Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Two cubes of the same mass but different sizes (smaller Cube A and bigger Cube B) are dropped from same height on to a tray of sand.Which cube will create a deeper impression and why?

share|cite|improve this question
up vote 3 down vote accepted

The smaller cube will create a deeper impression, since it has a smaller surface area impacting the sand but the same energy. To see this consider not dropping the cubes on sand but on an array of evenly spaced springs. It is easy to see that he spring will contract less if you can distribute the energy of the fall on more springs.

The energy for both cubes dropped from a height $h$ is $E=mgh$ A springs potential Energy goes like $E=kx^2$ where $k$ is the spring constant. If you have $n$ springs under the surface they all will be displaced by

$$E=nkx^2=mgh\Rightarrow x=\sqrt{\frac{mgh}{nk}}$$

from their equilibrium position

As you see the more springs you have (i.e. more surface with evenly spaced springs) the smaller the 'impression'.

PS: this is why spears und bullets and stuff like that are pointy at the top. All the energy they have will be focused on the small top, so they can exert much more pressure (force/area) and penetrate objects

share|cite|improve this answer
thanks, luksen for your help – Sudheer Sep 7 '11 at 3:18

both cubes come with the same speed as much downtime as the impact speed to not depend on mass, but the height. according to: $v^2 = 2gy$ (asumming that $V_0 = 0$ en $t =0$)

Now, the depth left by the bins will depend on the energy that each one comes and this energy is proportional to the mass, ie, more mass, more energy of impact. according to: $$E = 1/2 m.V^2$$

Therefore, the "cube" of more mass is buried deeper than the other cube.

share|cite|improve this answer
the OP required both cubes to have the same mass, thus same energy. – luksen Sep 1 '11 at 16:38
mmm... all right. its true. same mass= same energy. i dont see. sorry. jeje. – jormansandoval Sep 1 '11 at 17:16
@jorman If you realize your answer is incorrect, you should edit it. – Mark Eichenlaub Sep 2 '11 at 0:05
Ok marke. I follow. Your advice. Thank you – jormansandoval Sep 2 '11 at 0:35
thanks, jormansandoval and others – Sudheer Sep 7 '11 at 3:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.