Английский - 2курс_3семестр_physics

PROBLEM SOLVING

1.An object is observed to be moving at constant speed in a certain direction. Can you conclude that no forces are acting on it? Explain.

2.A car is normally capable of an acceleration of 3 m/s2. If it is towing a trailer with half as much mass as the car itself, what acceleration cat it achieve?

3.(a) Let T be the maximum tension that an elevator‘s cable can withstand

without breaking, i.e., the maximum force it can exert. If the motor is programmed to give the car an acceleration ɑ, what is the maximum mass that the car can have, including passengers, if the cable is not to break?

(b) Interpret the equation you derived in the special cases of ɑ = 0 and of a downward acceleration of magnitude ɡ.

(―Interpret‖ means to analyze the behavior of the equation, and connect that to reality.)

4. A helicopter of mass m is taking off vertically. The only forces acting on it are the earth‘s gravitational force and the force, Fair, of the air pushing up on the propeller blades.

(a)If the helicopter lifts off at t = 0, what is its vertical speed at time t?

(b)Plug numbers into your equation from part a, using m = 2300 kg, Fair = 27000 N, and t = 4.0 s.

5. In the 1964 Olympics in Tokyo, the best men‘s high jump was 2.18 m. Four years later in Mexico City, the gold medal in the same event was for a jump of 2.24 m. Because of Mexico City‘s altitude (2400 m), the acceleration of gravity there is lower that in Tokyo by about 0.01 m/s2. Suppose a high-jumper has a mass of 72 kg.

(a)Compare his mass and weight in the two locations.

(b)Assume that he is able to jump with the same initial vertical velocity in both locations, and that all other conditions are the same except for gravity. How much higher should he be able to jump in Mexico City?

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CHAPTER II. GRAVITY

UNIT 9

Kepler‟s Laws

Read the text and be ready to answer teacher’s questions.

Newton wouldn‘t have been able to figure out why the planets move the way they do if it hadn‘t been for the astronomer Tycho Brahe (1546-1601) and his protégé Johannes Kepler (1571-1630), who together came up with the first simple and accurate description of how the planets actually do move. The difficulty of their task is suggested by figure 1, which shows how the relativity simple orbital motions of the earth and Mars combine so that as seen from earth Mars appears to be staggering in loops like a drunken sailor.

Figure 1. As the Earth and Mars revolve around the sun at different rates, the combined effect of their motions makes Mars appear to trace a strange, looped path across the background of the distant stars.

Brahe, the last of the great naked-eye astronomers, collected extensive data on the motions of the planets over a period of many years, taking the giant step from the previous observations‘ accuracy of about 10 minutes of arc (10/60 of a degree) to an unprecedented 1 minute. The quality of his work is all the more remarkable considering that his observatory consisted of four giant brass protractors mounted upright in his castle in Denmark. Four different observers

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would simultaneously measure the position of a planet in order to check for mistakes and reduce random errors.

With Brahe‘s death, it fell to his former assistant Kepler to try to make some sense out of the volumes of data. Kepler, in contradiction to his late boss, had formed a prejudice, a correct one as it turned out, in favor of the theory that the earth and planets revolved around the sun, rather than the earth staying fixed and everything rotating about it. Although motion is relative, it is not just a matter of opinion what circles what. The earth‘s rotation and revolution about the sun make it a noninertial reference frame, which causes detectable violations of Newton‘s laws when one attempts to describe sufficiently precise experiments in the earth-fixed frame. Although such direct experiments were not carried out until the 19th century, what convinced everyone of the sun-centered system in the 17th century was that Kepler was able to come up with a surprisingly simple set of mathematical and geometrical rules for describing the planets‘ motion using the sun-centered assumption. After 900 pages of calculations and many false starts and dead-end ideas, Kepler finally synthesized the data into the following three laws:

Kepler‟s elliptical orbit law

The planets orbit the sun in elliptical orbits with the sun at one focus.

