Name Section Partners By Tyler Nordgren Laboratory Exercise for Chapter 7 Equipment: Ruler Sand box Meter stick Log-log paper Small balls such as those included in the table at the end of the lab THE FORMATION OF CRATERS Purpose: We have been discussing the dangers of impacts. But, what factors affect impacts? How much energy do they put out?
Page 2 1. List all the factors you think might affect impact craters. THE FORMATION OF CRATERS In the lab, you will drop a selection of projectiles into trays of sand in order to investigate what properties of the projectile affect the resulting crater. The properties we will investigate are: a) Size; b) Mass; c) Velocity. You may have come up with other possibilities. This is good. We will investigate them near the end of the lab. MASS OR SIZE 2. Chose six balls of the same composition (and therefore, same density) but different sizes (and therefore, different masses). Record the properties of the balls in table 1. 3. Drop the first ball into the sand. Do no throw the ball or it will destroy your results. Record the HEIGHT ABOVE THE SAND SURFACE from which the ball was dropped. Pick a nice round number, like 50cm or 100cm. Record the diameter of the crater in centimeters. Be certain to use the correct units! For best results, record the diameter to one decimal place. Repeat two more times, using the same ball from the same height, and recording the diameter of the resulting crater. Take the average of the three trials and record in the table. 4. Repeat step #3 for the other 5 balls, remembering to always use the same height.
Page 3 Table 1: Composition Size (in) Mass (g) Height (cm) Crater diameter (cm) Trial 1 Trial 2 Trial 3 Average Since these objects have the same density, the mass is related to the size by: M= density x volume M= 4/3 r 3 Where is the density and r is the radius of the ball. So, we can t determine if the crater diameter depends on size or mass because they are related. In the next section, we will test to see which is the important factor. 5. Plot crater diameter as a function of projectile mass on graph 1, which is a log-log graph. Be sure to label your axes and include units. 6. In what way does crater diameter depend on projectile mass? (i.e., describe your graph) 7. How might you determine what size crater would be made by a 100 gram ball dropped from the same height?
Page 4 Graph 1: On log-log paper graph crater diameter as a function of projectile mass.
Page 5 SIZE OR MASS Pick two balls of the same size but different mass. This means they are made of different substances and have different densities. Record the properties of the balls in the table below. If size matters, the craters should be the same size. If mass matters, then the craters should be different sizes. 8. Which do you think will matter? 9. Drop the first ball into the sand. Record the height. Record the diameter of the crater. Repeat and take the average as in step #3. 10. Repeat step 9 for the other ball, be sure to use the same height. Composition Size (in) Mass (g) Height (cm) Crater diameter (cm) Trial 1 Trial 2 Trial 3 Average 11. Pick two balls of the same mass but different size. Drop the balls into the sand (from the same height) and record the data in the following table. Composition Size (in) Mass (g) Height (cm) Crater diameter (cm) Trial 1 Trial 2 Trial 3 Average 12. Does projectile size affect crater size? 13. Does projectile mass affect crater size? 14. Which matters more, size or mass?
Page 6 VELOCITY 15. Pick one of the six balls you used in step #4. In this section, we will change the ball s impact velocity. How can we change that? We will change the height from which it is dropped. The farther the ball falls, the faster it will be going when it hits the sand. The impact velocity is given by the formula: v 2 gh, where g is the acceleration of gravity (980 cm/s) and h is the height from which you drop the projectile. The heights and velocities are already recorded in the table. Here, record the size, composition, and mass of the ball you have chosen. Size. Composition. Mass. 16. Drop the ball into the sand from the first height. Record the diameter of the crater in Table 2. Repeat and take the average as in step #4. 17. Repeat step #16 from the other heights. Table2: Height (cm) Velocity (cm/s) 20 198 Crater diameter (cm) Trial 1 Trial 2 Trial 3 Average 50 313 100 443 150 542 200 626 250 700
Page 7 Plot crater diameter versus impact velocity on graph 2, which is also a log-log plot. Note: in order to keep the range of velocities between 1 and 100 on the x-axis of the graph, you may wish to convert each velocity from centimeters to meters (simply divide by 100). 18. In what way does velocity matter? (i.e., describe the plot) 19. How might you determine what size crater would be made by the same ball with an impact velocity of 886 cm/s? 20. Which affects crater size more: Size, Mass or Velocity of the projectile? How can you tell? 21. Are there any properties you suggested in step #1 that we haven t tested? If the answer is no, think of one now. 22. How would you test this property for an effect on impact craters? Carry out this test and describe what you are doing and what your results are. Does this property affect crater size? Note: you will be graded on how scientifically valid your test is.
