# Friction: A non-uniform surface with a uniform weight

• ifnspifn
In summary, the conversation discusses a question about the coefficient of friction on a 2x4 piece of wood covered with sandpaper and teflon. The question is whether changing the proportion of sandpaper and teflon will affect the coefficient of friction. There are conflicting arguments about this, with one side citing Amontons' Second Law and the other arguing that a larger proportion of sandpaper would result in a greater frictional force. After researching online, it is concluded that this situation is not commonly discussed in physics classes. The question remains whether the coefficient of friction is a constant or depends on the ratio of sandpaper to teflon.
ifnspifn
Hello Physics Forums! Longtime lurker, first time poster here.

I've got a deceptively simple question that had my friends and me occupied (read: bickering) for quite some time during a road trip, and I thought I might pose it to you. The situation is this: we have a 2x4 piece of wood, and we've covered half of one of the long sides with sandpaper and the other half with teflon. Let's forget for now that the sandpaper would increase the height of that side compared to the teflon, and imagine that both halves would contact the ground equally. Now we push the piece of wood (textured side down) perpendicularly to the ground and calculate the coefficient of friction to be $\mu$$_{1}$.

The question is this: if we change the proportion of sandpaper/teflon and push the wood as before, will the coefficient change from $\mu$$_{1}$? In other words, if we make 90% of the surface covered in sandpaper, would it have a greater frictional force? It seems that, as per Amontons' Second Law, the surface area of either side would make it such that the frictional force (and thus the coefficient) wouldn't change with the surface area of the sandpaper or the teflon. However, it was also argued that given a large sandpaper/teflon value, there would be more weight on the sandpaper covered end, giving a larger frictional force. This implies that the force of friction would be something like this:

Given S = dimension of sandpaper covered wood, T = dimension of teflon covered wood, and W = total surface area in contact with the ground,

F$_{f}$ = F$_{N}$*($\frac{S}{W}$*$\mu$$_{sandpaper}$ + $\frac{T}{W}$*$\mu$$_{teflon}$)

After a good amount of time spent googling for an answer, it became clear that this situation just doesn't come up in PHY 101 classes, and thus isn't on the internet! What do you think?

Is the coefficient of friction here a constant, or is it dependent on the ratio of sandpaper to teflon? Thanks in advance!

## 1. What is friction?

Friction is a force that resists the relative motion or tendency of motion between two surfaces in contact.

## 2. What is a non-uniform surface?

A non-uniform surface is one that does not have a consistent texture or smoothness across its entire surface.

## 3. What is a uniform weight?

A uniform weight is a weight that is evenly distributed across an object. In other words, all points on the object have the same weight.

## 4. How does a non-uniform surface affect friction?

A non-uniform surface can increase or decrease friction depending on its texture and smoothness. Rough surfaces tend to have higher friction, while smooth surfaces have lower friction.

## 5. How does a uniform weight affect friction?

A uniform weight does not affect friction on a non-uniform surface, as long as the weight is evenly distributed. However, if the weight is not evenly distributed, it can cause uneven friction and affect the motion of the object.

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