91Ó°ÊÓ

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 \(5.0 \mathrm{~km} / \mathrm{s},\) and that 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 \(g^{\prime}\) 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 Bacillus subtilis bacteria survived after an acceleration of \(450.000 \mathrm{~g} .\) 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

Calculate Acceleration

To calculate acceleration, you have to apply the motion formula: \(a = (v_f^2 - v_i^2) / 2 * d\). Here \(v_f\) (final velocity) is 5 km/s that needs to be converted into m/s, so \(v_f = 5000 m/s\). \(v_i\) (initial velocity) is 0 (since it starts from rest), and \(d\) (distance) is given as 4 m. Substituting these values in, we get acceleration \(a = (5000^2 - 0^2) / (2 * 4) = 3125000 m/s^2\).

02

Convert Acceleration to g's

To convert acceleration from meter per second squared to g's, divide it by gravity's acceleration (9.81 m/s^2). Therefore, \(a = 3125000 / 9.81 = 318653 g'\).

03

Calculate the Time

To find the time interval for this acceleration to last, use the formula \(t = (v_f - v_i) / a\), which rearranges to \(t = 5000 / 3125000 = 0.0016 s\).

04

Analyze using Biological Data

Scientists found that over 40% of Bacillus subtilis bacteria survived an acceleration of 450000 g's. The calculated acceleration was higher (318653 g'), which means there is a possibility some bacteria could survive the trip from Mars to Earth.

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Key Concepts

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

Escape Velocity

Escape velocity refers to the minimum speed needed for an object to break free from the gravitational pull of a planet without further propulsion. Imagine kicking a ball hard enough that it doesn't come back down from Mars—it just keeps going until it's in space. For Mars, this speed is around 5,000 meters per second, or 18,000 kilometers per hour! To make an object reach Mars' escape velocity and overcome its gravitational pull, a significant force must be applied. This force is what gives the object the necessary acceleration. The escape velocity is crucial because it determines the limit of speed needed to launch something, say, a rock with microbes, away from Mars' surface into space. By knowing the escape velocity, we can start to calculate the other forces and influences, such as acceleration, that act on these Martian rocks during ejection.

Microbial Survival

The idea of microbial survival during high-acceleration events questions whether life could be transported across planets. When a meteor impacts a planet like Mars, rocks, potentially carrying microbes, could be blasted into space. The extreme forces involved could be lethal. But studies have shown that certain resilient microbes, like some bacteria, can survive intense acceleration. In tests, Bacillus subtilis, a type of bacteria, showed remarkable resilience. Over 40% of these bacteria survived accelerations up to 450,000 times the force of Earth's gravity! This suggests that some life forms could indeed endure the harsh journey through space, providing a fascinating insight into the possibility of interplanetary transfer of life. Microbial survival under these conditions hints at an exciting notion: life on Earth might have cosmic connections, potentially originating from or spreading to other celestial bodies.

Acceleration Calculation

Calculating the acceleration needed to propel a Martian rock involves understanding some basic physics principles of motion. Using the formula for constant acceleration, we find:\[ a = \frac{{v_f^2 - v_i^2}}{2d} \]Where:

• \( v_f \) is the final velocity (5,000 m/s)
• \( v_i \) is the initial velocity (0 m/s, since the rock starts from rest)
• \( d \) is the distance over which the acceleration occurs (4 m)

Plugging these into the formula gives an acceleration of 3,125,000 m/s². Converting this acceleration into "g's" (where 1 g = 9.81 m/s²) helps us understand the force in relation to Earth's gravity. Thus, dividing the acceleration by Earth's gravitational acceleration:\[ g' = \frac{3,125,000}{9.81} \approx 318,653 \]This enormous acceleration is crucial in understanding the forces experienced by rocks and potential life forms during Martian impacts.

Bacillus subtilis

Bacillus subtilis is a rod-shaped, gram-positive bacterium found in soil and vegetation. Known for its robustness, it can survive extreme environmental conditions by forming spores. These spores are highly resistant to heat, radiation, desiccation, and some chemical disinfectants and enzymes. In the context of Martian rock ejection, Bacillus subtilis becomes particularly interesting due to its demonstrated ability to survive extremely high accelerations, like those calculated for Martian rocks (318,653 g's). This resilience gives it a significant edge for surviving interplanetary journeys. Understanding the capabilities of Bacillus subtilis offers insights into the potential for microbial life to withstand space travel. This bacterium exemplifies the kind of life forms that might hitch a ride on a rock ejected from one planet and potentially land on another, such as Earth, preserving life across vast cosmic distances.