I have simple question: is it possible to calculate magnitude of force acting on some area by falling object?

Let's say I have an object with mass $5\text{ kg}$. I drop that object in height 1 meter. It potential energy was

$$\begin{align} E_p &= hmg \\ E_p &= 5(9.81) \\ E_p &= 49.05 \text{ J} \end{align}$$

Near the ground, kinetic energy of object is

$$E_k = E_p$$

So the velocity is

$$\begin{align} E_k &= \sqrt{2\frac{E_p}{5}} \\ E_k &= \sqrt {19.62} = 4.429 \frac{\mathrm{m}}{\mathrm{s}} \end{align}$$

Is there any way how to calculate force of object against ground when it falls on it? If not, what something (against ground) can be calculated for this problem?

EDIT: Let's say that ground is from glass, thickness $10\text{ cm}$. What properties would be affected?

  • $\begingroup$ There is no way at all in using physics 101 type skills unless I tell you something like "the ground acts as if it were a spring with constant $10^4\text{N/m}$". In a typical serious application this would be either computed (say FEA) or measured with a pressure transducer, or very often both. $\endgroup$ – dmckee Jun 10 '13 at 15:23
  • $\begingroup$ For many calculations of forces you can assume everything is absolutely rigid, but that approach can't work here. If the falling object and the ground were both completely rigid then it would have to go from speed to stationary in no time at all as it hit the ground, which is clearly impossible. $\endgroup$ – bdsl Mar 20 '16 at 17:14
  • $\begingroup$ The harder the object and the ground the greater the force when they hit. If you imagine harder and harder objects the forces get bigger and bigger, and there is no upper limit. $\endgroup$ – bdsl Mar 20 '16 at 17:15

Your data is not enough. You need some data on the ground material (such as modulus of elasticity), body material and shape, etc. For example, if the ground is not hard, the force will be small.

EDIT (06/10/2013): As I said, you need more input data. I don't have time to give you a detailed analysis. You may wish to look at https://www.endevco.com/news/archivednews/2009/2009_02/tp321.pdf to get an idea about the essential factors of the problem.

  • $\begingroup$ Ok, I have edited my question. It's glass 10cm thick. $\endgroup$ – user35443 Jun 10 '13 at 3:33
  • $\begingroup$ Still not enough (please see my answer). $\endgroup$ – akhmeteli Jun 10 '13 at 10:20
  • $\begingroup$ Ok, what physical quantities should I check? I know absolutely nothing except that there's some effect on the ground. What for an effect is it? $\endgroup$ – user35443 Jun 10 '13 at 16:12
  • $\begingroup$ Please see the edit to my answer. $\endgroup$ – akhmeteli Jun 11 '13 at 2:15
  • 1
    $\begingroup$ @user35443: At en.wikipedia.org/wiki/Impact_(mechanics) , there is the following reference: Goldsmith, W, Impact; The Theory and Physical Behaviour of Colliding Solids, 2001, Dover Publications, ISBN 0-486-42004-3 , but I did not read it. Let me just note that it is not very important for impact if it is an impact of a falling body: the mechanisms are pretty much the same for, say, an impact of two cars. $\endgroup$ – akhmeteli Jun 13 '13 at 12:04

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