fraction of an object’smass into energy. Cosmic rays, however, are continually strikingyou and your surroundings and converting part of their energy ofmotion into the mass of newly created particles.
A single highenergy cosmic ray can create a “shower” of millions ofpreviously nonexistent particles when it strikes the atmosphere.Even today, when the energy concept is relatively mature andstable, a new form of energy has been proposed based onobservations of distant galaxies whose light began its voyage tous billions of years ago. Astronomers have found that theuniverse’s continuing expansion, resulting from the Big Bang,has not been decelerating as rapidly in the last few billion yearsas would have been expected from gravitational forces. Theysuggest that a new form of energy may be at work.(1077)Text 4. Conservation of MomentumIn many subfields of physics these days, it is possible to readan entire issue of a journal without ever encountering an equationinvolving force or a reference to Newton’s laws of motion. In thelast hundred and fifty years, an entirely different framework hasbeen developed for physics, based on conservation laws.The new approach is not just preferred because it is infashion.
It applies inside an atom or near a black hole, whereNewton’s laws do not.42Even in everyday situations the new approach can be superior.We have already seen how perpetual motion machines could bedesigned that were too complex to be easily debunked byNewton’s laws. The beauty of conservation laws is that they tellus something must remain the same, regardless of the complexityof the process.So far we have discussed only two conservation laws, thelaws of conservation of mass and energy. Is there any reason tobelieve that further conservation laws are needed in order toreplace Newton’s laws as a complete description of nature? Yes.Conservation of mass and energy do not relate in any way to thethree dimensions of space, because both are scalars. Conservationof energy, for instance, does not prevent the planet earth fromabruptly making a 90-degree turn and heading straight into thesun, because kinetic energy does not depend on direction.
A newconserved quantity, called momentum, which is a vector, isdeveloped.(1208)Discussion to the texts1. Cosmic rays are particles from outer space, mostly protonsand atomic nuclei, which are continually bombarding the earth.Most of them, although they are moving extremely fast, have nodiscernible effect even if they hit your body, because theirmasses are so small. Their energies vary, however, and a verysmall minority of them has extremely large energies. In somecases the energy is as much as several Joules, which iscomparable to the KE of a well thrown rock! If you are in aplane at a high altitude and are so incredibly unlucky as to be hitby one of these rare ultra-high-energy cosmic rays, what wouldyou notice, the momentum imparted to your body, the energydissipated in your body as heat, or both? Base your conclusionson numerical estimates, not just random speculation.
(At thesehigh speeds, one should really take into account the deviations43from Newtonian physics described by Einstein’s special theoryof relativity.)2. Show that for a body made up of many equal masses, theequation for the center of mass becomes a simple average of allthe positions of the masses.3. A refrigerator has coils in back that get hot, and heat ismolecular motion.
These moving molecules have both energy andmomentum. Why doesn’t the refrigerator need to be tied to thewall to keep it from recoiling from the momentum it loses out theback?4. Good pool players learn to make the cue ball spin, whichcan cause it not to stop dead in a head-on collision with astationary ball. If this does not violate the laws of physics, whathidden assumption was there in the example above?5. A jet plane traveling due east at 300 km/hr collides with ajumbo jet which was heading southwest at 150 km/hr. The jumbojet’s mass is 5.0 times greater than that of the jet plane.
Whenthey collide, the jet plane sticks into the fuselage of the jumbo jet,and they fall to earth together. Their engines stop functioningimmediately after the collision. On a map, what will be thedirection from the location of the collision to the place where thewreckage hits the ground? (Give an angle.)6. Suppose that you were trying out different equations forkinetic energy to see if they agreed with the experimental data.Based on the meaning of positive and negative signs of velocity,why would you suspect that proportionality to mv would be lesslikely than mv2?7. If a pendulum is released at A and caught by a peg as itpasses through the vertical, B. To what height will the bob rise onthe right?8.
Can kinetic energy ever be less than zero? Explain.44SUPPLEMENTARY READING TO UNIT 3Read, translate and render the texts. Discuss the questionsgiven below.Text 1. Period, Frequency, and AmplitudeWe have discussed how to measure how fast somethingvibrates, but not how big the vibrations are. The general term forthis is amplitude, A. The definition of amplitude depends on thesystem being discussed, and two people discussing the samesystem may not even use the same definition. In the example ofthe block on the end of the spring, the amplitude will bemeasured in distance units such as cm. One could work in termsof the distance traveled by the block from the extreme left to theextreme right, but it would be somewhat more common inphysics to use the distance from the center to one extreme. Theformer is usually referred to as the peak-to-peak amplitude, sincethe extremes of the motion look like mountain peaks or upsidedown mountain peaks on a graph of position versus time.In other situations we would not even use the same units foramplitude.
The amplitude of a child on a swing would mostconveniently be measured as an angle, not a distance, since herfeet will move a greater distance than her head. The electricalvibrations in a radio receiver would be measured in electricalunits such as volts or amperes.(937)45Text 2. Energy in VibrationsOne way of describing the collapse of the bridge is that thebridge kept taking energy from the steadily blowing wind andbuilding up more and more energetic vibrations. In this section,we discuss the energy contained in a vibration, and in thesubsequent sections we will move on to the loss of energy and theadding of energy to a vibrating system, all with the goal ofunderstanding the important phenomenon of resonance.Going back to our standard example of a mass on a spring, wefind that there are two forms of energy involved: the potentialenergy stored in the spring and the kinetic energy of the movingmass.
We may start the system in motion either by hitting themass to put in kinetic energy by pulling it to one side to put inpotential energy. Either way, the subsequent behavior of thesystem is identical. It trades energy back and forth betweenkinetic and potential energy. (We are still assuming there is nofriction, so that no energy is converted to heat, and the systemnever runs down.)The most important thing to understand about the energycontent of vibrations is that the total energy is proportional to thesquare of the amplitude.(958)Discussion to Unit 31.
Consider the same pneumatic piston described in the previousproblem, but now imagine that the oscillations are not small. Sketcha graph of the total force on the piston as it would appear over thiswider range of motion. For a wider range of motion, explain why thevibration of the piston about equilibrium is not simple harmonicmotion, and sketch a graph of x vs t, showing roughly how the curveis different from a sine wave. (Hint: Acceleration corresponds to thecurvature of the x–t graph, so if the force is greater, the graph shouldcurve around more quickly.)462.
3 Archimedes’ principle states that an object partly orwholly immersed in fluid experiences a buoyant force equal tothe weight of the fluid it displaces. For instance, if a boat isfloating in water, the upward pressure of the water (vector sum ofall the forces of the water pressing inward and upward on everysquare inch of its hull) must be equal to the weight of the waterdisplaced, because if the boat was instantly removed and the holein the water filled back in, the force of the surrounding waterwould be just the right amount to hold up this new “chunk” ofwater.
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