normal force and hard-soft surfaces

Question

If i keep a heavy ball on a hard surface then it does not penetrate through the surface but if I keep that same ball on a soft surface it penetrates through the surface. Why is it so? why do some objects have an ability to exert a greater magnitude of normal force then others?

Answer 1

It is not the object but the surface which has the ability to exert a normal force.

The object always has its weight to press downwards with, and the surface responds with a normal force to balance it out.

But that might not be possible. The normal force is of course limited by the strength of the material.

• A hard and strong material has a high ultimate tensile strength $\sigma_{max}$. As long as the necessary normal force stays below this value, there are no problems.
• On the other hand, for a hard and weak material the necessary normal force might overcome the $\sigma_{max}$. The material then can't produce the necessary normal force so it deforms (breaks).

A note: $\sigma_{max}$ is actually a per-area measure. To compare them, the normal force must be divided by area as well (called normal pressure).

In soft materials the same takes place but in stages so to say. The very top layer of atoms in e.g. a sponge is very weakly supported from below and cannot create a high enough normal force. So it deforms. Soon it touches the next layer which adds a bit of force but still not enough - so also that deforms.

• After sinking many layers in like this, enough normal force has accumulated to balance out the pressure from the weight. Then the object will sink no further, and also nothing will break.
• If there are not enough layers for this then the necessary normal force can't be produced, and the object will naturally break all the way through.

Also, even with enough layers, each layer has to be flexible enough to stretch down to the object and "hold on" as the object sinks further in. If it can't, then it breaks and doesn't contribute any more. Such soft but inflexible materials will thus also break and let the object right through.