Potential energy as a form of mass?

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SUMMARY

The discussion centers on the calculation of potential energy and its relationship to mass using the equation E = mc². A mass of 5 kg at a height of 3 m yields a potential energy of 147 J, which was incorrectly converted to electron volts (eV) resulting in a miscalculated mass of 10.2e3 kg. The correct interpretation reveals that the total energy contribution of the system (Earth plus mass) differs from the rest energy of the test mass, leading to a corrected mass of approximately 3 kg.

PREREQUISITES
  • Understanding of gravitational potential energy calculations
  • Familiarity with Einstein's mass-energy equivalence principle (E = mc²)
  • Basic knowledge of unit conversions, particularly between joules and electron volts
  • Concept of total energy in a system involving gravitational fields
NEXT STEPS
  • Explore gravitational potential energy calculations in different contexts
  • Study the implications of mass-energy equivalence in relativistic physics
  • Learn about unit conversions between joules and electron volts in physics
  • Investigate the concept of total energy in systems involving gravitational interactions
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Students of physics, educators teaching energy concepts, and anyone interested in the relationship between mass and energy in gravitational fields.

Vitani11
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Homework Statement


Let's say we have a mass of 5kg at a height of 3 m so it's potential energy is mgh = 147J/1.6e-19 = 9.19 e20 eV. Now we know that E = mc^2... so when finding the mass of this potential energy we get 10.2e3 kg. What the hell is that supposed to mean?

Homework Equations


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The Attempt at a Solution

 
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Vitani11 said:
mgh = 147J/1.6e-19 = 9.19 e20 eV
Something went wrong with the units here.
Vitani11 said:
Now we know that E = mc^2... so when finding the mass of this potential energy we get 10.2e3 kg
And again here.

If you fix the calculation, you'll get a result of something like 3.000000000000001 kg (didn't count the zeros). It means total contribution to energy of the overall system (Earth+mass) is not the same as the rest energy of the small test mass.
 
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