This resource supports any classroom study of Mars Exploration. It is especially effective used in conjunction with the following Yes I Can! Scientific Adventure:

See Yes I Can Science! Home Page for further information regarding archived, current and planned Scientific Adventures.

(See also Labs, Demos and Classroom Activities:

• Introduction to Geologic Processes
• Impact Cratering on a Rainy Day
• Introduction to Planetary Atmospheres
• Aeolian Processes
• Geologic Features of Mars
• Introduction to Planetary Geologic Mapping
• Photogeologic Mapping of Mars
• Glossary)

The following activities demonstrate the fundamental principles of impact crater formation. The activities are simulations; true impact or volcanic events take place under conditions different from the classroom. Although some aspects of the simulations do not scale directly, the appearance of the craters formed in these activities closely approximates natural, full size craters. These laboratory exercises can be used to stimulate discussions of planetary landscapes, terrestrial craters, and the evolution of planetary surfaces.

In these experiments, students will study the craters formed when objects of different masses and traveling with different velocities strike a target of fine sand. This activity demonstrates important concepts: first, there is a relationship between the velocity and mass of the impactor and the size of the crater formed; and second, craters can be divided into distinct zones: floor, wall, rim, ejecta. The "Rainy Day" experiment illustrates the relation between crater frequency and relative surface age, as well as demonstrating the effect of illumination angle on identifying craters.

On Earth, volcanic explosion craters are often formed when magma rises through water-saturated rocks and causes a phreatic, or steam explosion. Volcanic explosion craters from phreatic eruption often occur on plains away from other obvious volcanoes. Other volcanic eruptions can cause mild explosions, often in a series of events. Some volcanic craters form by collapse with little or no explosive activity. Volcanic craters are typically seen either on the summits or on the flanks of volcanoes. Volcanic craters have also been identified on the Moon, Mars, Venus, and Io. The exercise comparing these cratering processes will help the student learn to identify the differences in the resultant craters.

Purpose

This exercise demonstrates the mechanics of impact cratering and will show the student impact crater morphologies. Upon completion of this exercise the student should understand the relationship between the velocity and mass of the projectile and the size of the resultant crater. The student should also be able to identify the morphologic zones of an impact crater and, in certain cases, be able to deduce the direction of the incoming projectile.

Materials Suggested:

If performed as an instructor demonstration, one set of the following:

• sand (very fine and dry), tray (e.g., kitty litter box), dyed sand, slingshot, scale, ruler, lamp, calculator, safety goggles, drop cloth, fine screen or flour sifter
• projectiles: 4 different sizes of steel ball bearings; 4 identical ball bearings of one of the inter- mediate sizes, one each of the three other sizes (sizes should range from 4mm to 25 mm)
• 3 identical sized objects with different densities (e.g., large ball bearing, marble, balsa- wood or foam ball, rubber superball)

If performed by students, enough sets of the above list for all students/groups.

Substitutions: dry tempera paint can be dry-mixed with sand to make dyed sand (but do not get this mixture wet!), a thick rubber band can be substituted for a slingshot.

Background

This exercise demonstrates the mechanics of impact cratering and introduces the concept of kinetic energy (energy of motion): KE = 1/2 (mv ² ), where m = mass and v = velocity. The effects of the velocity, mass, and size of the impacting projectile on the size of the resultant crater are explored. By the conclusion of the exercise, the student should understand the concept of kinetic energy, and know that the velocity of the impactor has the greatest effect on crater size [KE = 1/2 (mv ² )].

Use of a slingshot to fire projectiles is required in this exercise. It is the instructor's decision whether this exercise should be done as a demonstration or by the student. Students should be supervised carefully at all times during the firing of the projectiles and everyone should wear protective goggles. Place the tray on a sheet of plastic or drop cloth; this will make cleanup easier. Fill the tray completely with sand, then scrape the top with the ruler to produce a smooth surface. The dyed sand is best sprinkled on the surface through a fine screen, or a flour sifter.

