| Contents for this page | Related topics |  |
|---|---|---|
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Energy Potential energy Gravitational potential energy Kinetic energy Mechanical energy Constancy of mechanical energy for a falling body Principle of conservation of energy Additional questions |
Conservation of momentum in two dimensions Projectiles Work Power |
 Data Glossary |
| Learning Outcomes | ||
| After studying this section, you will (a) understand and be able to apply the concept of energy, (b) know the difference between gravitational potential energy and kinetic energy, (c) know the Principle of Conservation of Energy, and (d) be able to solve numerical problems involving energy. | ||
ENERGY IS THE CAPACITY TO DO WORK. It is a scalar quantity and, like work, has the units of JOULES, (J).
There are various types of energy, listed in the table below:
| Energy type | Source |
|---|---|
| Kinetic energy | Energy of a moving body due to its motion |
| Potential energy | Energy of a body due to its position |
| Chemical energy | Energy that is absorbed or released as a result of chemical reactions |
| Light energy | Energy carried by light |
| Elastic energy | Energy that is stored in an object that has changed its shape reversibly |
| Electrical energy | Energy due to the presence of electric charges in an electric field |
| Magnetic energy | Energy magnetic objects placed in a magnetic field |
| Nuclear energy | Energy that is released as a result of nuclear reactions |
| Thermal energy | Energy of a body resulting from the difference between its temperature and that of the surroundings |
| Sound energy | Energy that is carried by sound waves |
Mass is also a form of energy.
Objects possess POTENTIAL ENERGY when they can do work on other objects by virtue of their position with respect to those other objects.
Various types of potential energy can be defined - each type associated with a particular force.
The energy that an object has due to its height above a reference point is known as the GRAVITATIONAL POTENTIAL ENERGY.
It is easy to see how an object on which the force of gravity acts if we consider two masses m and m' linked by a massless cord passing over a frictionless pulley. |
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If the mass, m, which is slightly greater than m' and is held at a height h above ground level were to be released, it would fall towards the ground. In the process, the mass m' would rise against the force of gravity, m'g, on it. When m reaches the ground the work done on m' would be the product of the force required to lift it, m'g, and the distance moved, h, that is, m'gh. |
At the start of the experiment the weight mg has the potential to do work, or POTENTIAL ENERGY due to its location in the gravitational field relative to some reference position. In this case, a height, h, above the ground.
The GRAVITATIONAL POTENTIAL ENERGY acquired by a weight, mg, in lifting it a distance, h, above the ground is equal to the work done in lifting the weight, that is, mgh.
A moving object has energy resulting from its velocity. This is known as the KINETIC ENERGY of that object. The kinetic energy of an object having mass, m, moving with a velocity, v, is given by
Consider a body of mass m subjected to a force F = ma, moving from rest to a velocity v. From the equations of motion for uniform acceleration, a = v² /2s.
The work done if the acceleration took place for a distance s will be W = Fs = mas = mv² s/2s = ½mv². Thus, we may define the kinetic energy of a moving body moving at velocity v, as the work done in accelerating it from rest to v. (Note for educators.)
Assuming that no energy is lost,in the process, a moving object has the capacity to do an amount of work equal to its kinetic energy.
The MECHANICAL ENERGY of a body is the sum of its gravitational potential energy Ep and its kinetic energy Ek:
If an object of mass, m, is suspended at rest at a height, h, above the ground, its potential energy is mgh, and its kinetic energy is zero. This means that its mechanical energy is mgh, that is, mhg + 0. |
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If it is released and falls a distance, h', then its potential energy is mg(h - h'), and its kinetic energy is ½mv2. From the equations of motion, v2 = 2gh', thus the mechanical energy is given by: Mechanical energy = mg(h - h') + ½mv2 |
Immediately before hitting the ground, the velocity will be given by v2= 2gh, the potential energy will be zero, and the kinetic energy will be given by Ek = ½mv2 = mgh. Thus as the body falls, its potential energy is converted to kinetic energy, but the mechanical energy has a constant value, namely mgh. |
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In general, energy may be present in a system in a variety of forms, for example, electrical energy, chemical energy, heat energy and so on. In mechanics we are concerned with gravitational potential energy, kinetic energy, and, to a lesser extent, heat energy.
The PRINCIPLE OF CONSERVATION OF ENERGY states that the total energy of a system remains constant.
By implication, energy cannot be created or destroyed. It is only converted from one form to another. During conversion of one form into another, an APPARENT LOSS of energy may occur, due to its conversion to other, unwanted forms.
For example, conversion of chemical energy into electrical energy takes place with production of heat, which is wasted. Similarly, conversion of electrical energy into light energy (such as takes place in light bulbs) is also accompanied by production of heat, which is wasted.
Einstein showed that mass, m, and energy E were related by the equation E = mc2, where c is the velocity of light in a vacuum (3.0x108 m.s-1).
The equation predicts that a large amount of energy is released when mass is converted to energy. This has been confirmed by experiment, and is the principle underlying nuclear bombs and nuclear power stations.
The force acting of the object need not be constant. The kinetic energy of a body is dependent only on its mass and velocity, not the vay in which the velocity was acquired. A more general way of deriving the equation is shown below.
Consider a force F acting through an infinitesimally small distance δs. Then, the work done will be δW = Fδs.
If the force accelerates the body from rest to a velocity v, the total work done will be
From Newton's second law, F = ma = mdv/dt, so,
But v = ds/dt, then
Integrating, we get
