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\(\bullet\) \(\bullet\) \(\bullet\) Mass extinctions. One of the greatest mass extinc- tions occurred about 65 million years ago, when, along with many other life-forms, the dinosaurs went extinct. Most geologists and paleontologists agree that this event was caused when a large asteroid hit the earth. Scientists esti- mate that this asteroid was about 10 \(\mathrm{km}\) in diameter and that it would have been traveling at least as fast as 11 \(\mathrm{km} / \mathrm{s}\) . The density of asteroid material is about \(3.5 \mathrm{g} / \mathrm{cm}^{3},\) on the aver- age. (a) What would be the approximate mass of the aster- oid, assuming it to be spherical? (b) How much kinetic energy would the asteroid have delivered to the earth? (c) In perspective, consider the following: the total amount of energy used in one year by the human race is roughly 500 exajoules (see Appendix E). If this rate of energy use remained constant, how many years would it take the human species to use an amount of energy equal to the amount delivered by this asteroid?

Step by step solution

01

Calculate the Volume of the Asteroid

To find the mass of the asteroid, we first need to calculate its volume. A sphere's volume is given by the formula \[ V = \frac{4}{3}\pi r^3 \]where \( r \) is the radius. Given the diameter is 10 km, the radius \( r = 5 \text{ km} = 5000 \text{ m} = 5 \times 10^5 \text{ cm} \). Plug these values into the formula:\[ V = \frac{4}{3} \pi (5 \times 10^5)^3 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Asteroid Impact

Asteroid impacts have the power to drastically change life on Earth. Some 65 million years ago, a massive asteroid collided with our planet, believed to have triggered the extinction of the dinosaurs. This event is thought to have been caused by an asteroid approximately 10 kilometers in diameter. It's important to picture the enormity of this event: such an impact would have released an enormous amount of energy, equivalent to billions of nuclear bombs. Scientists identify the Chicxulub crater on the Yucatán Peninsula in Mexico as the potential site of this impact. These colossal events create shockwaves, intense heat, and throw dust into the atmosphere, affecting the climate and causing mass extinctions.

Kinetic Energy Calculation

Kinetic energy is the energy an object possesses due to its motion. In the case of an asteroid hurtling towards Earth, calculating its kinetic energy can give us a sense of the impact's devastation. The kinetic energy (K.E.) of an asteroid can be calculated using the formula:

• \( K.E. = \frac{1}{2} m v^2 \)

where \( m \) is the mass of the asteroid and \( v \) is its velocity. For our 10 km diameter asteroid traveling at 11 km/s, first, we determine its mass. A spherical volume equation is used:

• \( V = \frac{4}{3} \pi r^3 \)

Following this, we use the density to find the mass \( (m = \text{density} \times V) \). By plugging into the kinetic energy equation, we understand the catastrophic energy involved, which significantly surpasses any human-made energy release in recent times.

Dinosaur Extinction

Dinosaurs dominated Earth for over 160 million years before mysteriously going extinct approximately 65 million years ago. While several theories circulate about their extinction, the asteroid impact theory is widely accepted among scientists. The ash cloud from the impact might have blocked sunlight for years, causing drastic changes in climate, known as the "nuclear winter" effect.

• Food chains were disrupted.
• Plant life, reliant on sunlight, suffered massively.
• Carnivores lost their herbivore prey.

This mass extinction wiped out about 75% of Earth's species. Only small mammals, birds, and certain reptiles managed to survive and evolve, setting the stage for the rise of mammals, including humans.

Geology

Geology is the study of Earth's physical structure and substance, its history, and the processes that act on it. When we investigate the history of asteroid impacts, geologists play a crucial role in uncovering evidence of such catastrophic events. The sedimentary layers from 65 million years ago reveal changes in rock formations that can be linked to drastic shifts in the planet's environment. By studying the minerals and isotopes in these layers, geologists can determine the presence of extraterrestrial materials, same as those found in asteroids. This helps them confirm the hypothesis of an asteroid impact triggering the mass extinction event.

Paleontology

Paleontology is the scientific study of life that existed in the prehistoric past through the examination of fossils. Paleontologists help us recreate the puzzle of past mass extinction events. They study dinosaur fossils to understand more about their extinction. By examining bone fragments and other fossils, they can piece together the biodiversity before and after the impact. The sudden disappearance of many fossils in layers corresponding with the time of the Chicxulub impact supports the idea of a rapid extinction. Additionally, paleontological evidence provides insight into how life rebounded after the mass extinction, showcasing the resilience and adaptability of life on Earth.