Additional texts

Read the texts “Kinetic energy” and “Potential energy’ and translate them in written form.

Kinetic energy

Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy. Kinetic energy is a property of a moving object or particle and depends not only on its motion but also on its mass. The kind of motion may be translation (or motion along a path from one place to another), rotation about an axis, vibration, or any combination of motions.

Translational kinetic energy of a body is equal to one-half the product of its mass, m, and the square of its velocity, v, or 1/2mv.

This formula is valid only for low to relatively high speeds; for extremely high-speed particles it yields values that are too small. When the speed of an object approaches that of light (300000 metres per second, or 186,000 miles per second), its mass increases, and the laws of relativity must be used. Relativistic kinetic energy is equal to the increase in the mass of a particle over that which it has at rest multiplied by the square of the speed of light.

The unit of energy in the metre-kilogram-second system is the joule. A two-kilogram mass moving at a speed of one metre per second has a kinetic energy of one joule.

For a rotating body, the moment of inertia, I, corresponds to mass, and the angular velocity (omega), corresponds to linear, or translational, velocity. Accordingly, rotational kinetic energy is equal to one-half the product of the moment of inertia and the square of the angular velocity, or 1/2I .The total kinetic energy of a body or a system is equal to the sum of the kinetic energies resulting from each type of motion.

Potential energy

Potential energy is stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to the Earth. In the raised position it is capable of doing more work. Potential energy is a property of a system and not of an individual body or particle.

Potential energy arises in systems with parts that exert forces on each other of a magnitude dependent on the relative position of the parts. In the case of the Earth-ball system, the force of gravity between the two depends only on the distance separating them. The work done in separating them farther, or in raising the ball, transfers additional energy to the system, where it is stored as gravitational potential energy.

Potential energy also includes other forms. The energy stored between the plates of a charged capacitor is electrical potential energy. What is commonly known as chemical energy, the capacity of a substance to do work or to evolve heat by undergoing a change of composition, may be regarded as potential energy resulting from the mutual forces among its molecules and atoms. Nuclear energy is also a form of potential energy.

The potential energy of a system of particles depends only on their initial and final configurations; it is independent of the path the particles travel. In the case of the steel ball and the earth, if the initial position of the ball is ground level and the final position is ten feet above the ground, the potential energy is the same, no matter how or by what route the ball was raised. The value of potential energy is arbitrary and relative to the choice of reference point. In the case given above, the system would have twice as much potential energy if the initial position were the bottom of a ten-foot-deep hole.

Gravitational potential energy near the Earth's surface may be computed by multiplying the weight of an object by its distance above the reference point. In bound systems, such as atoms, in which electrons are held by the electric force of attraction to nuclei, the zero reference for potential energy is a distance from the nucleus so great that the electric force is not detectable. In this case, bound electrons have negative potential energy, and those just free of the nucleus and at rest have zero potential energy.

Potential energy may be converted into energy of motion, called kinetic energy, and in turn to other forms such as electrical energy. Thus, water behind a dam flows to lower levels through turbines that turn electric generators, producing electric energy plus some unusable heat energy resulting from turbulence and friction.

Historically, potential energy was included with kinetic energy as a form of mechanical energy so that the total energy in gravitational systems could be calculated as a constant.

Pre-reading tasks

Task 1. The text you are to read is headlined “Mechanical energy”. Below you’ll find named the problems this text could contain. Choose the most appropriate problems to be mentioned in this text:

• definition of mechanical energy;

• description of experiments revealing the existence of mechanical energy;

• names of scientists contributed to the study of mechanical energy;

• forms of mechanical energy;

• facts related to the history of mechanical energy investigations.

After reading the text check whether your choice was correct.

Read the text “Mechanical energy” and fulfill the tasks given below.