Relativistic Energy of a Ball: Understanding the Equivalence of Mass and Energy

[astro2cosmos]

according to mass-energy equivalent theorem, Regardless of whether the object is at rest or moving, the object of mass m having energy E=mc2.

suppose a ball of mass m is placed on ground, then how much energy this ball have?
Is it equal to E=mc2 ??
now if we place this ball above the ground up to height h, Is this mean all Energy of ball (i.e E=mc2) is converted to potential energy (mgh) ?
if so this ball have so much tremendous energy!
how it can be possible?

 

[utesfan100]

according to mass-energy equivalent theorem, Regardless of whether the object is at rest or moving, the object of mass m having energy E=mc2.

suppose a ball of mass m is placed on ground, then how much energy this ball have?
Is it equal to E=mc2 ??
now if we place this ball above the ground up to height h, Is this mean all Energy of ball (i.e E=mc2) is converted to potential energy (mgh) ?
if so this ball have so much tremendous energy!
how it can be possible?

If the ball went up to h all by itself, then yes. Usually ball's don't do that, and the rest energy of a small fraction of its mass would usually blast the ball well above escape velocity if it did.

Usually the energy to raise the ball h is added by some other force, thus the rest energy of the ball is constant.

 

[starthaus]

according to mass-energy equivalent theorem, Regardless of whether the object is at rest or moving, the object of mass m having energy E=mc2.

suppose a ball of mass m is placed on ground, then how much energy this ball have?
Is it equal to E=mc2 ??
now if we place this ball above the ground up to height h, Is this mean all Energy of ball (i.e E=mc2) is converted to potential energy (mgh) ?

No, it isn't. But , if the ball is made out of a radioactive material and you let it sit on your desk, it will release an energy:

$$\Delta E=c^2 \Delta m$$

Now, this can be a tremendous amount of energy due to the huge value of the conversion factor $$c^2$$

if so this ball have so much tremendous energy!
how it can be possible?

If it is radioactive, this is how it is possible. Be careful when you play with radioactive tennis balls :-)

 

[GRDixon]

Energy of ball (i.e E=mc2) is converted to potential energy (mgh) ?

mc² is descriptive of the isolated ball. mgh is an energy of the ball/earth system. Unfortunately, this potential energy is often said to be part of the ball's energy (e.g. in quantum theory).

 

[astro2cosmos]

mc² is descriptive of the isolated ball. mgh is an energy of the ball/earth system. Unfortunately, this potential energy is often said to be part of the ball's energy (e.g. in quantum theory).

what is the "descriptive of the isolated ball"?? then does the total energy of the ball contain both quantities i.e (T.E = mc2 + mgh)??
but in this case the quantitative value of mgh is very much higher than the mc2 in terms of Joule.!
wat is confusion!