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Are We Martians? It has been suggested, and not facetiously, that life might have originated on Mars and been carried to the earth when a meteor hit Mars and blasted pieces of rock (perhaps containing primitive life) free of the surface. Astronomers know that many Martian rocks have come to the earth this way. (For information on one of these, search the Internet for "ALH \(84001 . "\) ') One objection to this idea is that microbes would have to undergo an enormous lethal acceleration during the impact. Let us investigate how large such an acceleration might be. To escape Mars, rock fragments would have to reach its escape velocity of \(5.0 \mathrm{km} / \mathrm{s},\) and this would most likely happen over a distance of about 4.0 \(\mathrm{m}\) during the meteor impact. (a) What would be the acceleration ( in \(\mathrm{m} / \mathrm{s}^{2}\) and \(g^{\prime} \mathrm{s}\)) of such a rock fragment, if the acceleration is constant? (b) How long would this acceleration last? (c) In tests, scientists have found that over 40\(\%\) of Bacillius subtilis bacteria survived after an acceleration of \(450,000 g .\) In light of your answer to part (a), can we rule out the hypothesis that life might have been blasted from Mars to the earth?

Step by step solution

01

Understand the problem

We need to find the acceleration required for a rock fragment to reach Mars' escape velocity of \(5.0 \text{ km/s}\) over a distance of 4.0 m, and also analyze the effect of this acceleration on bacteria survival.

02

Use kinematic equations

We use the kinematic equation \(v^2 = u^2 + 2as\) to find acceleration, where \(v = 5.0 \times 10^3 \text{ m/s}\) is the final velocity, \(u = 0\) is the initial velocity, and \(s = 4.0 \text{ m}\) is the distance over which the acceleration occurs.

03

Calculate acceleration in \(\text{m/s}^2\)

Substituting the values in the equation, \( (5.0 \times 10^3)^2 = 0 + 2 \cdot a \cdot 4.0 \). Solving for \(a\), we get:\[ a = \frac{(5.0 \times 10^3)^2}{2 \times 4.0} = \frac{25.0 \times 10^6}{8} = 3.125 \times 10^6 \text{ m/s}^2 \]

04

Convert acceleration to g's

To convert \(3.125 \times 10^6 \text{ m/s}^2\) to \(g\)'s, divide by the acceleration due to gravity (\(9.81 \text{ m/s}^2\)):\[ a = \frac{3.125 \times 10^6}{9.81} \approx 318,040 \ g \]

05

Calculate acceleration duration

Using the formula \(v = u + at\), substitute for \(t\) with \(v = 5.0 \times 10^3 \text{ m/s}\), \(a = 3.125 \times 10^6 \text{ m/s}^2\), and \(u = 0\):\[ t = \frac{5.0 \times 10^3}{3.125 \times 10^6} \approx 0.0016 \text{ s} \]

06

Analyze survival hypothesis

Given that bacteria can survive accelerations up to \(450,000 \ g\), and our calculated acceleration is \(318,040 \ g\), we find that the acceleration experienced by rock fragments is below the threshold that some bacteria can survive.

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Key Concepts

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

Acceleration Calculations

When we talk about acceleration, we are discussing the rate of change in velocity of an object over time. For a rock to escape Mars, it must reach Mars' escape velocity quickly. To determine the necessary acceleration, we use the formula from the kinematic equations:

• Start with the equation:
  \[v^2 = u^2 + 2as\]
• Here, \(v\) is the final velocity (5.0 km/s), \(u\) is the initial velocity (0 m/s), \(s\) is the distance (4.0 m), and \(a\) is the unknown acceleration.
• After substituting the known values and solving for \(a\), we found the acceleration to be approximately \(3.125 \times 10^6 \text{ m/s}^2\).

This value indicates how quickly the rock must speed up to escape Mars' gravitational pull, highlighting the extreme conditions present during such an escape.

Kinematic Equations

Kinematic equations are fundamental in physics for describing motion with constant acceleration. The equation we used, \(v^2 = u^2 + 2as\), is one of these key equations and is often utilized in problems involving uniform acceleration. Let's break down its components:

• \(v\) is the final velocity that the object is trying to reach.
• \(u\) is the initial velocity from which the object started.
• \(a\) is the constant acceleration applied to reach the final velocity.
• \(s\) is the distance over which this acceleration occurs.

In our exercise, we assumed the initial velocity \(u\) was zero, meaning the rock was initially at rest. This simplifies the calculations, allowing us to directly link the distance to the final velocity and acceleration. The key takeaway is how these equations help predict motion by linking physical quantities, making them indispensable tools in both theoretical and applied physics.

Bacterial Survival

The notion of bacterial survival under extreme conditions is fascinating. In the context of our exercise, it becomes highly relevant as we evaluate whether bacteria can survive the acceleration involved in being ejected from Mars. Studies have shown that some bacteria, like Bacillus subtilis, can endure remarkable stresses.

• Scientists tested these bacteria by exposing them to accelerations of up to \(450,000 \ g\). Surprisingly, over 40% survived.
• In our scenario, the calculated acceleration needed to escape Mars is \(318,040 \ g\), which is below the threshold these bacteria can tolerate.

This information suggests that the hypothesis of life originating from Mars and surviving the journey to Earth is plausible. This exciting notion challenges us to rethink the extreme resilience of life.

Mars Escape Velocity

Escape velocity is the minimum speed an object needs to break away from a planet's gravitational pull without additional propulsion. For Mars, this speed is set at 5.0 km/s, a significant figure guiding the calculations in our exercise.

• This required velocity is a function of Mars' gravity and mass.
• It ensures that once reached, the object can continue into space without further force applied.

Understanding escape velocity is crucial for space missions and studying meteor impacts. It helps explain how Martian rocks, and possibly life, could travel between planets. The physics behind this empowers us to explore possibilities beyond earth, delving into the origins of life itself.