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Chapter 8: Problem 37

The object that created Arizona's Meteor Crater was estimated to have a radius of 25 meters and a mass of 300 million \(\mathrm{kg}\) Calculate the density of the impacting object, and explain what that may tell you about its composition.

Short Answer

Expert verified
The density of the object is approximately 4590 kg/m³, suggesting it was likely composed of dense material like iron or nickel.

Step by step solution

01

- Understand the formula for density

Density is defined as mass per unit volume. The formula for density is given by \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume.
02

- Write down the given values

The radius of the object, \( r \), is given as 25 meters and the mass, \( m \), is given as 300 million kilograms (i.e., 300,000,000 kg).
03

- Calculate the volume of the spherical object

The volume \( V \) of a sphere is given by \( V = \frac{4}{3} \pi r^3 \). Substituting the radius, \( r = 25 \) meters, we get: \[ V = \frac{4}{3} \pi (25)^3 = \frac{4}{3} \pi (15625) \approx 65345.6 \text{ cubic meters} \].
04

- Calculate the density

Using the formula for density, \( \rho = \frac{m}{V} \), and substituting the mass and volume calculated: \[ \rho = \frac{300,000,000 \text{ kg}}{65345.6 \text{ m}^3} \approx 4590 \text{ kg/m}^3 \].
05

- Interpret the density

The density calculated is approximately 4590 kg/m³. This high density suggests that the object was composed of a dense material, likely metallic in nature, such as iron or nickel.

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Key Concepts

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

density calculation
Understanding density is essential for many scientific calculations. Density is a measure of how much mass is contained within a given volume. It's calculated using the formula: \( \rho = \frac{m}{V} \). Here, \( \rho \) represents density, \( m \) is mass, and \( V \) is volume. For the meteor that created the Arizona Meteor Crater, we know its mass and volume. By plugging these values into the density formula, we can determine the object's density.
volume of sphere
The volume of a sphere is crucial to estimating the density of spherical objects like meteors. The volume \( V \) of a sphere can be calculated with the formula: \[ V = \frac{4}{3} \pi r^3 \]. This formula needs the radius of the sphere \( r \). For instance, if the radius of our meteor is 25 meters, then substituting in the formula gives: \[ V = \frac{4}{3} \pi (25)^3 \], which computes to approximately 65345.6 cubic meters. Understanding how to calculate volume is the first step towards finding the density.
mass
Mass is the amount of matter in an object and is usually measured in kilograms (kg). For our meteor, the mass is given as 300 million kilograms or 300,000,000 kg. This value is critical when calculating density since it directly affects the result. Remember, the higher the mass for a given volume, the higher the density, and vice versa.
meteor composition
Knowing the density of the meteor helps us make educated guesses about its composition. A high-density value, like the 4590 kg/m³ calculated for the Arizona Meteor Crater object, suggests that the meteor was made of a heavy, dense material. This is often indicative of a composition that includes metals. Hence, knowing the density allows scientists to speculate about the kind of materials that make up the meteor without having a physical sample.
metallic materials
Meteorites often contain metallic elements, which contribute to their high density. Common metals found in meteors include iron and nickel. These metals are much denser than most non-metallic materials. For example, iron has a density of about 7874 kg/m³ and nickel about 8908 kg/m³. When we calculate a high density for a meteor, it is a strong indicator that metals are a significant part of its composition. This insight is valuable for understanding the nature and origin of the meteor.

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Most popular questions from this chapter

Scientists know the history of Earth's magnetic field because a. the magnetic field hasn't changed since Earth formed. b. they see today's changes and project backward in time. c. the magnetic field becomes frozen into rocks, and plate tectonics spreads those rocks apart. d. they compare the magnetic fields on other planets to Earth's.

Geologists can determine the actual age of features on a planet by a. radiometric dating of rocks retrieved from the planet. b. comparing cratering rates on one planet to those on another c. assuming that all features on a planetary surface are the same age. d. both a and b e. both b and c

Geologists can determine the relative age of features on a planet because a. the ones on top must be older. b. the ones on top must be younger. c. the larger ones must be older. d. the larger ones must be younger.

Compare the kinetic energy \(\left(=\frac{1}{2} m v^{2}\right)\) of a 1 -gram piece of ice (about half the mass of a dime) entering Earth's atmosphere at a speed of \(50 \mathrm{km} / \mathrm{s}\) to that of a 2 -metric-ton SUV (mass \(=2 \times\) \(10^{3} \mathrm{kg}\) speeding down the highway at \(90 \mathrm{km} / \mathrm{h}\).

Scientists propose an early period of heavy bombardment in the Solar System because a. the Moon is heavily cratered. b. all the craters on the Moon are old. c. the smooth part of the Moon is nearly as old as the heavily cratered part. d. all the craters on the Moon are young.
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