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European Journal of Applied Sciences – Vol. 11, No. 6

Publication Date: December 25, 2023

DOI:10.14738/aivp.116.16169

Chanana, R. K. (2023). Falling Bodies on Earth at Constant Acceleration Due to Gravity Exhibit Universal Mass-Energy Equivalence

Relation. European Journal of Applied Sciences, Vol - 11(6). 270-271.

Services for Science and Education – United Kingdom

Falling Bodies on Earth at Constant Acceleration Due to Gravity

Exhibit Universal Mass-Energy Equivalence Relation

Ravi Kumar Chanana

Self-Employed Independent Researcher, Gr. Noida-201310, India

ABSTRACT

In this research article, it is shown that a falling body on earth at constant

acceleration due to gravity will also exhibit the universal mass-energy equivalence

relation given as dE/E = dm/m, neglecting a 1 to 2 % change in potential energy due

to the change in height.

Keywords: Acceleration due to gravity, mass-energy equivalence, falling body.

SHORT COMMUNICATION

It has been shown that the big and small bodies travelling at constant velocity exhibit universal

mass-energy equivalence relation given as dE/E = dm/m. Here dE is the differential energy, E

is the total energy, dm is the differential mass and m is the total mass [1-2]. In this article it is

shown that a falling mass under constant acceleration due to gravity also exhibit the universal

mass-energy equivalence relation. Consider a ball falling from 10 or 100 or even 1000 meters

above the earth’s surface towards the earth under constant acceleration due to gravity, g which

is 9.8 meters/s2. The potential energy of the mass at a height h is given by the equation E =

mgh, where m is the mass and h is the height. The potential energy will be in Joules, if the mass

is in Kg, acceleration due to gravity g, is in meters/sec2 and height h is in meters. Differentiating

this equation once gives

dE = gh (dm) + mg (dh) (1).

Here, dm is a differential mass that can be achieved by say, taking a larger mass, dE is a

differential potential energy and dh is the differential height. Dividing this equation by the

original equation of E =mgh gives:

dE / E = dm/m + dh/h (2).

Now, gravity is known to be inversely proportional to height which is measured from the centre

of earth. The radius of the earth assuming it to be a sphere is very large at about 6370 Kms.

Therefore, g will remain constant at 9.8 meters/s2 for a considerable height h above the earth.

Neglecting the change in energy of a falling body due to 1 to 2 % change dh, of h above earth,

one can say that the equation (2) can be written as:

dE / E = dm/m (3).

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271

Chanana, R. K. (2023). Falling Bodies on Earth at Constant Acceleration Due to Gravity Exhibit Universal Mass-Energy Equivalence Relation. European

Journal of Applied Sciences, Vol - 11(6). 270-271.

URL: http://dx.doi.org/10.14738/aivp.116.16169

This is the universal mass-energy equivalence relation, with E as energy and m as the mass. It

is thus concluded that the universal mass-energy equivalence relation is valid not only for

masses travelling at constant speed, but also for masses travelling at constant acceleration

neglecting a 1 to 2% change in energy due to change in height.

References

[1]. R.K. Channa, Linear model for the variation of semiconductor bandgap with high temperature for high

temperature electronics, IOSR-J. Electrical and Electronics Engg., 2021, 16(6), p. 5-8.

[2]. R.K. Chanana, Universal mass-energy equivalence for relativistic masses, International J. of Engg. and

Science Invention, 2023, 12(3), p. 35-36.