Kepler‟s equal-area law

The line connecting a planet to the sun sweeps out equal areas in equal amounts of time.

Kepler‟s law of periods

The time required for a planet to orbit the sun, called its period, is proportional to the long axis of the ellipse raised to the 3/2 power. The constant of proportionality is the same for all the planets.

Put 10 questions to the text and let other students answer them.

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True or false?

1)Newton came up with the first simple and accurate description of how the planets actually do move.

2)Brahe collected extensive data on the motions of the planets over a period of many years.

3)The quality of Brahe‘s work is all the more remarkable considering that his observatory consisted of four giant brass protractors mounted upright in his castle in Denmark.

4)With Kepler‘s death, it fell to his former assistant Brahe to try to make

some sense out of the volumes of data.

5)The planets orbit the Mars in elliptical orbits with the sun at one focus.

Matching

Find synonyms for the following words. tell, get, have, go, begin

Express the main idea of the text.

What questions would you like to ask Kepler or Brahe?

Write a summary to the text.

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GRAMMAR

The Infinitive

We use the to – infinitive:

after verbs such as advise, agree, decide, expect, hope, manage, offer, promise, refuse, seem, want, etc.

He refused to answer my question.

 after be + adjective such as glad, happy, nice, sorry, etc.

It is nice to be back home.

Jack will be glad to see you.

after some verbs such as know, learn, remember, ask, want to know, etc. when there is a question word (who, what, where, how, etc.) after

them. „Why‟ is not followed by an infinitive, but by a subject + verb.

I don‘t know how to answer this question. but I didn‘t know why he was crying.

 with too and enough.

It‘s too cold to go outside.

Joe isn‘t old enough to vote.

 to express purpose.

I went to the florist‘s to buy some flowers.

We use the bare infinitive:

 after modal verbs (can, may, must, etc.).

You can go home now.

 after the verbs let and make.

My parents let me have a party for my birthday last month.

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The Subject of the Infinitive

 When the subject of the main verb and the subject of the infinitive is the same, then the subject of the infinitive is omitted.

I would like to stay here. (The subject of the main verb and the infinitive is

―I‖.)

When the subject of the infinitive is different from the subject of the main verb, then the subject of the infinitive is not omitted. The

subject of the Infinitive can be a name (Mark), a noun (the boys) or an object pronoun (me, you, them, etc.) and goes before the infinitive.

Lucy

her

EXERCISES

1. Fill in the gaps with one of the verbs from the list in the correct form.

climb, help, go, open, buy, post, stay, take, wash, ask

1)I think I will …buy… some flowers for my mother.

2)Bill went to the post office … some letters.

3)Let me … you with your homework.

4)I want … a mountain before I‘m thirty.

5)We must … the car today. It‘s very dirty.

6)He‘s too young … in the house alone.

7)I don‘t know how … the windows in this room.

8)I couldn‘t … on holiday last summer.

9)Can I … you a question, please?

10)They made her … the money out of the safe.

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2. Rephrase the following, as in the example.

1) You must help me.

I want you to help me.

2)They mustn‘t leave now. I don‘t want…

3)She must eat her dinner.

I want …

4)He must visit Aunt Linda.

I want …

5)You mustn‘t talk to strangers. I don‘t want …

6)Fiona mustn‘t go on holiday by herself. I don‘t want …

7)They must do their homework now.

I want …

8)You must go to bed now.

I want …

3. Fill in the gaps with one of the verbs from the list in the correct form of the

infinitive.

be – leave – do – make – meet – tell

1)I really don‘t know what …to do… .

2)You mustn‘t … anyone about this.

3)I can … my own clothes.

4)I want you … quiet.

5)I don‘t think the boss will let me … earlier today.

6)I‘m pleased … you.

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4. Put the verbs in brackets into the correct form of the infinitive.

Dear Emma,

I‘m writing (1) …to invite… (invite) you to my birthday party next

Saturday.

