An asteroid that slammed into Earth about 65 million years ago (low on the dinosaurs' hit parade) was estimated to be about 8 km in diameter and about 10^15 kg in mass. A) If a similar asteroid headed toward Earth now with a speed of 21 km/s, how much kinetic energy would it have? B) Compare this answer to the energy used by the US in one year (about 10^20 J) and discuss. Problems
KE = 1/2 mv^2 = 1/2 * 10^15 * 21000^2 = 1.05*10^19 J
Now compare and discuss
A) KE = 1/2 m v^2 = 1/2 * 1E15 kg * (2.1E4 m/s)^2 ≈ 1E23 J
B) about a thousand times annual US energy consumption
the largest man-made explosion was a 50 MT thermonuclear weapon
detonated by the Soviet Union in October of 1961 ... 2.1E17 J
the largest recorded explosion in human history was the Krakatoa volcano in Indonesia ... August, 1883 ... estimated at 8.4E17 J
oops. I forgot to evaluate v^2 ...
To find the kinetic energy of an asteroid, you can use the formula:
Kinetic energy (KE) = 0.5 * mass * velocity^2
A) To determine the kinetic energy of the asteroid headed toward Earth with a speed of 21 km/s, we need to calculate it using the given mass and velocity.
Mass of the asteroid = 10^15 kg
Velocity of the asteroid = 21 km/s
We need to convert the velocity to meters per second before we can use the formula. There are 1000 meters in one kilometer and 1 second in 1,000 milliseconds. So, the conversion factor is:
21 km/s * (1000 m/km) * (1 s/1000 ms) = 21000 m/s
Now, we can substitute the values into the formula to calculate the kinetic energy:
KE = 0.5 * (10^15 kg) * (21000 m/s)^2
Let's calculate this:
KE = 0.5 * (10^15) * (21000^2) = 0.5 * (10^15) * (441,000,000) = 2.205 * 10^23 Joules
Therefore, the kinetic energy of the asteroid would be approximately 2.205 * 10^23 Joules.
B) To compare this answer to the energy used by the US in one year, we can convert the energy used by the US to the same unit (Joules).
Energy used by the US in one year = 10^20 J
Now, let's compare the two values:
2.205 * 10^23 J (kinetic energy of the asteroid)
10^20 J (energy used by the US in one year)
As we can see, the kinetic energy of the asteroid is significantly higher than the energy used by the US in one year. The energy of the asteroid is about 220,500 times more than the energy used by the US in a year.
This comparison highlights the immense destructive potential of asteroids and underscores the importance of monitoring and potentially diverting them from collision courses with Earth.