This exercise requires the calculation of kinetic energies. All of the velocities necessary for these calculations have been provided in the student's charts. Calculation of velocity for dropped objects is simple using the formula:

v = (2ay) ^.5 where v is the velocity, a is the acceleration due to gravity (9.8 m/s ² ), and y is the distance dropped

Calculation of the velocity for objects launched by a slingshot is a time consuming procedure for values used in only two entries in the exercise; however, it is an excellent introduction to the physics of motion and can be done in a class period before performing this exercise. The procedure for calibrating the slingshot and for calculating velocities of objects launched by the slingshot follows the answer key (where it may be copied for student use).

Advanced students and upper classes can answer the optional starred (*) questions, which apply their observations to more complex situations.

Student Activity

Answer Key

Objective

To determine the initial velocity of a mass that is propelled by a slingshot.

Background

This procedure applies two physical laws, Hooke's Law and the Law of Conservation of Energy. Hooke's Law (F=kx) states that the force (F) applied to an elastic material depends upon how stiff the material is (k) and how far you pull the elastic material (x). The stiffness of the elastic material (k) is small if the elastic material is soft, and large if the elastic material is stiff. The Law of Conservation of Energy (W = PE = KE) states that there is a relationship between work (W) performed on a system (the force applied to an object to move it a certain displacement in the same direction as the force is acting) and the potential energy (PE, stored energy) of a system and the kinetic energy (KE, energy of motion) of the system. The equations for Hooke's Law, work, and potential energy are derived from a graph of force versus elongation.

The velocity term that we want to solve for is found in the kinetic energy portion of the Law of Conservation of Energy.

KE = 1/2 mv ² , where m is the mass of the object being launched and v is the velocity.

The potential energy of elasticity is a combination of Hooke's Law and work.

PE = 1/2kx ² where k is the spring constant and x is the elongation distance of the slingshot - how far back it is pulled.

Because the Law of Conservation of Energy states that the potential and kinetic energies of a system are equal, we can set these equations equal to each other.

1/2mv ² = 1/2kx ² ; solving for v gives: v = (kx 2 /m) ^.5

We will control x (the distance pulled back) and will measure m (the mass of the object being launched). But to solve for v (the velocity) we must first calibrate the slingshot by experimentally solving for the spring constant, k.

How to Solve For k

1. Place the slingshot on the edge of a table or counter so that the elastic band hangs free. Immobilize the slingshot by placing a large weight on it or by duct-taping it to the counter. Rest a meter stick on the floor and tape it along side the slingshot. Pull down on the elastic tubing of the slingshot until all the slack is taken out, but do not stretch the tubing. Mark this point on the meter stick. This is the point of equilibrium.
2. Place slotted masses in increments of 100, 150 or 500 grams (depending on the stiffness of the slingshot) in the pocket of the slingshot until it begins to elongate or stretch past the point of equilibrium. This initial mass is called the "pre-load force" and is not counted as a recordable force in the data table. (On the graph of force versus elongation, the preload force will appear as a y-intercept.) Once the slingshot starts to elongate or stretch, begin recording the amount of mass you are adding to the pocket and how far from the point of equilibrium the pocket is displaced. Maximize your range of data! Keep taking measurements until you have 7 or 8 data points.
3. Convert the mass from grams into kilograms and multiply by 9.8 m/s ² to get force in the unit of Newtons. example: 150 g (1 kg/1000g) = .150 kg; .150kg(9.8 m/s ² ) = 1.47 N Convert the elongation measurements from centimeters to meters. Now you are ready to graph force (in Newtons) versus elongation (in meters).
4. Graph force (on the y-axis) versus elongation (on the x-axis). The graph will be a linear function with the slope representing the spring constant, k (in N/m). If you are using a computer graphing program it will automatically calculate the slope and y-intercept of the graph. If you are graphing on graph paper, calculate the slope of the graph using two data points and the equation: slope = (y2-y1)/(x2-x1) example: (3,5) (4, 6) slope = (6-5)/(4-3) = 1/1 = 1 N/m, in this case k = 1 N/m If the graph has a y-intercept, disregard it (it is simply part of the preload force). The slope of the line is the value of the spring constant, k, and can now be used in the velocity equation above.