The energy yield of a nuclear weapon is often defined in...

The energy yield of a nuclear weapon is often defined in terms of the equivalent mass of a conventional explosive. 1 ton of a conventional explosive releases 4.2 GJ. A typical nuclear warhead releases 250,000 times more, so the yield is expressed as 250 kilotons. I'hat is a staggering explosion, but the asteroid impact that wiped out the dinosaurs was significantly greater. Assume that the asteroid was a sphere $10 \mathrm{km}$ in diameter, with a density of $2500 \mathrm{kg} / \mathrm{m}^{3}$ and moving at $30 \mathrm{km} / \mathrm{s} .$ What energy was released at impact, in joules and in kilotons?

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Key Concepts

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion and is given by the formula KE = 1/2 * m * v^2. In impact scenarios, such as an asteroid striking the Earth, this concept is used to calculate the total energy released upon impact by computing the energy of the asteroid moving at a given velocity.

Volume and Mass Calculation for Spherical Objects

The calculation of mass for a spherical object involves determining its volume using the formula V = (4/3)?r^3, where r is the radius of the sphere, and then multiplying by the object's density. This concept allows for the estimation of the mass of objects like asteroids when provided with dimensions and density, which is critical for subsequent kinetic energy calculations.

Energy Unit Conversion

Energy unit conversion is crucial when comparing different forms of explosive yields. In this context, converting energy values from joules to kilotons of TNT (where one kiloton is defined based on the energy release from conventional explosives) enables a direct comparison between the energy of a nuclear explosion and that of a natural impact event like an asteroid collision.

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