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Answer :
To calculate the amount of energy in a person's body, we use Einstein's famous equation, [tex]\(E = mc^2\)[/tex]. In this equation:
- [tex]\(E\)[/tex] represents energy, measured in joules.
- [tex]\(m\)[/tex] is the mass of the object, measured in kilograms.
- [tex]\(c\)[/tex] is the speed of light in a vacuum, approximately [tex]\(299,792,458\)[/tex] meters per second.
Let's go through the calculation step-by-step:
1. Identify the mass ([tex]\(m\)[/tex]): In this case, the person's mass is given as [tex]\(61.4\)[/tex] kilograms.
2. Use the speed of light ([tex]\(c\)[/tex]): The speed of light is a constant value, approximately [tex]\(299,792,458\)[/tex] meters per second.
3. Apply the formula [tex]\(E = mc^2\)[/tex]:
- Substitute the given mass ([tex]\(61.4\)[/tex] kg) and the speed of light ([tex]\(299,792,458\)[/tex] m/s) into the formula:
[tex]\[
E = 61.4 \times (299,792,458)^2
\][/tex]
4. Calculate the energy ([tex]\(E\)[/tex]):
- Compute the square of the speed of light:
[tex]\[
(299,792,458)^2 = 89,875,517,873,681,764
\][/tex]
- Multiply the mass by the squared speed of light to find the energy:
[tex]\[
E = 61.4 \times 89,875,517,873,681,764
\][/tex]
- This results in an energy value of approximately:
[tex]\[
E \approx 5.51835679744406 \times 10^{18} \text{ joules}
\][/tex]
Therefore, the amount of energy in this person's body, according to Einstein's equation, is approximately [tex]\(5.518 \times 10^{18}\)[/tex] joules. This immense amount of energy reflects the substantial energy stored within matter due to its mass.
- [tex]\(E\)[/tex] represents energy, measured in joules.
- [tex]\(m\)[/tex] is the mass of the object, measured in kilograms.
- [tex]\(c\)[/tex] is the speed of light in a vacuum, approximately [tex]\(299,792,458\)[/tex] meters per second.
Let's go through the calculation step-by-step:
1. Identify the mass ([tex]\(m\)[/tex]): In this case, the person's mass is given as [tex]\(61.4\)[/tex] kilograms.
2. Use the speed of light ([tex]\(c\)[/tex]): The speed of light is a constant value, approximately [tex]\(299,792,458\)[/tex] meters per second.
3. Apply the formula [tex]\(E = mc^2\)[/tex]:
- Substitute the given mass ([tex]\(61.4\)[/tex] kg) and the speed of light ([tex]\(299,792,458\)[/tex] m/s) into the formula:
[tex]\[
E = 61.4 \times (299,792,458)^2
\][/tex]
4. Calculate the energy ([tex]\(E\)[/tex]):
- Compute the square of the speed of light:
[tex]\[
(299,792,458)^2 = 89,875,517,873,681,764
\][/tex]
- Multiply the mass by the squared speed of light to find the energy:
[tex]\[
E = 61.4 \times 89,875,517,873,681,764
\][/tex]
- This results in an energy value of approximately:
[tex]\[
E \approx 5.51835679744406 \times 10^{18} \text{ joules}
\][/tex]
Therefore, the amount of energy in this person's body, according to Einstein's equation, is approximately [tex]\(5.518 \times 10^{18}\)[/tex] joules. This immense amount of energy reflects the substantial energy stored within matter due to its mass.
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