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UNIT 7

Newton‟s Second and Third Laws

Read the text and be ready to discuss the given topic.

What about cases where the total force on an object is not zero, so that Newton‘s first law doesn‘t apply? The object will have an acceleration. The way we‘ve defined positive and negative signs of force and acceleration guarantees that positive forces produce positive

accelerations, and likewise for negative values. How much acceleration will it have? It will clearly depend on both the object‘s mass and on the amount of force.

Experiments with any particular object show that its acceleration is directly proportional to the total force applied to it. This may seem wrong, since we know of many cases where small amounts of force fail to move an object at all, and larger forces get it going. This apparent failure of proportionality actually results from forgetting that there is a frictional force in addition to the force we apply to move the object. The object‘s acceleration is exactly proportional to the total force on it, not to any individual force on it. In the absence of friction, even a very tiny force can slowly change the velocity of a very massive object.

Experiments also show that the acceleration is inversely proportional to the object‘s mass, and combining these two proportionalities gives the following way of predicting the acceleration of any object:

Newton‟s second law

ɑ = Ftotal / m ,

where

m is an object‘s mass

Ftotal is the sum of the forces acting on it, and

ɑ is the acceleration of the object‘s center of mass

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As with the first law, the second law can be easily generalized to include a much larger class of interesting situations:

Suppose an object is being acted on by two sets of forces, one set lying along the object‘s initial direction of motion and another set acting along a perpendicular line. If the forces perpendicular to the initial direction of motion cancel out, then the object accelerates along its original line of motion according to ɑ = Ftotal / m.

According to Newton‘s third law for every action there is an equal and opposite re-action. What does this mean? This means that for every force there is a reaction force that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard.

Let‘s study how a rocket works to understand Newton‘s Third Law.

The rocket‘s action is to push down on the ground with the force of its powerful engines, and the reaction is that the ground pushes the rocket upwards with an equal force.

Answer the following questions.

1.Who was the scientist who gave us the Laws of Motion?

2.How many Laws of Motion are there?

3.What is another name for the first law of motion?

4.Which law explains why we need to wear seatbelts?

5.Which law says that force is equal to mass times acceleration (F=MA)?

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6.Which law says that heavier objects require more force than lighter objects to move or accelerate them?

7.Which law explains how rockets are launched into space?

8.Which law says that for every action there is an equal and opposite reaction?

Discussion Questions

A Show that the Newton can be reexpressed in terms of three basic mks units as the combination kg·m/s.

B

What is wrong with the following statements?

(1)

―g is the force of gravity.‖

(2)

―Mass is a measure of how much space something takes up.‖

C

Criticize the following incorrect statements:

―If an object is at rest and the total force on it is zero, it stays at rest. There can also be cases where an object is moving and keeps on moving without having any total force on it, but that can only happen when there‘s no friction, like in outer space.‖

―If you shove a book across a table, friction takes away more and more of its force, until finally it stops.‖

D You hit a tennis ball against a wall. Explain any and all incorrect ideas in the following description of the physics involved: ―The ball gets some force from you when you hit it, and when it hits the wall, it loses part of that force, so it doesn‘t bounce back as fast. The muscles in your arm are the only things that a force can come from.‖

Make a summary of Newton’s laws of motion. State the main idea of his three laws.

Make a report about Newton’s laws of motion.

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GRAMMAR

Reported Speech

Direct Speech is the exact words someone said. We use quotation marks

(„‟) in direct speech. „I‟m very tired,‟ Mary said.

Reported Speech is the exact meaning of what someone said, but not the exact words. We do not use quotation marks in reported speech. We can

either use the word that after the introductory verb or we can omit it.

Mary said (that) she was very tired.

Say – Tell

We use the verb say:

both in direct and reported speech without the preposition to when it is not followed by the person being spoken to.

Jerry said, ‗I need some money.‘ Jerry said (that) he needed some money.

both in direct and reported speech with the preposition to when it is followed by the person being spoken to.

Jerry said to me, ‗I need some money.‘ Jerry said to me (that) he needed some

money.

in expressions such as: say good morning/afternoon, etc., say something, say one‘s prayers, say so, etc.

