Answer to Question #158565 in Physics for Emily

Question

Let’s say I have two rocks, one with a mass of 22g and the other of 17.6g. The rock with the mass of 22g is dropped into a bowl of flour from a height of 0.178m, and the rock with the mass of 17.6g is dropped from a height of 0.279m. Out of the two, which one will create a bigger impact crater in the flour? In other words, which has the greater effect on the depth of the impact crater: a larger rock, or a smaller rock dropped from a greater height?

Answer 1

The depth of the impact crater depends on the kinetic energy of the rock just before the impact. In its turn, this kinetic energy is equal to the initial potential energy (according to the energy conservation law):

$$E = mgh$$

where $m$ is the mass of the rock, $g$ is the gravitational acceleration, and $h$ is the initial height.

Thus, for the first rock ($m = 22g = 0.022kg, h = 0.178m$) obtain:

$$E_1 = 0.022\cdot 0.178g = 0.003916g$$

For the second rock ($m = 17.6g = 0.0176kg, h = 0.279m$) obtain:

$$E_1 = 0.0176\cdot 0.279g = 0.00491046g$$

Thus, the smaller rock dropped from a greater height will create a deaper crater.

Answer. Smaller rock dropped from a greater height.