Dimensional Formula of Kinetic Energy

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What is Kinetic energy?

Kinetic energy, the energy forms an object or a particle has because of its motion. If work is performed on an object by applying a net force, which transfers energy, the object accelerates and thus absorbs kinetic energy. Kinetic energy is a property of a moving object or particle which depends on its movement as well as its mass. Translation (or motion along a path from one position to another), rotation around an axis, acceleration, or any combination of motions may be the kind of motion.

In the metre-kilogram-second system the unit of energy is the joule. A two-kilogram mass (something that weighs 4.4 pounds on Earth) moving at a speed of one metre per second (slightly more than two miles per hour) has one joule of kinetic energy. The energy unit in the centimetre-gram-second system is the erg, 10−7 joule, equivalent to a mosquito's kinetic energy in flight. Other units of energy are also used on an atomic and subatomic scale in specific contexts, such as the still smaller unit, the electron volt.


Dimensional Formula of Kinetic Energy

Derivation, using algebra alone (and assuming constant acceleration). Start from the theorem of work-energy, then add in the second law of motion by Newton.

The dimensional formula of Kinetic Energy is expressed by below equation

[M1 L2 T-2]

Where,

  • M = Mass

  • L = Length

  • T = Time


Derivation

Kinetic energy (K.E) = [Mass × Velocity2] × 2-1 ---------------- (1)

The dimensional formula of Mass = [M1 L0 T0] --------------(2)

Subsequently, Velocity = Distance × Time-1 = [L] × [T]-1

Therefore, The dimensional formula of velocity = [M0 L1 T-1] --------------------(3)

Now substitute equation (2) and (3) in equation (1) then we get,

⇒ K.E= [Mass × Velocity2] × 2-1

Or, K.E = [M1 L0 T0] × [M0 L1 T-1]2 = [M1 L2 T-2]

If kinetic energy is the energy of motion then the kinetic energy of an object in rest should naturally be zero. So we don't need the second term and the kinetic energy of an object is just

Hence, Kinetic Energy is dimensionally expressed as [M1 L2 T-2].

FAQ (Frequently Asked Questions)

1. What is the Dimension Formula of Heat?

Ans. Dimensional Formula of Specific Heat Capacity
M = Mass. K = Temperature. L = Length. T = Time.

2. What are the 7 Fundamental Dimensions?

Ans. There are 7 main measurements in all. The primary dimensions (sometimes called basic) are defined as independent or fundamental dimensions from which other dimensions can be derived. The primary dimensions are: mass, volume, time, temperature, electrical current, luminosity, and matter.

3. How many Dimensions are there?

Ans. There are three dimensions of space — length, width and depth — and one dimension of time in the universe as we know it. Yet there is the chance of mind-bending, that there are even other worlds out there. The universe works with 10 dimensions according to string theory, one of the leading physics models of the last half century.

4. What is the formula of Energy?

Ans. The formula linking power and energy is: Energy = Power x Time. The unit of energy is the joule, the watt is the unit of power and the second is the unit of time.

5. What is the SI unit of Energy?

Ans. The energy / work unit SI is the joule (J), named after English physicist James Prescott Joule (1818-1889). One joule is equal to the work done by a force of one newton moving one metre of object (J = N · m).