Calculate the rest mass (In grams) of an object whose rest energy is equal to the energy released by a tonne of tnt the energy liberated by 1 g of tnt = 4kJ
Rest energy = moc 2
1 tonne of tnt equals 10^6 x 4kJ =
4 x 10^6 kJ x (3.0^8)sqrd = 3.6 x 10^23kJ
is this right ?? i cannot work out the grams can anyone help please .. thanks
You're done. J * (m/s)^2 = kg
Your result is 3.6*10^23 kg, not J
Always keep track of the units!!!
Thank you ....
To calculate the rest mass of an object, you can use Einstein's famous equation: E = mc^2, where E is the rest energy, m is the rest mass, and c is the speed of light.
In this case, the rest energy is given as the energy released by a tonne of TNT, which is 4 x 10^6 kJ or 4 x 10^9 J.
So, we have E = 4 x 10^9 J and c = 3 x 10^8 m/s.
Rearranging the equation, we can solve for m: m = E / c^2.
Substituting the values, we get:
m = (4 x 10^9 J) / (3 x 10^8 m/s)^2
Now, let's simplify the equation:
1. Determine the value of c^2:
c^2 = (3 x 10^8 m/s)^2 = 9 x 10^16 m^2/s^2
2. Substitute the value of c^2 into the equation:
m = (4 x 10^9 J) / (9 x 10^16 m^2/s^2)
Now, let's simplify the equation using scientific notation:
1. Divide the numbers:
m = (4 / 9) x (10^9 / 10^16) J
2. Divide the exponents:
m = (4 / 9) x 10^-7 J
Finally, we need to convert Joules to grams. Please note that 1 Joule is equivalent to 1 kg · m^2/s^2. To convert it to grams, we use the relationship 1 kg = 1000 g.
So, m = (4 / 9) x 10^-7 J x (1 kg / 1000 g)
Simplifying further, we have:
m = (4 x 10^-7) / (9 x 1000) kg
m = (4 x 10^-7) / 9000 kg
Now, multiply by 1000 to convert to grams:
m = (4 x 10^-7) / 9000 kg x 1000 g/kg
m = 4 x 10^-10 g
Therefore, the rest mass of the object is approximately 4 x 10^-10 grams.