Energy is the capacity or ability of a body to do work. It is a scalar quantity. Its SI unit is the same as that of work i.e. joule (J). In CGS system, energy is measured in calorie (4.2 joule= 1 calorie).
There are various forms of energy. Some of them are as follows:
The energy possessed by a body by the virtue of its motion or its position or its configuration is called mechanical energy. It is two types: Kinetic energy and potential energy.
Kinetic energy
The energy possessed by a body by the virtue of its motion is called kinetic energy. Examples: A flying bird, a moving car, running water etc.
The Kinetic energy of a moving body is determined by the formula:
Kinetic energy (KE)=1/2mv^{2}
Here, m = mass of the body
V =velocity of the body
Derivation of KE = \(\frac{1}{2}\)mv^{2}
Let us consider a body of mass 'm' is at rest on a smooth surface whose initial velocity is 0. If a constant force 'F' is applied on it then it displaces the body by displacement 'd' in its own position. If 'v' be the final velocity then the workdone by the force is given by
W = Fd
Or, W = mas...........(i) (since,F=ma and d=s)
We also have,
a = \(\frac{v - u}{t}\) and s = \(\frac{ u + v}{2} \times t\)
substuting these values on equation (i)
Or, W = m\(\frac{ v - u}{t}\) \(\times\) \(\frac{u +v}{2} \times t\)
Or, W = m \(\frac{v^2 - u^2}{2}\)
Or, W = \(\frac{1}{2}\)mv^{2 } (since, initial velocity u=0)
The workdone becomes the kinetic energy of the body. Thus, the kinetic energy of a body of mass 'm' moving with the velocity equal to 'v' is\(\frac{1}{2}\)mv^{2.}
Potential energy
The energy possessed by a body by the virtue of its position or its configuration is called potential energy.
The potential energy (PE) of a body at a height is determined by the formula:
P.E. = mgh
Here, m = mass
g = acceleration due to gravity
h = Height
Work done is stored in the body as potential energy which is called gravitational potential energy.
The potential energy possessed by a stretched rubber, a compressed spring etc. is called elastic potential energy.
Derivation of PE = mgh
Let us consider a body of mass 'm' . The weight 'mg' of the body acts vertically downwards, where 'g' is the acceleration due to gravity. Let 'h' be the height upto which body is lifted. In order to lift the body, force 'mg' should be applied in upward direction.
Now, the workdone is given by
W = F.d
i.e. W =mgh (Since F= mg and d =h)
This work done is stored in the body as potential energy which is called gravitational potential energy.
\(\therefore\) Gravitational potential energy (P.E.) = mgh.
Electrical energy is the energy possessed by the continuous flow electrons or by the change in a number of electrons in bodies. Electronic devices like computers, telephones, televisions, radios, calculators etc. use electrical energy.
A substance is made of tiny particles called molecules. The sum total of the kinetic energy of all constituent molecules of the body is heat energy. Sun is the main source of heat energy. Heater is an example of heat energy.
Light is a form of energy which produces the sensation of sight. The main source of heat and light energy in the earth is the sun. Some examples of light energy are lightbulb, torch light, tube light, etc.
A sound is a form of energy which is produced by the vibration of sounding bodies. Sound requires material medium to for its propagation. Speakers, radio, television etc are some examples of sound energy
The energy possessed by the magnet or a current carrying conductor that effect on magnetic bodies is called magnetic energy. Magnets are used in many electronic devices such as radio, telegraph. Loudspeaker, etc.
The energy stored in a body, which is released from it, when it undergoes chemical change is called chemical energy. Generally, food, fuel and cells store chemical energy.
The energy possessed from a nuclear fission or nuclear fusion is called nuclear energy. Nuclear fission is a process of splitting up of a heavy nucleus into light nuclei with the release of energy. Nuclear fusion is a process in which lighter nuclear fuse to form heavier nuclei.
Conversion of energy from one form to another form is called transformation of energy.
When a candle burns, it changes chemical energy into light and heat energy. Similarly, when a lamp glows, it changes electrical energy into light and heat energy. These examples show that one type of energy can be changed into another type.
Examples:
Energy can neither be created nor destroyed but can only be changed from one form to other. This is called the principle of conservation of energy.
The energy of a body is the capacity of doing work. Its SI unit is Joule(J).
As the energy means the amount of work that a body can do, they have same SI unit.
A person needs energy to do anything. Even if he is sleeping, the internal activities like respiration, circulation, digestion were doing. To perform these activities, energy is required. So, he will be in energy less condition.
The energy acquired by the bodies subjected to forces is called mechanical energy. For example: A falling stone, the wound up spring a watch, etc.
Energy possessed by a body in virtue of its state or position is called potential energy. Example: water stored in a reservoir, stretched rubber, lifted leg before kicking a football, etc.
Let us suppose a body of mass 'm', at a place 'x' on the ground. The force is applied on the body to displace it up to a point 'y' at height 'h' from the surface. The force to be applied to lift the body is 'mg'.
The factors affecting Potential energy are as follows:
Considering the same capacity of the tank filled with water at position B, potential energy will be more because potential energy is directly proportional to the height and height is more in B than in A.
The factors affecting KE of a body are as follows:
Kinetic energy of a moving body is directly proportional to the square of velocity of the moving body.
i.e. K.E ∝ v^{2}
Potential energy | Kinetic energy |
It is the energy possessed by a body in rest. | It is the energy possessed by a moving body. |
It is calculated by P.E = mgh | It is calculated by: K.E = ½ mv^{2}. |
The mathematical formula of Kinetic energy (K.E) is ½ mv^{2}.
As we know that potential energy is gained when an object gains height i.e.PE = mgh. Since, PE ∝ h, the stone stores potential energy when it is lifted to a certain height.
The muscular energy, which is potential energy, is used in climbing staircase.
The energy produced from a nuclear fission or fusion is called nuclear energy.
Work and energy are directly related such that work done on a system is equal to the increase in energy.
Solution:
Here,
Mass(m) = 2kg
Height (h) = 2m
Potential energy (P.E) = ?
Acceleration due to gravity (g) = 9.8 m/s^{2}
As we know that,
PE = mgh
Or, PE = 2 x 9.8 x 2
Hence, PE = 39.2 J
Here Mass (m) = 10kg
Velocity (v 0 = 0.4 m / s
Kinetic energy (KE) = ?
we have,
KE = \(\frac{1}{2}\) mv \(^{2}\)
KE = \(\frac{1}{2}\) \(\times\) 10 (0.4)\(^{2}\) = 0.8J
Thus, the kinetic energy of the body is 0.4J .
Here
Mass (m) = 200kg
Potential energy (PE) = 9800J
Height (h) = ?
Acceleration due to gravity (g) = 9.8m / \(s^{2}\)
We have,
PE = mgh
or, 9800 = 200 \(\times\) 9.8 \(\times\) h
or, 9800 = 100 \(\times\) 9.8 \(\times\) h
or, h = \(\frac{9800}{200\times 9.8}\)
= 5m.
Thus, required height is 5m.
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