Work, Energy and Power

Various forms of Energy: The Law of Conservation of Energy

Energy is simply the capacity of an object to do work. Energy change occurs during most events and processes in the Universe. In all of these Energy, conservation is followed! Our Universe has a fixed amount of energy. Energy can neither be created nor be destroyed, it may change form. Here, we will learn about various forms of energy with a special focus on the energy conservation.

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Mechanical Energy

The capacity of an object to do work by virtue of its motion or position is its Mechanical Energy. It is the sum of the kinetic energy and potential energy. Since in most of the physical processes, we usually come across Kinetic and Potential energy only, we can use it to study energy conservation.

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Kinetic Energy

The ability of an object to do work because of its motion is called Kinetic Energy.  For example, the wind’s kinetic energy pushes the sail of a boat and the boat moves forward.  Flowing water has kinetic energy, and it has been harnessed to drive the grinders of flour mills for centuries.  Kinetic Energy is denoted by K and its unit is joules (J).  It is expressed as:

Here, K is the kinetic energy of the object, m is the mass of the object and v is the velocity of the object

Potential Energy

Potential energy can be defined as the capacity of an object to do work by virtue of its position.  For example, a stretched bow string possesses potential energy.  When the bowstring is released, it propels the arrow forward. Another example might be that of an object raised above the ground.  When the said object is released, it rushes downwards.

A compressed spring also possesses potential energy, when it is released, it expands with a force. Potential Energy is denoted by V and its unit is joules (J).  Here, we will concentrate on the potential energy of an object by virtue of its position with respect to the earth’s gravity.  Let us consider the following illustration:

Here, m is the mass of the object in kilograms and h is the height of the object from earth’s surface in meters.  Here, the potential energy of the object at a height of h can be expressed as:

V(h) = mgh

Here, g is considered to be the earth’s gravitational constant and its value is set at 9.8m/s².  We know that an object will accelerate at different rates with respect to its distance from earth’s center of gravity.  But the surface heights are minuscule as compared to the earth’s radius, and hence, for all practical purposes, the acceleration under the earth’s gravitational force is taken to be a constant.

In the physical world, energy is transferred in many forms. Let us discuss some of these forms.

Heat Energy

Heat energy is associated with the frictional force. For example, if we rub our hands together in the winter, they feel warm.  Similarly, the tip of a dentist’s drill gets extremely heated while drilling into a tooth.  So a cooling mechanism is incorporated in the drill that regulates the temperature by a jet of water.

Let us consider the following illustration where we consider an object in motion. Let us say that this object comes to a complete rest by virtue of the friction of the surface alone.

Here m is the mass of the object, vi is the initial velocity of the object, x is the displacement of the object and vf is the final velocity of the object vf= 0. After we apply the work-energy theorem, work done by the frictional force of the surface will be:

W(friction) = ΔK

W(friction) = Kf – Ki; since, Kf = 0 then, W(friction) = – Ki = 1/2 [mvi2]

We also notice that work done by friction, in this case, is negative. The frictional force transforms the kinetic energy of the block into heat energy. This heat energy increases the temperature of both the object as well as the surface.

Chemical Energy

Chemical energy can be most simply defined as the energy that binds together the atoms and molecules of various materials. When these molecular bonds are broken, a large amount of energy is released. For example, when we light a fire to some wooden logs, we break down the complex organic molecules, and their chemical energy is released. Basically, a chemical reaction is carried by the transaction of energy. On which basis there are two  types of reactions:

  • Exothermic reactions:  A chemical reaction that releases energy. For example, oxidation of coal. A kilogram of coal releases 3×107 J of energy when burnt.
  • Endothermic reaction: A chemical reaction that absorbs energy. For example, the reaction of ammonium nitrate and water requires heat to proceed.

Nuclear Energy

Nuclear energy binds together the protons and neutrons in the nucleus of each element. It is the strongest force in the universe. Nuclear bombs harness the nuclear energy of uranium and plutonium. The devastation of Hiroshima and Nagasaki at the end of the Second World War was caused by a minuscule amount of nuclear matter when compared to the traditional bombing materials. Nuclear reactions can be categorized into:

  • Fission: When a larger nucleus disintegrates into smaller nuclei.  For example, the fission of uranium nucleus into smaller nuclei like thorium and radium etc.
  • Fusion: When two or more smaller nuclei fuse together to form a bigger nucleus.  For example, our sun’s energy is derived by the fusion of hydrogen atoms.

Electrical Energy

Charges exert forces on each other and hence give rise to an electrical energy. The flow of electrical current has energy. This energy can be harnessed by passing the electrical current through various materials and apparitions. For example, when electrical current passes through the filament of a bulb, it produces light. And when electrical current is passed through the motor of a fan, it rotates the blades.

Law of Conservation of Energy

The law of energy conservation states that energy we can neither create nor destroy energy. Energy merely changes its form. For example, the kinetic energy of a moving object transforms into heat energy when the object comes to a full rest by the virtue of friction.

Broader perspective

Einstein proposed that matter and energy are interchangeable and their relation can be expressed as E = mc². Here, E is the total energy of the matter, m is the mass of the matter and c is the velocity of light in vacuum. C is a constant at 300000000 m/s. Thus, a mere kilogram of matter has the equivalent energy of 9×1016 J or the equivalent annual output of a large power station (3000 MW capacity)!

Energy Conservation Under the Confinement of Mechanical Energy

Let us confine ourselves to the boundaries of mechanical energy under a conservative force. Here, we can prove the law of energy conservation. Before we do that, let us understand the nature of a conservative force. A conservative force has following characteristics:

  • We get it from a scalar quantity. Hence, it is one dimensional.
  • Work done by a conservative force depends only on end points of the motion.
  • If the endpoints of the motion are same i.e. the motion is in a closed loop, the work done by a conservative force is zero.

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 Conservation of Energy

Now, let’s consider the following illustration:

Solved Example for You

Example: Suppose an object falls from a height Δx towards the ground. Evaluate the energy conservation in this system.

Solution. Here, Δx is the displacement of the object under the conservative force F. By applying the work-energy theorem, we have ΔK = F(x) Δx

Since the force is conservative, the loss of potential Energy can be defined as ΔV = F(x) Δx

It means: ΔK + ΔV = 0

Therefore: Δ(K + V) = 0

This means, that for every displacement of Δx, the difference between the sums of an object’s kinetic and potential energy is zero. In other words, the sum of an object’s kinetic and potential energies is constant under a conservative force.

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