Solving E=mc^2: Exploring the Error in Results

In summary, there was a question about the equation E=mc^2 and why two different conversions resulted in different answers. The error was found to be in the calculation of 300 million x 300 million, as it should be 90000 million million instead of 90000 million. The use of scientific notation was suggested to avoid such errors.
  • #1
matttan
25
0
I was doing the equation of E=mc^2

So its like this:

If M = 1kg and C=300 million m/s,

Then E= 1 x 300 million x 300 million = 90 000 million joules/90 billion joules

But the qs is,

If I convert c to 0.3 billion m/s,

then E = 1 x 0.3 billion x 0.3 billion = 0.09 billion joules

Why are both different? Can anyone explain the error?

Thanks (:
 
Last edited:
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  • #2
Neither of these answers are right. (3*10^8)^2 = 9*10^16
 
  • #3
300 million x 300 million = [itex](300 \times 10^6) \times (300 \times 10^6) = (300^2) \times 10^{12} = (9 \times 10^4) \times 10^{12} = 9 \times 10^{15}[/itex]
while
0.3 billion x 0.3 billion = [itex](0.3 \times 10^9) \times (0.3 \times 10^9) = (0.3^2) \times 10^{18} = (9 \times 10^{-2}) \times 10^{18}) = 9 \times 10^{15}[/itex].

I think your problem is that you are writing
300 million x 300 million = 90000 million
while it is actually
90000 million million.

Scientific notation is handy! :)
 

1. How did Einstein come up with the equation E=mc^2?

Einstein's famous equation, E=mc^2, was derived from his theory of special relativity. This theory states that energy and mass are interchangeable and can be converted into each other. To prove this, Einstein used the fact that the speed of light is constant and found that the amount of energy contained in an object is equal to its mass multiplied by the speed of light squared.

2. What does E=mc^2 actually mean?

E=mc^2 is an equation that demonstrates the relationship between energy (E), mass (m), and the speed of light (c). It shows that energy and mass are equivalent and can be converted into each other. The equation suggests that even small amounts of mass contain a large amount of energy.

3. Is E=mc^2 always accurate?

While E=mc^2 is a fundamental equation in physics and has been proven to be accurate in many experiments, it is not always accurate. This is because it is based on the assumptions of special relativity, which do not hold true in extreme conditions such as near the speed of light or in the presence of strong gravitational fields.

4. Are there any errors associated with E=mc^2?

There are no inherent errors in the equation E=mc^2 itself, as it is a fundamental law in physics. However, errors can occur in the measurement of mass and energy, which can affect the accuracy of the results obtained from the equation. Additionally, as mentioned before, the equation is not valid in all situations, which can lead to errors in certain cases.

5. How is E=mc^2 used in practical applications?

E=mc^2 has many practical applications in various fields such as nuclear energy, nuclear weapons, and nuclear medicine. It is also used in particle accelerators to convert mass into energy and vice versa. The equation also plays a crucial role in understanding the structure and formation of stars and galaxies, as well as in the development of new technologies such as nuclear fusion reactors.

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