Problem 20 - College Physics

Question

\(\cdot\) Meteor crater. About \(50,000\) years ago, a meteor crashed into the earth near present-day Flagstaff, Arizona. Recent \((2005)\) measurements estimate that this meteor had a mass of about \(1.4 \times 10^{8} \mathrm{kg}\) (around \(150,000\) tons) and hit the ground at 12 \(\mathrm{km} / \mathrm{s}\) . (a) How much kinetic energy did this meteor deliver to the ground? (b) How does this energy compare to the energy produced in one day by a standard coal-fired power plant, which generates about 1 billion joules per second?

Step-by-Step Solution

Answer

(a) Kinetic energy: \(1.008 \times 10^{16}\) joules; (b) Meteor's energy is much greater than a day's energy from a power plant.

Step 1: Identify Known Values

From the problem, we know the following values:- Mass \( m = 1.4 \times 10^8 \) kg - Velocity \( v = 12 \, \mathrm{km/s} = 12,000 \, \mathrm{m/s} \)These values will be used in the kinetic energy formula.

Step 2: Use the Kinetic Energy Formula

The formula for kinetic energy \( KE \) is given by:\[KE = \frac{1}{2}mv^2\]Substitute \( m = 1.4 \times 10^8 \) kg and \( v = 12,000 \) m/s into the formula.

Step 3: Calculate Kinetic Energy

Plug the known values into the kinetic energy formula:\[KE = \frac{1}{2} \times 1.4 \times 10^8 \, \mathrm{kg} \times (12,000 \, \mathrm{m/s})^2\]Simplify the expression:\[KE = 0.7 \times 10^8 \times 144 \times 10^6 \]Continuing with calculations:\[KE = 100.8 \times 10^{14} \text{ Joules}\]This simplifies to:\[KE = 1.008 \times 10^{16} \text{ Joules}\]

Step 4: Compare to Daily Energy from a Power Plant

A standard coal-fired power plant produces 1 billion joules per second, which is equivalent to:\[1 imes 10^9 \, \text{Joules} / \text{second}\]To find the daily energy output, multiply by the number of seconds in a day (86,400 seconds):\[ ext{Daily energy} = 1 \times 10^9 \, \text{Joules/second} \times 86,400 \, \text{seconds}\]which equals:\[8.64 \times 10^{13} \, \text{Joules}\]Compare this to the meteor's energy:\[KE = 1.008 \times 10^{16} \text{ Joules}\]

Step 5: Conclusion on Energy Comparison

The energy delivered by the meteor \(1.008 \times 10^{16}\) joules is significantly larger than the energy produced by a power plant in a day \(8.64 \times 10^{13}\) joules.

Key Concepts

Meteor Impact

Meteor impacts are extraordinary events that can cause significant changes to the Earth's surface. Imagine a colossal rock from space traveling at an incredibly high speed and crashing into our planet.
50,000 years ago, near Flagstaff, Arizona, such an event occurred. The meteor was estimated to have a mass of around 140 million kilograms and was traveling at an impressive speed of 12 kilometers per second.
This high-speed impact resulted in a massive release of energy, enough to create a large crater and drastically alter the landscape around the impact site. This incident not only emphasizes the destructive power of meteors but also their potential to affect our environment.
Meteor impacts can lead to the release of large amounts of dust and gases into the atmosphere, which might even alter the climate.
Understanding meteor impacts allows us to appreciate the dynamic nature of our planet and the role these cosmic events play in shaping Earth's geological history.

Energy Comparison

Energy comparison helps us understand the scale of energy released in different processes or events. The kinetic energy from the meteor impact in Arizona is compared to the energy output of a standard coal-fired power plant.
Let's break it down:

• Kinetic energy from the meteor is calculated to be approximately \(1.008 \times 10^{16} \) Joules.
• A standard power plant generates 1 billion Joules every second or \(1 \times 10^9 \) Joules per second.
• In a day, this power plant produces \(8.64 \times 10^{13} \) Joules.

When we compare these numbers, the energy from the meteor is many times greater than the daily energy output of the power plant.
This comparison showcases the vast amount of energy released by such a space object impact. It's an excellent example of the immense forces present in our universe and how they can occasionally interact with Earth in dramatic ways.

Physics Problem Solving

Physics problem solving involves using scientific principles and formulas to understand and solve real-world phenomena. When approaching a problem like calculating the energy of a meteor impact, we follow a systematic process.
Here's a step-by-step approach:

• Identify Known Values: Recognize the given information, such as mass and velocity for the meteor.
• Apply Relevant Formulas: Use the kinetic energy formula \( KE = \frac{1}{2} mv^2 \) to find the energy involved.
• Perform Calculations: Substitute the known values into the equation and perform the necessary operations to arrive at the answer.
• Analyze and Compare: Interpret the result within the given context, such as comparing it to other energy outputs like those from a power plant.

Understanding each component in this process allows students to apply their physics knowledge to various scenarios effectively. It also enhances their problem-solving skills by giving them the tools to tackle both theoretical and practical problems in physics.