# Crater experiment for Newton's second law of motion

I am looking for interesting, easy to do experiments to Newton's second law of motion. This is for a high school, so nothing is known about momentum and the law is just $\mathbf{F}=m~\mathbf{a}$.

I found that some people do "crater" experiments dropping objects into flour (see for instance here), however I am still trying to understand how exactly this relates to Newton's law.

As far as I understand all objects dropped from the same height arrive with the same velocity at the flour. The flour provides a force on the object that decelerates it from its velocity down to zero velocity.

If I assume that the force is constant during impact (Does this make sense at all?), I get from Newton's law that the deceleration (absolute value) is smaller for the heavier objects, therefore they leave a deeper impact crater.

Does this sound like a good interpretation of the experiment?

They also mention measuring the width of the crater. How can this be used?

Are there any other (easy to do) experiments related to Newton's second law?

• – Kyle Kanos Jan 18 '18 at 13:08
• Actually because drag force is not proportional to mass, heavier objects fall faster. So you need to make sure you drop your marbles from low enough a height that they do not have enough time to get appreciably different speed on impact. – frapadingue Jan 23 '18 at 0:26

The depth of the crater will depend primarily on three things:

1. The height the marble is dropped from.
2. The diameter of the marble.
3. The mass of the marble.

To investigate Newton's 2nd law, you are going to have to keep 1. and 2. constant. That means finding marbles of different mass but the same size -- not easy. Assuming the size of the marble is fixed, then it is ok to assume a constant force from the flour. I am not sure what they are trying to suggest with the crater width -- don't worry about it.

Check out this video by Bruce Yeany on Newton's 2nd and 3rd law. His YouTube channel is very good, so you might want to come back to it sometime for future experiments and demonstrations.

• How do you relate the depth of the crater to Newton's 2nd Law? – sammy gerbil Jan 22 '18 at 22:03

Suspend two identical heavy pendulum bobs A, B from the same point. Let B be stationary. Draw A back and let it go to strike B. The result is that they swap over. A stops and B starts moving.

Galileo explained this very simply using imclined planes each of the same angle.

From this the principle of inertia easily follows by assuming the angle of the second inclined plane is zero.

.

• I wouldn't say that's really a good demonstration for Newton's second law in particular, though... – Chris Jan 18 '18 at 13:53

Put an elastic string across a table and launch rolling marbles at it. Redo the experiment by weaving two strings, and then three strings. Notice that the stopping time gets shorter with more strings, and that more strings means a bigger force. A bit of fine-tuning is necessary to get a large enough difference of stopping distance (time).

... some people do "crater" experiments dropping objects into flour ... however I am still trying to understand how exactly this relates to Newton's law.

There is no simple way to explain the size of the impact crater using Newton's 2nd Law. As the links provided by Kyle Kanos show, for astronomical craters the diameter cubed is proportional to the kinetic energy of the impacting meteor. This relation is experimental (not derived from theory) and assumes that the crater is much larger than the dimensions of the impacting object. This is not a suitable experiment to demonstrate $F=ma$.

• FWIW, one of the links I provided makes no distinction between astronomical craters and terrestrial ones, suggesting that it can even be done with mostly everyday objects. – Kyle Kanos Jan 22 '18 at 22:46