About 50,000 years ago, in an area located outside Flagstaff, Arizona, a giant 4.5x10^7 kg meteor fell and struck Earth, leaving a 180 m hole now known as Barrington crater. If the meteor was traveling 20000 m/s upon impact, with what average force did the meteor hit Earth? Help I am not sure how to solve this problem!
1x10^14
To solve this problem, we can use the formula for average force, which is the rate of change of momentum. The formula is:
Average Force = (Change in momentum) / (Time taken)
Here's how we can approach the problem step by step:
Step 1: Calculate the momentum of the meteor upon impact.
Momentum = mass × velocity
Momentum = 4.5×10^7 kg × 20000 m/s
Step 2: Determine the change in momentum.
Since the meteor came to a stop upon impact, the change in momentum is equal to the initial momentum.
Change in momentum = 4.5×10^7 kg × 20000 m/s
Step 3: Find the time taken for the collision.
Time taken = Distance / Velocity
The distance is the diameter of the crater, which is twice the radius.
Distance = 2 × (radius of Barrington crater)
Radius = 180 m / 2 = 90 m
Time taken = (2 × 90 m) / 20000 m/s
Step 4: Calculate the average force.
Average Force = Change in momentum / Time taken
By calculating the above steps, you will be able to determine the average force with which the meteor hit the Earth.
To calculate the average force with which the meteor hit the Earth, you can use the concept of impulse. Impulse is the change in momentum of an object, and it can be calculated by multiplying the force exerted on the object by the time interval during which the force acts.
Given that the mass of the meteor is 4.5x10^7 kg and its initial velocity is 20000 m/s, we can calculate its initial momentum using the formula:
Initial momentum (p1) = mass x velocity
p1 = 4.5x10^7 kg x 20000 m/s
Now, let's calculate the final momentum of the meteor. The meteor comes to rest after the impact, so its final velocity (v2) is 0 m/s. Therefore, the final momentum (p2) can be calculated as:
Final momentum (p2) = mass x final velocity
p2 = 4.5x10^7 kg x 0 m/s
Now, we can calculate the change in momentum (Δp), which is the difference between the initial and final momentum:
Δp = p2 - p1
Δp = (4.5x10^7 kg x 0 m/s) - (4.5x10^7 kg x 20000 m/s)
Δp = -4.5x10^7 kg x 20000 m/s
Since the magnitude of velocity is the same as the magnitude of speed, it's often written as -4.5x10^7 kg x 20000 m/s (negative sign indicates a decrease in velocity).
The average force (Favg) can be calculated by dividing the change in momentum by the time interval during which the force acts. Since the time interval is not given, we'll use the definition of average force as the rate of change of momentum:
Favg = Δp / t
However, as the time interval is not provided in the question, we cannot directly calculate the average force.