Question

Activity 21.7 Impact Cratering Experiment Continued

Observe the equipment shown in Figure 21.10 and conduct the following experiment:

Step 4: One at a time, drop each of the projectiles from heights of 0.5 meter or to the height of your knees, 1.0 meter or to the height of your waist, and 1.5 meters or to the height of your shoulders on the sand in the box and measure the diameter, in millimeters, of the crater produced each time. Make sure to flatten the surface of the sand between trials. Repeat the experiment three (3) times and average your results. Record the average for each of the trails on the data sheet in the table below (see Table 21.1 in lab book).

Please do a copy of this table, complete, and paste into the comments box below. Thank you!

Table 21.1 Impact Crater Data Sheet (you are not recording the mass)

Projectile Type	Crater Diameter
Description	0.5 M Height Crater Diameter (mm)	1.0 M Height Crater Diameter (mm)	1.5 M Height Crater Diameter (mm)
Average

Answer 1

Solution:

The diameter of the crater will be proportional to the energy stored in the projectile. As the projectiles are dropped from a height, its potential energy will be proportional to the volume of the crater.

A crater can be described as a hemisphere with volume = 1/2 volume of a sphere = 1/2 * 4/3*pi*(D/2)³

Or, it can be said that energy E will be proportional to D³

Now,

In the 1st case:

The projectile is dropped from a distance of 0.5 M

As it's given the problem that mass has not to be recorded, we can say that

Height (h) = Diameter (D³)

Or, D³ = 0.5M

Or, D = Cube root of 0.5M = 0.79 M = 790 mm

Thus, the diameter of crater shall be equal to 790 mm

In the 2nd case:

The projectile is dropped from a distance of 1 M

Height (h) = Diameter (D³)

Or, D³ = 1M

Or, D = Cube root of 1M = 1 M = 1000 mm

Thus, the diameter of crater shall be equal to 1000 mm

In the 3rd case:

The projectile is dropped from a distance of 1.5 M

Height (h) = Diameter (D³)

Or, D³ = 1.5 M

Or, D = Cube root of 1.5 M = 1.14 M = 1140 mm

Thus, the diameter of crater shall be equal to 1140 mm