I'm not too good with these special relativity problems :/

The question is: A 20 kiloton bomb releases 8 x 10^13 joules. How much mass must be converted into other forms of energy?

You are already given Energy, would I still use the E=mc^2 formula??

E=(2.0*10^7 kg)(3*10^8 m/s)^2 ?

unlessss....

I just solve for mass and the 20 kiloton is just extra useless information meant to throw people off and do this:

e=mc^2 m = E/c^2

m = 8*10^13 J / (3.0*10^8 m/s)^2

m= 8.89 * 10 ^-4 kg hmm

I agree with this:

e=mc^2 m = E/c^2

m = 8*10^13 J / (3.0*10^8 m/s)^2

m= 8.89 * 10 ^-4 kg hmm

A gram of mass is a lot of energy.

thank you! How would I know not to use the mass of 20 kilotons though? I wish they didn't put that in the question it really throws you off haha

Yes, you would still use the equation E=mc^2 to solve this problem. However, you need to rearrange the equation to solve for mass (m) instead of energy (E). The equation should be:

m = E / c^2

Where:
m = mass (in kilograms)
E = energy (in joules)
c = speed of light (approximately 3 x 10^8 meters per second)

Plugging in the given energy:
E = 8 x 10^13 joules

And the speed of light:
c = 3 x 10^8 m/s

You can now substitute these values into the equation:

m = (8 x 10^13 joules) / (3 x 10^8 m/s)^2

Let's simplify this equation. Squaring the speed of light:

m = (8 x 10^13 joules) / (9 x 10^16 m^2/s^2)

Canceling out the units:

m = 8 x 10^13 / 9 x 10^16 kg

Now, you can divide the numerator by the denominator using the rule of exponents:

m = (8 / 9) x (10^13 / 10^16) kg

Simplifying further:

m = (8 / 9) x 10^(13-16) kg
m = (8 / 9) x 10^(-3) kg
m ≈ 0.888 x 10^(-3) kg

So, the mass that must be converted into other forms of energy is approximately 0.888 milligrams.