What is 1600 joules in kg?

What is 1600 joules in kg?

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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