Physics of "force Spreading" On Impact On a Surface

Understanding the Physics of “Force Spreading” on Impact on a Surface

When an object hits a surface, there is a force that is exerted on the surface. In some cases, this force can be so great that it causes damage or failure to the surface. To prevent this from happening, it is important to understand how this force is spread out over a larger area resulting in a lower maximal force acting on the surface.

Calculating Pressure Distribution

Let’s consider a plate of thickness $d$ made of a material (let’s say wood) laying on a hard surface $S$ (for example on concrete floor). If we have a maximum value of pressure $p_{\mathrm{max}}$ that the surface $S$ can tolerate before it fails, then we need to calculate the pressure distribution on $S$ to determine if $p_{\mathrm{max}}$ is respected everywhere.

If we know the force ( $F$ ) acting on an area ( $A$ ) on plate $P$ , we can calculate the pressure distribution on $P$ using the formula $p = \dfrac{F}{A}$ .

To calculate the pressure distribution on surface $S$ , we need to consider the area of contact between plate $P$ and surface $S$ . Let’s assume that this area is $A'$ . Then, the pressure distribution on surface $S$ can be calculated using the formula $p' = \dfrac{F}{A'}$ .

If $p' \le p_{\mathrm{max}}$ , then we can say that the surface $S$ is safe.

Parameter of Material that Determines Force Spreading

So, what parameter of the material of plate $P$ determines how the force acting on $P$ is spread out over a larger area resulting in lower maximal forces acting on $S$ ?

The answer lies in the stiffness of the material. Stiffer materials (like wood) are better at spreading the force over a larger area than softer materials (like rubber). This is because stiffer materials resist deformation more, which means that they exert a larger force over a larger area when they are compressed.

Example of Weightlifting Platform

Let’s take an example to understand this better. Consider a barbell falling from height $h$ directly on a concrete floor. This creates a pressure distribution $p_0$ on the concrete floor.

Now, let’s lay a plate of rubber on the concrete floor and drop the barbell again. Since the rubber deforms by a distance $s$ , it enlarges the stopping distance and thus reduces the force on the concrete floor. Additionally, it “spreads” the force a little bit over the area of the plate resulting in a pressure distribution (acting on the concrete floor) $p_{\mathrm{rubber}} < p_{0}$ .

If we repeat this with a wooden plate (same dimensions as the rubber plate), we find that it deforms much less, but “spreads” the force much better because it is stiffer than the rubber. The combined effect is much better than in the rubber case (but we don’t know the order of magnitude of difference between the materials), resulting in pressure distribution $p_{\mathrm{wood}}$ with $p_{\mathrm{wood}} \ll p_{\mathrm{rubber}} < p_0$ .

This is why, in weightlifting platforms, one uses relatively stiff wooden plates to “spread the force over a large area”. Since rubber is much less stiff than wood, the effect of spreading the force is much smaller than in the case of a wooden plate. However, if we use high-density rubber tiles, this effect could also potentially play an important role, although we would need to quantify it to know for sure.

Three Main Effects of Rubber Tile

For the case of the barbell and the rubber tile, we can say that the rubber layer seems to have three main effects:

Cushioning effect: Since the barbell plate sinks a bit into the rubber tile, the contact area is increased (compared to the contact with the bare concrete), thus the force is spread over a specific area on the top of the rubber tile.
Increasing the “breaking distance”: Since the rubber tile is softer than the concrete, it enlarges the breaking distance and thus reduces the total impact force significantly.
Spreading the force over an even larger area: This effect is usually utilized in weightlifting platforms where one uses relatively stiff wooden plates to “spread the force over a large area”. Since rubber is much less stiff than wood this effect will be much smaller than in the case of a wooden plate, but it still plays an important role when you use high-density rubber tiles. However, we cannot quantify this effect without further experimentation.

It is difficult to estimate how large each of these effects is compared to each other. Nevertheless, it is clear that using a rubber tile on a surface can significantly reduce the impact force and protect the surface from damage.

Conclusion

Understanding the physics of force spreading on impact is crucial to prevent damage to surfaces. The stiffness of the material of the plate determines how the force is spread over a larger area resulting in lower maximal forces acting on the surface. We can use the pressure distribution formula to calculate the pressure distribution and determine if a surface is safe. Using high-density rubber tiles can help in reducing the impact force and protecting surfaces from damage, but it is important to understand the different effects of rubber tiles to use them most effectively.

Physics of “force Spreading” On Impact On a Surface