Simulating Asteroid Impact
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Mechanics Coursework Simulating Asteroid Impact In this experiment the ball bearings will be the free falling objects which will simulate a meteorite or asteroid impact. Any object which is allowed to free fall in the Earth's gravitational field will experience an acceleration (g) equal to 9.8 m/s2. In order to determine the velocity of the ball bearing at the moment of impact, two equations are needed. The equation, (1) vf = vi - gt states that the final velocity, vf, is equal to the initial velocity, vi, minus the acceleration due to gravity, g, multiplied by the amount of time, t, it takes the object to fall. During this experiment you will be unable to accurately measure the fall time. Because of this, another equation is needed to determine the final velocity. (2) d = vit - 0.5gt2 Equation (2) allows you to calculate the distance, d, an object will fall within the Earth's gravitational field, if the amount of fall time is known. It should be noted that d is negative (-) for objects moving towards the Earth. In other words a falling object has a negative displacement.
Smooth the surface of the white sand and sprinkle a light covering layer of colored sand on top. This layer of colored sand lets you see where the ball bearing pushes the white sand up to the surface as crater ejecta. This enables you to easily measure the crater diameter and to see the changes in crater morphology that result when using heavier ball bearings dropped from larger heights. Activity 1: The size of a crater is related to the energy of the impacting object (the asteroid). This makes sense -- as the energy of the asteroid increases, it releases more energy on impact, making a bigger crater. The relationship is not linear however, but rather some form of power law: D = k * En where E is the energy of the asteroid (kinetic and potential) and D is the diameter of the crater. Also, k is an unknown constant, and n is some unknown factor that describes how the diameter of the crater depends on the energy of the asteroid. We want to find out what n and k might be by looking at our scaled version of asteroids and craters.
So we know n from the slope on the graph. We also need to know the constant k in the equation relating crater diameter and impact energy. To find k, you will use one of your data points. Pick a data point that is close to your best-fit line (one that you think is a good value), and plug D, E, and your value for n into the equation D = k En. Now you can solve that equation for the value of k. For example, suppose you dropped a 0.03kg ball bearing from a height of 2m. This give you an impact energy of E = mgh = (0.03kg) * (9.81m/s^2) * (2m) = 0.59Joules. And suppose that when you dropped the ball bearing, you measured the crater diameter to be 5cm = 0.05m, and also your graph had given you a slope = n = .25. Then, D = 0.05m, E = 0.59Joules, and n = 0.25, plugged into the equation D = k En k = D / (En) = 0.05 / (0.59^0.25) = 0.057 . Now, go and put all this knowledge to work in the Activity #1 Questions!
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