JET PROPULSION

I. The most important application of the principle of conservation of momentum in technology is the jet propulsion. Motion of a body when part of it is ejected from the body at a certain velocity is called jet propulsion.

A simple example of jet propulsion is the motion of a balloon (fig. 68). Pressure inside the balloon is higher, than atmospheric and therefore air escapes through its bottom opening. This causes the balloon to move forward, and it starts flying about the room. The air escaping from the balloon, though during a short-time interval, forces the balloon to move in an opposite direction.

The principle of jet propulsion is used in motions of octopuses, squids, cuttlefishes, jellyfishes. Flights of

rockets are based on the same principle. The principle of

jet propulsion allowed creating the planes moving at a

speed of several thousand kilometers per hour, artificial

satellites of the Earth, the interplanetary space rockets

that turned into reality the long-cherished ambitions of Fig.68

mankind to explore the Universe.

Long and dedicated work, precise calculations, complicated equipment and strong heroism allowed a man to leave for space.

II. The first ideas on space discovery belong to K. E. Tsiolkovsky (1857 -1935). They were developed in his work "The Exploration of Cosmic Space by Means of Reaction Devices" published in 1903. He theoretically motivated the possibility of space exploration using rockets: he offered and developed a rocket design capable to give the orbital speed to the aircraft, described multistage rockets, calculated the motion of bodies with a variable mass and also he put forward important ideas about space flights. K.E.Tsiolkovsky's ideas contain the fantasy and scientific calculations to be in surprising harmony.

Only half a century later the dream of mankind to travel into space come true. Tsiolkovsky's ideas were realized at the guidance of outstanding scientist Sergey Korolyov.

Tokhtar Aubakirov Talgat Musabayev

The first artificial satellite of the Earth was launched from the Baikonur spaceport on October 4, 1957. On the spacecraft “Vostok” on April 12, 1961 astronaut Yu.A.Gagarin for the first time completed an orbit around the Earth. Each year spaceships and research programs are being improved. Among the astronauts who participated in works on space exploration and scientific research are the astronauts from Kazakhstan -Tokhtar Aubakirov and Talgat Musabayev.

III. Let's consider the principle of jet propulsion on the example of the rocket. A simple rocket consists of the case containing the combustion chamber filled with fuel (fig. 69). The burned fuel turns into gas of high temperature and big pressure. Gas at a high speed (up to 4 km/s) is ejected from the jet of a special form called nozzle and the rocket moves speeding up at continuous burning of fuel.

For simplicity of calculations we consider the gas produced at combustion of fuel to be instantly ejected from the rocket with velocity and thus the gas gains momentum , where is the velocity of the ejected gas; m is the mass of the burned fuel. The force of interaction between gas and rocket is much greater compared with external forces therefore the system of rocket and gas can be considered as isolated system. Thus the momentum of the system is conserved. Let M denote the mass of the rocket with fuel before start. After ejection of burned fuel with mass m the total momentum of the system remains constant. Then the rocket with mass M-m acquires the momentum equal in magnitude but opposite in direction to the momentum of the ejected gas, i.e. , where is the rocket velocity. So, . “Minus” sign before brackets means that velocities and are opposite in direction (fig.69). Hence

.

Thus the rocket gains the velocity opposite in direction to the velocity of the ejected gas.

Propulsion of a body by means of ejecting some of its parts at a certain speed is called jet propulsion.

IV. Modern rocket engines are divided on engines that operate on liquid and solid fuel. In solid-propellant engines special types of gunpowder are used and in liquid-propellant engines kerosene, gasoline, alcohol, aniline, liquid hydrogen, etc. are used. As an oxidizer for combustion the oxygen, nitric acid and etc. are used. Liquid-propellant jet engines are used to launch spacecrafts.

Air jet engines that are used in aircraft construction differ from the rocket engines in that they use as an oxidizer for fuel combustion the oxygen that comes in from the atmosphere. At present many aircrafts are supplied with similar jet engines.

V. Modern rockets are multistage and each stage contains its own jet engine and propellant (fig. 70). As the fuel is being burned out the first stage separates from the carrier, then the remaining part of the rocket with mass equal to the sum of masses of the second and third stages moves forward. Reduction of mass of the rocket promotes economy of fuel at the second and third stages and achievement of high speeds of the rocket. If rocket have to return to the Earth, before switching on the third stage the spaceship is turned round on 180°. Products of burning of the third stage produce momentum opposite in direction to the rocket’s motion and thus slow down its motion.

Exit of a person into space opened new opportunities in space exploration and study of other planets. The obtained data benefits greatly the development of various sciences and creation of new production technologies. They expand opportunities for study of the natural phenomena and exploration of the deep underground.. Kazakhstan having Baikonur spaceport located on its territory became one of the few space powers in the world.

Self-testing questions

1. How does the rocket move?

2. What is the jet propulsion? Give examples.

3. For what purpose are the rockets multistage?

4. What quantities does the velocity of jet propulsion depend on?

5. What successes in space exploration do you know?

6. If the speed of the ejected gas is less than the speed of the rocket, whether the rocket speed increases?

Exercise 18

1. The small rocket with its initial mass plus propellant of 250 g, flies vertically upward and reaches the height of 150 m. Considering that the propellant burns instantly, calculate the speed of gases ejected from the rocket. The mass of the propellant is 50 g.

