12MJ of energy is released when 1kg of dynamite is exploded. How much matter is converted into energy in the process?
12E6=mc^2
solve for m c^2=9E16
m= 12E6joules/9E16(m/s)^2 = 1.33E-10kg
check that.
To calculate the amount of matter converted into energy in the process, we can use Einstein's mass-energy equivalence principle, which states that energy (E) is equal to mass (m) times the speed of light squared (c²), expressed by the equation E = mc².
First, we need to convert the energy released into a more suitable unit. Since the given energy is in megajoules (MJ), we will convert it to joules (J) by multiplying by 10^6. Therefore, 12 MJ is equal to 12 × 10^6 J.
Next, we need to convert the energy into mass. Rearranging the equation E = mc², we can solve for mass (m): m = E / c².
The speed of light, c, is approximately 3 × 10^8 meters per second (m/s). So, c² is equal to (3 × 10^8)² = 9 × 10^16 m²/s².
Substituting the values, we can calculate the mass converted into energy: m = (12 × 10^6 J) / (9 × 10^16 m²/s²).
Simplifying the expression, the mass is approximately equal to 1.33 × 10^-10 kg.
Therefore, when 1 kg of dynamite is exploded, approximately 1.33 × 10^-10 kg of matter is converted into energy.