What is 1600 joules in kg?

Physics
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What is 1600 joules in kg?

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How to Convert Joules to Kilograms

To convert energy measured in joules to mass in kilograms, we use Einstein’s famous equation from the theory of relativity, which is given by:

E = mc^2

where:

  • E is the energy (in joules),
  • m is the mass (in kilograms),
  • c is the speed of light in a vacuum, which is approximately 3 \times 10^8 \, \text{m/s}.

Step-by-Step Conversion

Step 1: Rearrange the formula to solve for mass m:

m = \frac{E}{c^2}

Step 2: Plug in the known values. Here, E = 1600 \, \text{joules} and c = 3 \times 10^8 \, \text{m/s}.

Step 3: Calculate the mass m using the formula:

m = \frac{1600}{(3 \times 10^8)^2} \, \text{kg}

Step 4: Simplify the expression under the division:

First, calculate c^2:

c^2 = (3 \times 10^8)^2 = 9 \times 10^{16}

Now, divide 1600 by this value:

m = \frac{1600}{9 \times 10^{16}}

Step 5: Perform the division:

m \approx 1.78 \times 10^{-14} \, \text{kg}

Conclusion

In summary, 1600 joules is equivalent to approximately 1.78 \times 10^{-14} kilograms. This result illustrates the small mass equivalent of a comparatively large amount of energy according to the principles of relativistic physics.

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