2. The spacecraft with mass 10 t moves at a speed of 9 km/s. During brake 1450 kg of products of combustion were thrown out by brake engines at a speed of 3 km/s relative the case in the direction of motion. Determine the spacecraft speed after brake.

3. The small rocket has the mass of 200 g. The mass of gunpowder in it is 50 grams. Considering that gases are instantly ejected from the nozzle at a speed of 100 m/s, determine the speed of the rocket.

ENERGY

I. In the previous chapter you have learned about momentum and conservation of momentum. In physics there is one more physical quantity that is conserved in the isolated systems. This quantity is called energy.

Physics of the 7th class gave you initial knowledge about mechanical energy, its types and its SI unit, introduced the relationship between work and energy. Now we will use these concepts to consider them more deeply. For this reason we introduce the concept of a condition of a body which will be widely used in all subsequent sections of physics.

The words "condition of a body" and "condition" are often used in our everyday life. For example, when we tell about a condition (health) of a person we mean his arterial blood pressure, body temperature and other data characterizing the general condition of the person at a given time. Spaceship flight control center continuously receives information about conditions of astronauts, about temperature, pressure, humidity inside ship cabin at any time. In other words, by the condition of an object we mean a set of parameters characterizing the object at a given time.

Mechanics considers a mechanical condition of a body (a material point or particle). To specify a mechanical condition of a particle means to answer two main questions of mechanics: where is it and how does it move at a given time, i.e. it is necessary to determine coordinates and velocity of the particle at a given time. Coordinates of the particle (x,y, z) and its speed (u) at the given time are called the parameters of a mechanical condition; the mechanical condition is known if parameters of the condition are set.

In a motion the condition of the particle (coordinates, speed) continuously changes, the particle passes from one condition to another. The quantity characterizing the mechanical condition of a body or a particle is called mechanical energy. Thus, mechanical energy determines the mechanical condition of a body. It possesses two features: depends on parameters of the condition (coordinates and speed) and its change is related with the work done during transition of a body from one condition into another.

Hence we define the mechanical energy as the ability of a body to do mechanical work. Energy as well as work is the scalar quantity that has only numerical value. The SI unit of energy is the same as the unit of work, i.e. joule (J). You know two types of a mechanical energy - kinetic (E_k) and potential (Е_p). All bodies in motion are capable to do mechanical work.

II. Energy the body possesses due to its motion is called kinetic energy. For example, the flying bird, a bullet shot from a gun and wind possess kinetic energy. Kinetic energy characterizes the condition of a moving body. It is expressed by the following formula:

.

Kinetic energy has two features: it depends on body’s velocity and its change is equal to the work done the force that acts on the body. Therefore,

.

III. Now we will consider potential energy. Potential energy is the energy the body possesses due to interaction with other bodies and it depends on the position, shape and state of the body. Potential energy is possessed by bodies which are acted on by potential forces (force of gravity and elastic force).

For example, dammed up water, the strained bow, the compressed or stretched spring, the rubber ball filled with compressed air - all of them possess potential energy. So, the potential energy is the energy possessed by a body that acted on by potential forces. Potential energy has two features: it depends on body’s coordinates and its change is related to the work of potential forces. In other words,

or .

“Minus” sign in front of the equation means when the force of gravity does the positive work, i.e. a body falls down its potential energy decreases and vice versa.

IV. Mechanical work is a measure of change of energy. If work is done then one of the energies changes, i.e.

.

Thus, the body in a motion possesses kinetic energy and its potential energy depends on its position relative other bodies in the system or on the position of its parts relative each other.

Self-testing questions

1. What is called mechanical energy? What types of a mechanical energy are known to you?

2. What is the SI unit of a mechanical energy?

3. What is called kinetic energy? What are the features of a kinetic energy?

4. What is called potential energy? What are the features of a potential energy?

5. What is the potential energy of a body at a certain height above the ground?

6. What is the expression for the elastic potential energy?

7. In what of the given cases the energy is either kinetic or potential: a) bent spring; b) compressed air; c) moving air; d) water falling from the dam; e)a stone on the edge of the roof?

8. What is the relationship between work and energy?

Exercise 19

1. Calculate the kinetic energy of an artificial satellite of the Earth with mass 1300 kg moving round the Earth in a circular orbit at the height of 100 km.

2. A load with mass 2,5 kg falls from the height of 10 m. What is the change of its potential energy after 1 s it starts to fall? Initial speed of the load is equal to zero.

3. What work is done by the force of gravity when the person with mass 75 kg walks upstairs from the first to the sixth floor if height of each floor is 3 m?

4. The boy determined the maximum force with which he can stretch a dynamometer. It appeared to be equal to 400 N. How much work is done by this force to stretch the spring? The force constant of the spring of a dynamometer is 10 000 N/m.

5. The body with mass 18 kg is suspended on a spring with fixed top end. The stretched length of a spring is 10 cm. When a body with mass 30 kg is suspended to the spring its length becomes 12 cm. Calculate the work done by external force to stretch the spring from 10 to 15 cm. How much work is done by elastic force?

Assignment

Fill in the table 3

Table 3

Date: 2015-01-12; view: 1019