Find in the text verbs in the Passive Voice, define the tense and aspect of the verbs, give possible variants for their translations.

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4. Define the following word combinatios. Use them in the sentences or situations of your own:

· to solve realistic problems

· to be associated with

· non-mathematical form

· to formulate the problem

· to interpret the solution

· can be illustrated

· to be central to

· might be interested in

· broadly speaking

· to become skillful at

Scan the text again, find the part which is of special interest and great importance to you, and explain why.

Write the plan of the text and make a report, based on it. It is desirable that you should apply new terms, concepts and phrases from above.

7. Work in pairs. Make up the English-Russian glossary on the theme of the lesson. Your glossary should contain 20 – 30 (or more) lexical units. Give the sources you referred to. Exchange your version with your partner’s one, then compare them, and complete each other’s variants of the glossary, if necessary.

8. Listen to the text Language of Math and retell it:

http: //englishon-line.ru/chtenie-nauchnii-tekst47.html

9. Watch the video Introduction to Modeling Lesson to define its main theses. Name at least 5 of them. Discuss the matters given in the video with your partner (you are expected to ask your partner some questions, give your reasons in explaining various phenomena, support different points of views, etc).

http: //www.youtube.com/watch? v=GnlgGmLNn5o

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Basics of Mathematical Modelling and Mechanics. Present this information to the group.

Lesson 2

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Force Around Us

If an object which is initially at rest suddenly starts to move, then something must have caused the motion to start. For the object to start moving it must be acted upon by a net force. For example, a yacht moored in a harbour may begin to move when the sail is hoisted; the cause of the movement is the wind in the sail.

Suppose that you are towing a car up a 1 - in - 5 hill; it is important to know that the tow rope is strong enough not to break! What forces are acting in such a situation? You may have some idea already: there is the tension in the rope, the weight of the car, the reaction between the car and the road (hopefully the brakes are off! ).

Examples of force are all around us. You probably have an intuitive idea of force from your own experience of pushing and pulling things. But what is a force? It is difficult to define a force precisely but what you can do is to describe the effect of a force. It has already been said that a force can start motion. A force is required to stop motion: for example, the American space shuttle returning from orbit glides towards the airforce base in California without any power. To stop the shuttle on landing, a force is produced by a parachute.

A force is required to make an object move faster or slower. For example an ice puck in ice hockey can glide across the ice in a straight line with constant speed; to make it go faster a player hits the puck. If the puck is hit in its direction of motion then it will continue in that direction. However, if hit across its path, the puck will change its direction.

So, in summary, a force can: start motion (1); make an object move faster or slower (2); stop motion (3); change the direction of motion (4).

In other words a force causes a change in motion. As you will see, a force is not required to maintain motion. An object can move with constant speed with no force acting on it. For example a spacecraft in deep space, far from the influence of all planets, can maintain a constant speed without using its engines; only if it needs to change its motion does it need to uses its engines.

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. For the object to start moving it must be acted upon by ___________.

2. It’s difficult to define a force ________ but what you can do is to _______.

3. A force is required to make an object move __________ or ___________.

4. If hit across its path, the puck will change its ______________.

5. A force causes a change in __________________.

6. An object can move with ___________ speed with no force acting on it.

2. In each of the ten situations give a brief description of the motion:

(a) a table tennis ball hit without spin;

(b) a table tennis ball hit with spin;

(d) a ball thrown horizontally from a tower;

(e) an aircraft coming in to land at Heathrow;

(f) a ball rolling down a hill;

(g) a snooker ball sliding over the table (a 'stun shot');

(h) a swimmer diving from a springboard;

(i) cyclists going round a corner;

(j) a person in the chairoplane ride at Alton Towers.

3. Find in the text ing-forms, and say if they are Gerunds, Participles or forms of Progressive Tenses. Define the function in the sentence, give translations.

4. Consider the following situations and discuss whether there is a change in motion:

· An apple falling off a tree.

· A parachutist falling at a constant rate.

· A bouncing ball while it is in contact with the ground.

· A person in a car going round a roundabout.

· An astronaut floating freely close to an orbiting satellite.

Scan the text again, find the part which is of special interest and great importance to you, and explain why.

Write the plan of the text and make a report, based on it. It is desirable that you should apply new terms, concepts and phrases.

8. Listen to the text Powers and retell it:

http: //englishon-line.ru/chtenie-nauchnii-tekst25.html

9. Watch the video Maths Mechanics to define its main theses. Name at least 5 of them. Discuss the matters given in the video with your partner (you are expected to ask your partner some questions, give your reasons in explaining various phenomena, support different points of views, etc).

http: //www.youtube.com/watch? v=Rkzxr1ojA4I

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Force in Our Life. Present this information to the group.

Lesson 3

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Newton’s Law of Gravitation

Earlier in this section the force of gravity on an object of mass m near the earth’s surface was introduced as a force of magnitude 9.8m kg in the vertically downwards direction. Galileo, after dropping many objects from the leaning tower of Pisa, deduced that an object fell to the earth with an acceleration of 9.8 ms². So Newton with his second law was able to deduce the force on the object as 9.8 m.

However, one of Newton’s great achievements was to generalize gravity in his law of gravitation. Newton postulated that the force of gravity on an object near the earth depended on the mass of the object, the mass of the earth and inversely on the square of the distance between the earth’s centre and the object.

To validate his law of gravitation, Newton clearly could not carry out experiments since he could not measure the mass of the earth and could not move objects very far from the earth’s surface. Indeed, Newton studied the work of Kepler and realised that if he could ‘prove’ Kepler's laws using the law of gravitation and his law of motion, F = ma, then he was on to a winner! History tells us that Newton got it right and in the process developed Calculus.

Sir Isaac Newton (1642 – 1726) was, in fact, a prolific scientist and mathematician and turned his hand to a variety of problems including alchemy, optics and planetary motion. He was elected in 1689 as M.P. for Cambridge, and in 1699 accepted the post of Master of the Mint. Although he wrote that " if I have seen further than Descartes, it is because I have stood on the shoulders of giants", he undoubtedly must be regarded as one of the most influential mathematicians and scientists of all time. With the success of the law of gravitation applied to the planetary system, Newton postulated the Universal Law of Gravitation.

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. Galileo, after dropping many objects from the leaning tower of Pisa, deduced that an object fell to the earth with ____________________ of 9.8 ms².

2. One of Newton’s great achievements was to _____________ in his law of gravitation.

3. To validate his law of gravitation, Newton clearly could not carry out experiments since he could not ___________________ and could not move objects very far from the _______________________.

4. Sir Isaac Newton was a prolific scientist and mathematician and turned his hand to a variety of problems including ___________, ___________ and ___________.

5. With the success of the law of gravitation applied to _______________, Newton postulated the Universal Law of Gravitation.

2. Work in pairs to find out:

1. How did Galileo deduce that an object fell to the earth with an acceleration of 9.8 ms²?

2. What did Newton postulate about the force of gravity?

3. Why couldn’t Newton carry out experiments?

4. Whose work did Newton study and what did he realise?

5. What happened to Newton in 1689 and in 1699?

6. Must he be regarded as one of the most influential mathematicians and scientists of all time?

7. With the success of the law of gravitation applied to the planetary system, Newton postulated the Universal Law of Gravitation, didn’t he?

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