Length of acceleration for a rock fragment escaping Mars

In summary, the conversation discusses the possibility of life originating on Mars and being transported to Earth through meteor impacts. The objection to this idea is that microbes would have to undergo a high acceleration during the impact. The question asks for the acceleration and duration of such an impact, and the conversation provides the equations and calculations to find these values. Ultimately, the correct answer for the acceleration is 3.13e6 m/s^2, and the duration is approximately 0.0016 seconds.
  • #1
flip290
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Homework Statement



It has been suggested, and not facetiously, that life might have originated on Mars and been carried to 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 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 km/s , and this would most likely happen over a distance of about 4.0m during the impact.

a) What would the acceleration in such a rock fragment be?
I got this part! 3.13e6 m/s^2

b) How long would this acceleration last?
This the part I am confused about. I thought it was 0.0016 s but that is incorrect. Any help would be appreciated!
 
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  • #2
Let the acceleration, in kilometers per second, of the object after after the impact be "a". Then the speed, t seconds after initial impact, is at and the distance moved is (a/2)t^2. We know that the distance is 4m= .004 km so we can solve (a/2)t^2= 4 for t in terms of a. Put that into at= 5 km/s to get an equation for a.
 
  • #3
Thanks for the reply! I figured out that I actually had the right answer I was just confusing the units.
 
  • #4
how did you find part A?
 
  • #5


The length of acceleration for a rock fragment escaping Mars would depend on several factors, such as the size and shape of the fragment, the angle of impact, and the composition and density of the Martian surface. Therefore, it is difficult to accurately determine the exact length of acceleration without more specific information.

However, we can estimate the approximate duration of acceleration using the equation for acceleration: a = (vf-vi)/t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.

In this case, the final velocity is the escape velocity of Mars, 5.0 km/s, and the initial velocity is assumed to be 0 m/s. Substituting these values into the equation, we get:

a = (5.0 km/s - 0 m/s)/t

To determine the time, we need to convert the units of velocity from km/s to m/s, which gives us a final velocity of 5000 m/s. Substituting this into the equation, we get:

3.13e6 m/s^2 = (5000 m/s)/t

Solving for t, we get t = 1.6 x 10^-3 seconds, which is the approximate duration of the acceleration. However, as mentioned before, this is just an estimate and the actual length of acceleration may vary.
 

Related to Length of acceleration for a rock fragment escaping Mars

1. How long does it take for a rock fragment to accelerate and escape Mars' gravity?

The length of acceleration for a rock fragment escaping Mars depends on several factors, such as the size and weight of the fragment, the angle and velocity at which it is launched, and the strength of Mars' gravitational pull. Generally, it would take a few seconds to a few minutes for a rock fragment to reach escape velocity and break free from Mars' gravitational pull.

2. What is the escape velocity of Mars?

The escape velocity of Mars is about 5 kilometers per second (11,180 miles per hour). This means that in order for a rock fragment to escape Mars' gravity, it would need to be launched with a speed of at least 5 kilometers per second.

3. How does the atmosphere of Mars affect the length of acceleration for a rock fragment?

The thin atmosphere of Mars has a minimal effect on the length of acceleration for a rock fragment escaping the planet. Unlike Earth, where the atmosphere can slow down objects and provide resistance, Mars' atmosphere is not dense enough to significantly affect the acceleration of a rock fragment.

4. Can a rock fragment escape Mars' gravity without any external force?

No, a rock fragment cannot escape Mars' gravity without some external force or acceleration. This is due to the fact that Mars has a significant gravitational pull, which would require a certain amount of force to overcome in order to break free.

5. What other factors may affect the length of acceleration for a rock fragment escaping Mars?

Aside from the size and weight of the fragment, launch angle and velocity, and Mars' gravitational pull, other factors that may affect the length of acceleration for a rock fragment escaping Mars include the presence of other celestial bodies that may interfere with its trajectory and the presence of any obstacles or debris in its path.

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