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 the 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 kilometers per second, and this would most likely happen over a distance of about 4.0
meters during the impact.
(a) What would be the acceleration, in meters per second squared and g’s, of such a rock fragment?
(b) How long would this acceleration last?
(c) In tests, scientists have found over 40% of Bacillus subtilis bacteria survived after an acceleration
of 450, 000g. In light of your answer to part (a), can we rule out the hypothesis that life might
have been blasted from Mars to Earth?
vf^2=vi^2+2ad
5000^2=0+2a*4
a=5000^2/8
for time:
vf=at solve for time t.
To answer the questions about the acceleration of rock fragments and the survival of bacteria during the impact, let's break it down step by step:
(a) To calculate the acceleration of a rock fragment, we need to use the knowledge that it would have to reach the escape velocity of Mars, which is 5.0 kilometers per second. We also know that this would most likely occur over a distance of about 4.0 meters during the impact.
To find the acceleration, we can use the equation:
acceleration = (change in velocity) / (change in time)
Since the object starts from rest, the initial velocity is 0. Final velocity will be the escape velocity of Mars, which is 5.0 kilometers per second (or 5000 meters per second).
So the change in velocity is:
change in velocity = final velocity - initial velocity
= 5000 m/s - 0 m/s
= 5000 m/s
The change in time is the distance over which this velocity change occurs, which is 4.0 meters.
So the acceleration can be calculated as:
acceleration = (5000 m/s) / (4.0 m)
This gives us the acceleration in meters per second squared.
We can also express this acceleration in terms of g's, which is a unit of acceleration relative to the acceleration due to gravity on Earth.
1 g = 9.8 meters per second squared.
To find the acceleration in g's, divide the acceleration in meters per second squared by 9.8.
(b) To calculate the duration of this acceleration, we need to know the time it takes for the rock fragment to cover the 4.0 meters distance at this acceleration.
To find the time, we can use the equation of motion:
distance = (initial velocity * time) + (0.5 * acceleration * time^2).
In this case, the initial velocity is 0, and the distance is 4.0 meters. We know the acceleration from part (a).
Plugging in these values and solving for time will give us the duration of this acceleration.
(c) The given information states that over 40% of Bacillus subtilis bacteria survived an acceleration of 450,000 g.
By comparing this information to the acceleration calculated in part (a), we can assess whether the hypothesis that life might have been blasted from Mars to Earth can be ruled out.
To calculate the acceleration in g's, divide the acceleration in meters per second squared by 9.8.
Now, armed with these calculations, we can answer the given questions.
(a) To find the acceleration, we can use the second equation of motion, which relates velocity, acceleration, and distance:
v^2 = u^2 + 2as
where:
v = final velocity (5.0 km/s)
u = initial velocity (0 m/s, assuming the rock starts from rest)
a = acceleration
s = distance (4.0 meters)
Rearranging the equation, we can solve for acceleration:
a = (v^2 - u^2) / (2s)
First, let's convert the velocity to meters per second:
5.0 km/s * (1000 m/km) = 5000 m/s
Now let's calculate the acceleration:
a = (5000^2 - 0^2) / (2 * 4.0)
a = 12,500,000 / 8
a = 1,562,500 m/s^2
To find the acceleration in g's, we can divide the acceleration by the acceleration due to gravity:
1,562,500 m/s^2 / 9.8 m/s^2 ≈ 159,694 g's
Therefore, the acceleration of the rock fragment would be 1,562,500 m/s^2 or approximately 159,694 g's.
(b) To find the duration of the acceleration, we can use the equation:
v = u + at
where:
v = final velocity (5.0 km/s = 5000 m/s)
u = initial velocity (0 m/s)
a = acceleration (1,562,500 m/s^2)
t = time (unknown)
Rearranging the equation, we can solve for time:
t = (v - u) / a
t = (5000 - 0) / 1,562,500
t = 0.0032 seconds
Therefore, the acceleration would last approximately 0.0032 seconds.
(c) Since the acceleration in the tests was measured at 450,000 g's, which is significantly lower than the calculated 159,694 g's, it suggests that some types of microbes can survive such high accelerations. Therefore, based on the survival of Bacillus subtilis bacteria at 450,000 g's, we cannot rule out the hypothesis that life might have been blasted from Mars to Earth.