As you know, I‘ll be sixteen, so this is going to be a very special occasion for me. I‘ve invited almost all of my friends and I really hope they‘ll all be able

(2) … (come). Could I (3) … (ask) you (4) … (help) me with the preparations, though? I would like (5) … (decorate) the house with white and pink flowers, but I‘m afraid I won‘t (6) … (have) time to do everything by myself. I‘ve also decided (7) … (make) my own cake and I‘ll certainly need your help with that!

Please write back soon and let me (8) … (know) if you can make it.

Best wishes,

Sandra

5. Rewrite the sentences using too or enough.

1)Don‘t wear a T-shirt. It‘s cold outside. It‘s too cold outside to wear a T-shirt.

2)It‘s very hot today. Let‘s go to the beach. It‘s …

3)We‘re not going to the party yet. It‘s early. It‘s …

4)You can‘t touch the ceiling. You‘re short. You‘re not …

5)You can buy this sweater. It‘s cheap.

This sweater is …

6)You can walk to school alone. You aren‘t too young. You‘re …

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UNIT 10

Newton‟s Law of Gravity

Read the text and be ready to state Newton’s law of gravity and give an example.

The proportionality F m/r2 for the gravitational force on an object of mass m only has a consistent proportionality constant for various objects if they are being acted on by the gravity of the same object. Clearly the sun‘s gravitational strength is far greater than the earth‘s, since the planets all orbit the sun and do not exhibit any very large accelerations caused by the earth (or by one another). What property of the sun gives it its great gravitational strength? Its great volume? Its great mass? Its great temperature? Newton reasoned that if the force was proportional to the mass of the object being acted on, then it would also make sense if the determining factor in the gravitational strength of the object exerting the force was its own mass. Assuming there were no other factors affecting the gravitational forces would be a proportionality constant. Newton called that proportionality constant G, so here is the complete form of the law of gravity he hypothesized.

Newton‟s law of gravity

separated by a distance r; r is not the radius of anything] Newton conceived of gravity as an attraction between any two masses in

the universe. The constant G tells us the how many newtons the attractive force is for two 1-kg masses separated by a distance of 1 m.

Although several of Newton‘s contemporaries had speculated that the force of gravity might be proportional to 1/r2, none of them, even the ones who had learned Newton‘s laws of motion, had had any luck proving that the resulting

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orbits would be ellipses, as Kepler had found empirically. Newton did succeed in proving that elliptical orbits would result from a 1/r2 force.

Newton also predicted that orbits in the shape of hyperbolas should be possible, and he was right. Some comets, for instance, orbit the sun in very elongated ellipses, but others pass through the solar system on hyperbolic paths, never to return. Just as the trajectory of a faster baseball pitch is flatter than that of a more slowly thrown ball, so the curvature of a planet‘s orbit depends on its speed. A spacecraft can be launched at relatively low speed, resulting in a circular orbit about the earth, or it can be launched at a higher speed, giving a more gently curved ellipse that reaches farther from the earth, or it can be launched at a very speed which puts it in an even less curved hyperbolic orbit. As you go very far out on a hyperbola, it approaches a straight line, i.e., its curvature eventually becomes nearly zero.

Newton also was able to prove that Kepler‘s second law was a logical consequence of his law of gravity. Newton‘s version of the proof is moderately complicated, but the proof becomes trivial once you understand the concept of angular momentum.

Self-check

Which of Kepler‘s laws would it make sense to apply to hyperbolic orbits?

Discussion Questions

AHow could Newton find the speed of the moon to plug in to a = v2/r?

BTwo projectiles of different mass shot out of guns on the surface of the earth at the same speed and angle will follow the same trajectories, assuming that air friction is negligible. (You can verify this by throwing two objects together from your hand and seeing if they separate or stay side by side.) What corresponding fact would be true for satellites of the earth having different masses?

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