Page 8 Graph 2: On log-log paper graph crater diameter as a function of projectile velocity.
Page 9 KINETIC ENERGY The size of an impact crater depends on the kinetic energy of the impactor. Kinetic energy, the energy of motion, is described as: KE = ½ mv 2 Where m is the mass and v is the velocity. During an impact, the energy is transferred to the target surface, breaking up rock and moving the particles around. You can calculate the kinetic energy in the craters you ve already made by plugging the velocity and mass into the formula above. As long as your mass is in grams and your velocity in centimeters per second then your energy is in a unit called ERGS. 23. In the following table, record the kinetic energy and average crater diameter for each of your results in steps #4 and #17. USE SCIENTIFIC NOTATION! Kinetic energy (ergs) Crater diameter (cm)
Page 10 24. Plot crater diameter versus kinetic energy on graph 3 (also log-log). 25. Fit a line to the data. Use your ruler to approximate a straight line that passes close by all of your data points. When a line is fit to a series of points on a log-log graph, you get a relationship between the x and y values on the graph: p y cx where p is the slope of the line. You can find the slope by taking two points on the line (x 1,y 1 ) and (x 2,y 2 ) and doing some math: y1 log y 2 p x1 log x2 26. What is the slope of the line you drew? p =. Because this is a log-log plot, the formula is p D c( KE) Now, use a data point near the line you drew and find the constant c: c=. Remember, in order to use the power and constant you found, you must have D and KE in the proper units, cm and ergs, respectively.
Page 11 Graph 3: On log-log paper graph crater diameter as a function of projectile kinetic energy.
Page 12 METEOR CRATER Meteor Crater is a large impact crater in northern Arizona. The crater s diameter is 1.24 km. The crater resulted from what was probably the most recent large meteorite to hit the Earth, some 25,000 years ago. In the previous section you found the Diameter of a crater as a function of its Kinetic Energy. In many circumstances we already know the Diameter of the crater and want to work backward to find the Kinetic Energy. Using algebra: becomes D c( KE) KE 27. Based on the analysis of your experiments in this lab, and on the extremely bold assumption that your relationships can be extrapolated to the event that caused Meteor Crater to form, what was the kinetic energy of the impact? Remember that you have been measuring craters in cm and this is in km. D c p 1/ p
Page 13 28. Assuming that the impactor hit with a velocity of 12.8 km/s (a typical impact speed for asteroids), what is the mass of the projectile? 29. Assuming that the impactor was made of iron with a density of 8 grams per cubic centimeter, what was its volume?
Page 14 30. Assuming that the impactor was a sphere, what was its diameter? 31. What is this diameter in meters?
Page 15 COPERNICUS CRATER One prominent crater on the Moon is called Copernicus. 32. When viewed from the earth, Copernicus is 0.014 degrees in diameter. Given that the distance from the earth to the moon is 384,000 km, how big is the crater? 33. Assuming that your lab results can be applied to the Moon, what was the kinetic energy of the impactor?
Page 16 34. Assuming that the impactor hit with a velocity of 12.8 km/s what is the mass of the projectile? 35. Assuming that the impactor was an iron sphere with a density of 8 grams per cubic centimeter, what was its volume?
Page 17 36. Assuming the impactor was a sphere, what was its diameter? 37. What is this diameter in kilometers?
Page 18 Composition Size Mass (g) Steel 3/8 3.54 Steel 13/32 4.50 Steel 7/16 5.63 Steel 1/2 8.40 Steel 5/8 16.4 Steel 3/4 28.3 Steel 1 67.2 Wood 1/2 0.8 Wood 3/4 2.3 Wood 1 6.4 Wood spool 3/4 x 1 4.0 Wood spool 3/4 x 5/8 1.8 Glass 1/2 3.7