Text 2 a Potential and Kinetic Energy

The capacity of a body to perform work is called its energy. This energy is designated potential if it is due to the position of the body. But a moving body can also do work. Energy in this form is designated as kinetic.

If a body is allowed to fall freely, its rate of descent steadily increases, and it attains its maximum velocity just as it reaches the ground. At this point the body possesses no potential energy at all, for its distance above the ground is zero, but it does have kinetic energy because of its motion. Evidently energy of position is converted into energy of motion.

Potential energy is usually not difficult to measure: it is the product of the resistance overcome and the distance covered.

But how can we determine the kinetic energy, or work-performing capacity, of a moving body from the knowledge of its weight and velocity?

Imagine that a moving body of mass m and velocity V strikes against an obstacle and is brought to rest. The change of velocity is the difference between the original and the final velocity; it is numerically equal to V, for the final velocity is zero. Acceleration equals the change of velocity divided by the time required for its accomplishment: i.e. acceleration = V/t. But we know that the force exerted on (or by) any body is its acceleration (rate of change of velocity) multiplied by the mass which undergoes this change. In this case the force exerted by the body must be equal to mass acceleration

(to be read: F equals m multiplied by V divided by t).

The work done is the force exerted multiplied by the distance through which it acts; but distance S equals average velocity

(i.e. )

so

Now

In this equation we shall substitute the equivalent values of F and S as found in the preceding paragraph, and also replace work by kinetic energy (KE), for we are really considering the work-accomplishing capacity of the moving body.

Hence

(to be read: the kinetic energy of a moving body is equal to one-half the product of its mass and the square of its velocity).

While this equation is familiar enough, its derivation is not always understood, and the reasoning given here is one of the easier ways of appreciating its logical grounding.

Answer the questions:

1. What is called energy?

2. What energy is designated as kinetic?

3. When does a body possess no potential energy at all?

4. Why does a body possess no potential energy when it reaches the ground?

5. How can the change of velocity be determined?

6. What is acceleration?

7. What values are to be substituted for determining kinetic energy?

Exercises

1. Translate the following worlds paying attention to the suffixes:

-ful useful, beautiful, wonderful, powerful, peaceful;

-less useless, careless, aimless, powerless;

-able attainable, changeable, valuable, probable, reasonable;

-ty capacity, possibility, safety, speciality;

-ly freely, steadily, originally, finally, really, considerably, easily, quickly, slowly, rapidly.

2. Translate the following words with the prefix “over”:

to overact, to overbuild, to overcharge to overflow, to overheat, to overload, to overproduce, to overweigh, to overwork, to overcome.

3. Fill in the blanks with the words given below:

Equal, unequal, to be equal to, to equal, equality, equation.

1. The values measured proved to be … .

2. Potential energy is … to the resistance multiplied by the distance covered.

3.The derivation of this … presents some difficulty in understanding.

4. These two bodies are of … weight.

5.Average velocity … one half the sum of original and final velocity.

6. This is the ... representing the relationship between distance of descent and time of descent.

7. The … of the amounts of potential and kinetic energy in the same body is quite evident.

8. The … derived proved the … of these two values.

9. One form of energy is converted into another, their amounts are … .

4. Translate into English using Passive Voice:

1. Цим рiвняням часто користуються.

2. На нього часто посилаються.

3. Цю величину треба взяти до відома.

4. Для виведення рiвняння кiнетичноi енергiї визначають величину сили i вiдстанi.

5. Потенцiальна енергiя вимiрюється як добуток опору, який треба подолати, i вiдстанi.

6. За рiвнянням сили i вiдстанi наведено рiвняння кiнетичноi енергii.

5. Translate the following word-combinations:

the position of a body; to perform work; to fall freely; the rate of descent; to attain its maximum velocity; to reach the ground; the product of the resistance overcome and the distance covered; work-performing capacity; strike against an obstacle to be brought to rest; the force exerted on any body; work-accomplishing capacity.

6. Make up pairs of the following words and translate them into Ukrainian:

1) moving a) velocity

2) maximum b) capacity

3) resistance c) values

4) work-performing d) energy

5) equivalent e) grounding

6) kinetic f) covered

7) logical g) body

8) distance h) overcome

7. Make up questions to the following answers:

1.When force is exerted through any distance, work is performed. 2.The measure of the work accomplished is the product of the resistance of force multiplied by the distance. 3. The energy of position is called potential. 4. On the ground the potential energy of the body is reduced to zero and its kinetic energy reaches its possible maximum. 5. To define force the value of mass which undergoes the change should be determined. 6. The law discovered showed that energy is converted from one form into another in equal amounts.