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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 Martian surface. Astronomers know that many Martian rocks have come to the earth this way. (For instance, search the Internet for "ALH 84001.") One objection to this idea is that microbes would have had 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 km/s, and that would most likely happen over a distance of about 4.0 m during the meteor impact. (a) What would be the acceleration (in m/s\(^2\) and \(g'\)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\(\text{%}\) of \(\textit{Bacillus subtilis}\) 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

Analyze the Given Information

We need to find the acceleration (in m/s² and g's) of a rock fragment escaping Mars when it reaches an escape velocity of 5.0 km/s over a distance of 4.0 m.

02

Use the Kinematic Equation for Constant Acceleration

The equation \( v^2 = u^2 + 2as \) relates final velocity \( v \), initial velocity \( u \) (assumed to be 0 for starting from rest), acceleration \( a \), and the distance \( s \). Substituting the known values: \( v = 5000 \text{ m/s} \), \( u = 0 \text{ m/s} \), and \( s = 4.0 \text{ m} \), we find the acceleration \( a \).

03

Calculate Acceleration in m/s²

Plugging values into the equation: \[ v^2 = 2as \] \[ (5000)^2 = 2a(4) \] \[ 25000000 = 8a \] Solving for \( a \), we get \( a = 3125000 \text{ m/s}^2 \).

04

Convert Acceleration to g's

The acceleration in g's is found by dividing \( a \) by the acceleration due to gravity \( g = 9.8 \text{ m/s}^2 \). Thus, \[ a = \frac{3125000}{9.8} \approx 318367.35 \text{ g's} \].

05

Calculate the Duration of Acceleration

To find the time \( t \) the acceleration lasts, use the formula: \[ v = u + at \] \[ 5000 = 0 + 3125000t \]Solving for \( t \), \[ t \approx 0.0016 \text{ seconds} \].

06

Assess the Microbial Survival Possibility

Given that 40\(\text{%}\) of \(\(\textit{Bacillus subtilis}\)\) survive up to 450,000 g's, and calculated acceleration is approximately 318,367.35 g's, some microbes might survive such impact based on these values.

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Key Concepts

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

Kinematic Equations

Kinematic equations are used in physics to describe the motion of objects. They can predict things like how far and how fast an object will go under constant acceleration. When dealing with martian rock acceleration, these equations become pivotal. One primary kinematic equation involves the relationship between velocity, acceleration, and distance. Given by \( v^2 = u^2 + 2as \), where:

• \( v \) is the final velocity,
• \( u \) is the initial velocity,
• \( a \) is acceleration, and
• \( s \) is the distance covered.

For a fragment of rock overcoming Mars' gravity and reaching the escape velocity of 5.0 km/s from rest, we substitute the relevant knowns. Assuming an initial velocity of 0, a distance of 4.0 m, and an escape velocity of 5000 m/s, the kinematic equation helps derive the acceleration. This equation helps forecast the seemingly overwhelming acceleration that any rock would need to achieve to break free off the martian surface, letting us explore whether microbes could endure such forces.

Microbial Survival in Extreme Conditions

Microbes have an astounding ability to survive in extreme conditions, both on Earth and possibly other planets. This makes the notion that life might have been transferred from Mars to Earth intriguing yet plausible. Certain microbes, such as \(\(\textit{Bacillus subtilis}\)\), can survive extraordinary G-forces. An experiment using 450,000 g's—the unit of acceleration based on Earth's gravity—has shown that a significant percentage of these hardy microbes can endure such rapid forces. Knowing that the calculated acceleration for Martian rocks is approximately 318,367 g's, there is potential for some microbial survivors.
Microbial life can survive prolonged periods of dormancy during space travel, aiding the theory that life might have hitched a ride on meteorite fragments from Mars. This resilience offers a new perspective on panspermia, the theory of life exchanging between planets, raising questions about the durability of life forms and their adaptability to different planetary environments.

Meteor Impacts on Mars

Meteor impacts are frequent on Mars; the thin atmosphere offers little protection compared to Earth. These impacts can propel rocks into space with significant force, which is central to the theory that life may have been transported via meteorites. When meteors collide with Mars at high speeds, they convert kinetic energy into significant heat and pressure, potentially scarring the landscape and ejecting materials.
This ejection can transport Mars rocks towards Earth, where influences such as Earth's atmosphere and gravitational pull could capture them. Famous meteorites, like ALH 84001, provide evidence of Martian origins, having been identified on Earth with characteristics unique to Martian geology. The forces involved in these impacts, as calculated through kinematic equations, raise important conversations on the conceivable transport of life between planets, challenging our conventional understanding of life's cosmic journey.