Equal, bring, avoid, do, result, call, correspond, lead, act.

1. Kinetic energy is the total work which must be done on the particle to ……it from a state of rest to a velocity v.

2. The equation states that the total work ….. by all forces ….. on a particle during an interval of its motion from condition 1 to condition 2 ….. the corresponding change in kinetic energy of the particle.

3. The work always …..in a change of kinetic energy.

4. When written in the form T₁ + U _1-2 = T₂ the terms ……to the natural sequence of events.

5. A major advantage of the method of work and energy is that it …...the necessity of computing the acceleration and ……directly to the velocity changes as functions of the forces which do work.

6. Application of the work-energy method …..for an isolation of the particle or system under consideration.

Ex.4. Use the correct form of the word in bracket.

These two particles are joined together by a ……(connect) which is …….(friction) and ………..(capable) of any ……(form). The forces in the ……(connect) constitute a pair of equal and opposite forces, and the points of …….(apply) of these forces ………(necessary) have identical ………(place) components in the …….(direct) of the forces. Hence, the net work done by these internal forces is zero during any ……(move) of the system of the two……(connect) particles. Thus, this equation is …….(apply) to the entire system.

Part 2. Power.

The capacity of a machine is measured by the time rate at which it can do work or deliver energy. The total work or energy output is not a measure of this capacity since a motor, no matter how small, can deliver a large amount of energy if given sufficient time. On the other hand, a large and powerful machine is required to deliver a large amount of energy in a short period of time. Thus, the capacity of a machine is rated by its power, which is defined as the time rate of doing work.

Accordingly, the power P developed by a force F which does an amount of work

U is P = dU/dt = F•dr/dt. Since dr/dt is the velocity v of the point of application of the force, we have

P = F•v ( 5 )

Power is clearly a scalar quantity, and in SI units it has the units of N•m/s = J/s. The special unit for power is the watt (W), which equals one joule per second (J/s).

Part 3. Efficiency.

The ratio of the work done by a machine to the work done on the machine during the same time interval is called the mechanical efficiency e_m of the machine. This definition assumes that the machine operates uniformly so that there is no accumulation or depletion of energy within it. Efficiency is always less than unity since every device operates with some loss of energy and since energy cannot be created within the machine. In mechan­ical devices that involve moving parts, there will always be some loss of energy due to the negative work of kinetic friction forces. This work is converted to heat energy which, in turn, is dissipated to the surroundings. The mechanical efficiency at any instant of time may be expressed in terms of mechanical power P by

e_{m =} P _{output :} P _input

In addition to energy loss by mechanical friction, there may also be electrical and thermal energy loss, in which case, the electrical efficiency e_e and thermal efficiency e_t are also involved. The overall efficiency e in such instances would be

e = e_me_ee_t

Comprehension check. (Parts 2 and 3.)

Ex. 5. Put the questions to the following answers.

1. By the time rate at which it can do work or deliver energy.

2. Because a motor, no matter how small, can deliver a large amount of energy if given sufficient time.

3. It equals one joule per second (J/s).

4. It is the mechanical efficiency e_m of the machine.

5. Because every device operates with some loss of energy.

6. Due to the negative work of kinetic friction forces.

7. To the surroundings.

Ex. 6. Match the verbs in the left column with the nouns in the right one, verbs and nouns can be used more than once.

Verbs		Nouns
1	accumulate	a	capacity of a machine
2	convert	b	an amount of work
3	create	c	with some loss of energy
4	deliver	d	sufficient time
5	deplete	e	with some loss of energy
6	develop	f	to heat energy
7	dissipate	g	uniformly
8	do	h	energy
9	express	i	to the surroundings
10	give	j	the power
11	measure	k	in terms of mechanical power
12	operate

Ex.7. Match the terms and their definitions. Compose 5 sentences with any of them.

1	accumulation	a	the reduction of the amount of smth that is available
2	amount	b	the quality of doing something well without wasting time, money, or energy
3	capacity	c	the objects, buildings, natural things etc that are around a person or thing at a particular time
4	depletion	d	an amount or unit in a measuring system
5	efficiency	e	a disadvantage caused by someone or something leaving or being removed
6	friction	f	gradual increase in numbers or amount of smth until there is a large quantity in one place
7	loss	g	energy that can be used to make a machine work or to make electricity
8	measure	h	an amount or quantity of something used as a standard of measurement
9	power	i	the number 1
10	surroundings	j	the natural law that prevents one surface from sliding easily over another surface
11	unit	k	the amount of something that a factory, company, machine etc can produce or deal with
12	unity	l	a quantity of smth such as time, money or a substance

Ex.8. Transform the following sentences from Active into Passive.

1. We cannot create energy within the machine.

2. We measure the capacity of a machine by the time rate at which it can do work or deliver energy.

3. A motor, no matter how small, can deliver a large amount of energy if given sufficient time.

4. A force F develops the power P.

5. The power P does an amount of work U.

6. Application of the work-energy method calls for an isolation of the particle or system under consideration.

7. The work – energy method permits the analysis of a system of particles without dismembering the system.

Comprehension check. (Parts 1, 2 and 3.)

Ex.9. Find 14 odd words which shouldn’t be used there.

The choice of a coordinate system is being frequently indicated by the number and geometry of the only constraints. Thus, if a particle is free to move in space, as if is the center of mass of the airplane or rocket in the free flight, the particle is said to have three degrees of freedom since three independent coordinates are not required to specify the po­sition of the particle at any an instant. All three of the scalar compo­nents of the equation of motion would have to be applied and integrated to obtain the space coordinates as a function as of time. If a particle is constrained to move along a surface, as is in the hockey puck or a marble is sliding on the curved surface of a bowl, only two coordinates are to needed to specify it’s the position, and in this case it is said to have had two degrees of its freedom. If a particle is constrained to move along a fixed linear path, as is the collar sliding along a fixed shaft, its position may to be specified by the coordinate measured along the shaft. In this case, the particle would have only one degree of freedom.

Ex.10. Use ing-form , infinitive with “to” or without “to” in the following sentences.

1. Although T is always positive, the change ∆ T may …….( be) positive, negative, or zero.

2. The equation tells us that the work always results in ………( change) of kinetic energy.

3. A major advantage of the method of work and energy is that it avoids ….. (compute) the acceleration.

4. The work-energy method permits ……..(analyze) a system of particles without dismembering the system.

5. Application of the work-energy method calls for …..(isolate) of the particle or system under consideration.

6. A free-body diagram lets us …..(show) all forces externally applied to a single particle.

7. It is worth ……(draw) an active –force diagram for a system of particles rigidly connected.

8. It is difficult enough …..(describe) dynamic behavior of a spring when its mass is accounted for.

Ex.11. Join two simple sentences into one complex with the help of the following words making some changes if necessary :