To find the energy equivalent of an object with a mass of 4.1 kg, we will use Einstein's famous equation for mass-energy equivalence:
[tex]\[ E = mc^2 \][/tex]
where:
- [tex]\( E \)[/tex] is the energy
- [tex]\( m \)[/tex] is the mass
- [tex]\( c \)[/tex] is the speed of light in a vacuum
1. Identify the given values:
- Mass [tex]\( m = 4.1 \, \text{kg} \)[/tex]
- Speed of light [tex]\( c = 3 \times 10^8 \, \text{m/s} \)[/tex]
2. Substitute the given values into the equation:
[tex]\[ E = 4.1 \, \text{kg} \times (3 \times 10^8 \, \text{m/s})^2 \][/tex]
3. Calculate the square of the speed of light:
[tex]\[ c^2 = (3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \][/tex]
4. Multiply the mass by the squared speed of light:
[tex]\[ E = 4.1 \, \text{kg} \times 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \][/tex]
5. Perform the multiplication:
[tex]\[ E = 36.9 \times 10^{16} \, \text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
6. Express the result in scientific notation:
[tex]\[ E = 3.69 \times 10^{17} \, \text{J} \][/tex]
Therefore, the energy equivalent of an object with a mass of 4.1 kg is [tex]\[ 3.69 \times 10^{17} \, \text{J} \][/tex].
Among the given options, the closest match is:
[tex]\[\boxed{3.7 \times 10^{17} \, \text{J}} \][/tex]