We use the verb tell without preposition to:

both in direct and reported speech when it is followed by the person we are talking to.

Jerry told me, ‗I need some money.‘ Jerry told me (that) he needed some

money. (NOT: Jerry told to me that he…)

in expressions such as: tell the truth, tell a lie, tell a secret, tell a story, tell the time, tell the difference, tell sb one‘s name, tell sb the way, etc.

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When the introductory verb is in the past indefinite, the verb tenses change as follows:

Direct Speech

 

Reported Speech

 

 

 

 

Present Indefinite

 

Past Indefinite

‗I want to find a better job,‘ he said.

 

He said he wanted to find a better job.

Present Continuous

 

Past Continuous

‗They are playing table tennis,‘ he said.

 

He said they were playing table tennis.

Present Perfect

 

Past Perfect

‗I have ordered a new fridge,‘ she said.

 

She said she had ordered a new fridge.

Past Indefinite

 

Past Perfect

‗Jack left the country,‘ they said.

 

They said Jack had left the country.

Future Indefinite

 

Conditional (would)

‗I will send you a letter,‘ he said.

 

He said he would send me a letter.

 

 

 

Certain words and time expressions change as follows:

Direct Speech

 

 

Reported Speech

 

 

 

tonight, today, this week/month/year,

 

that night, that day, that week/month/year,

etc.

 

etc.

 

 

 

now

 

then, at that time, at once, immediately

 

 

 

yesterday, last night/week/month/

 

the day before/the previous day, the

year, etc.

 

previous night/week/month/year, etc., the

 

 

night/week/month/year, etc. before

 

 

 

tomorrow, next week/month/year,

 

the day after/the following/next day, the

etc.

 

next/following week/month/year, etc.

 

 

 

two days/months/years, etc. ago

 

two days, months/years etc. before

 

 

 

this, these

 

that, those/the/some

 

 

 

here

 

there

 

 

 

come

 

go

 

 

 

 

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When the introductory verb is in the present indefinite, future indefinite or present perfect or when the sentence expresses something which is always true (general truth), there are no changes in the verb tenses in reported speech.

Direct Speech

Reported Speech

 

 

She says, ‗I don‘t like him.‘

She says (that) she doesn‟t like him.

‗It is cold in the Arctic,‘ said the

The teacher said (that) it is cold in the

teacher.

Arctic.

 

 

The past continuous, past perfect and past perfect continuous do not change in reported speech.

Certain modal verbs do not change in reported speech. These are would, could, might, should and ought to.

EXERCISES

1. Fill in the gaps with say or tell in the correct tense.

A Richard (1) …told… Sarah that he was having a party on Saturday night. He (2) … that it would start early but it would finish quite late. He (3) … her to bring her sister along as well. Sarah (4) … she was looking forward to going. Richard (5) … her he would probably call again on Friday to (6) … her the way to his house.

B‗What shall we do?‘ asked Carrie. ‗It‘s raining outside, so let‘s watch TV,‘ I (1) … . I turned on the TV and Carrie (2) … to me, ‗Look! That‘s my favourite programme. Let‘s watch it.‘ ‗To (3) … you the truth, I don‘t like it,‘ I

(4) … .

C‗Good morning, Mr Pearson,‘ (1) … Bella. ‗Good morning, Bella,‘ he replied. ‗I‘ve got lots of letters for you to type today,‘ he (2) … to her. ‗Alright,‘ Bella (3) … . ‗I‘ll type them after I finish writing this report for you.‘

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2. Turn from direct into reported speech.

1) ‗I can‘t find my bag,‘ she said.

She said (that) she couldn’t find her bag.

2)‗They are working in the garden,‘ he said.

3)‗We got married six months ago,‘ she said to us.

4)‗I‘ll go shopping tomorrow,‘ he said.

5)‗I bought a new car last week,‘ he said.

6)‗We aren‘t doing anything next week,‘ they said.

7)‗I can‘t go out tonight,‘ she said to me.

8)‗I forgot to pay the bill,‘ he said.

9)‗We‘ve bought you a present,‘ she said to me.

10)‗I‘ll phone you tomorrow,‘ she said to Peter.

3. Turn form direct into reported speech.

1)Mary said to me, ‗Come with me, please.‘

Mary asked me to go with her.

2)The shop assistant said to the child, ‗Don‘t touch anything.‘

3)The secretary said to me, ‗Wait here, please.‘

4)She said, ‗Shall we go swimming?‘

5)The park keeper said to them, ‗Don‘t walk on the grass.‘

6)He said to them, ‗Don‘t stay out late tonight.‘

7)Annie said to Barry, ‗Please, please help me.‘

4. Turn from direct into reported speech or vice versa.

1)‗I‘ve finished the housework,‘ she said.

She said she had finished the housework.

2)‗Why did you do that?‘ he asked her.

3)Susie told her mother that Titanic was the best film she had ever seen.

4)He told them to put the rubbish in the bin.

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5)‗Please answer the telephone,‘ he said to her.

6)Alex said that they were going to Hawaii for their honeymoon.

7)‗Are you going out on Saturday night?‘ Ben asked me.

8)Adam said that he had never ridden a horse before.

9)‗We‘ll go to the circus tomorrow,‘ said Mother.

10)Mr Carter told them to pick up the paper from the floor.

11)Julia begged her parents to let her go to the party.

12)Greg said, ‗Let‘s have a party on my birthday.‘

5. Correct the mistakes.

1)He asked me where was the post office.

2)She suggested to visit the zoo.

3)Mother said, ‗You must always say the truth.‘

4)The doctor told me to not exercise a lot.

5)My parents offered giving me a lift to the railway station.

6)Our teacher said to us that the test was quite easy.

7)She asked how could she contact me.

8)He said that Kate had left the last month.

9)The old man told good night and went to bed.

10)Jenny said me, ‗I hate Maths.‘

6. Translate into English.

1)Мені сказали, що ти мені телефонував.

2)Вона сказала, що ми ніколи не бачили її картини.

3)Моя мама сказала, що подруга запросила її у театр.

4)Його брат сказав, що хоче приїхати до нас сам.

5)Вона сказала, що її колеги завжди дають їй гарні поради.

6)Він сказав мені учора, що раніше він навчався в університеті.

7)Мені сказали, що Харків був столицею України.

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UNIT 8

Home-reading

Sir Isaac Newton

Sir Isaac Newton (4 January 1643 – 31 March 1727 [OS: 25 December 1642 – 20 March 1727]) was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history. His Philosophia Naturalis Principia Mathematica, published in 1687, is by itself considered to be among the most influential books in the history of science, laying the groundwork for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion which dominated the scientific view of the physical universe for the next three centuries. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.

In mechanics, Newton enunciated the principles of conservation of both momentum and angular momentum. In optics, he built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours that form the visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called "Newton's method" for

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approximating the zeroes of a function, and contributed to the study of power

series.

Newton remains influential to scientists, as demonstrated by a 2005 survey of scientists and the general public in Britain's Royal Society asking who had the greater effect on the history of science, Newton or Albert Einstein. Newton was deemed to have made the greater overall contribution to science, although the two men were closer when it came to contributions to humanity.

Newton was also highly religious, though an unorthodox Christian, writing more on Biblical hermeneutics than the natural science he is remembered for today.

French mathematician Joseph-Louis Lagrange often said that Newton was the greatest genius who ever lived, and once added that he was also "the most fortunate, for we cannot find more than once a system of the world to establish." English poet Alexander Pope was moved by Newton's accomplishments to write the famous epitaph:

Nature and nature's laws lay hid in night;

God said "Let Newton be" and all was light.

Newton himself was rather more modest of his own achievements,

famously writing in a letter to Robert Hooke in February 1676:

If I have seen further it is by standing on the shoulders of Giants.

Though some historians think the above quote was an attack on Hooke (who was short and hunchbacked), rather than – or in addition to – a statement of modesty. The two were in a dispute over optical discoveries at the time. The latter interpretation also fits with many of his other disputes over his discoveries, such as the question of who discovered calculus.

In a later memoir, Newton wrote:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

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