Why Does Tipler & Mosca Emphasize Mass Cancellation in Kinetic Friction?

[walking]

On page 120 of Tipler & Mosca 5th edition there is a worked example involving calculating the coefficient of kinetic friction of a situation. The authors then basically remark on why the final answer doesn't depend on the mass and why the mass cancels, adding at the end that "the net result is that the mass has no effect".

I understand this remark, but what I am a bit puzzled about is why it was necessary. Isn't it already clear by definition that $\mu_k$ doesn't depend on the mass? It only depends on the materials of the objects. On page 118 of the same book when defining $\mu_k$ it says that it depends only on the nature of the surfaces in contact.

Maybe their remark contains a useful idea which I am not seeing? I have attached the relevant worked example + remark.

 

[Dale]

I understand this remark, but what I am a bit puzzled about is why it was necessary. Isn't it already clear ...

I know that when I wrote a textbook I often included comments about things that were already clear. It turns out that things that are already clear for some readers are not clear to others, so such unnecessary comments can be highly beneficial.

 

[walking]

I know that when I wrote a textbook I often included comments about things that were already clear. It turns out that things that are already clear for some readers are not clear to others, so such unnecessary comments can be highly beneficial.

The reason I would prefer such remarks not to be included is because the authors did not refer at all to the basic reason of why mass is not relevant: because the coefficient of kinetic friction only depends on the nature of the surfaces. In my opinion, not adding this to the remark makes the remark confusing and multiplies notions within the beginner's mind, rather than clarifying things. The beginner ends up thinking there are many things at play when in fact they are all simply a result of a much more basic reason. That is just my opinion though because personally I don't like having to repeatedly take lots of things that look different and reduce them in my mind to one thing. I would prefer if the authors did that and I could just read the book without having to use my brain power to keep spotting equivalences.

 

[Vanadium 50]

I could just read the book without having to use my brain power

This is unlikely to be an effective strategy to learn physics.

 

[PeroK]

The reason I would prefer such remarks not to be included is because the authors did not refer at all to the basic reason of why mass is not relevant: because the coefficient of kinetic friction only depends on the nature of the surfaces. In my opinion, not adding this to the remark makes the remark confusing and multiplies notions within the beginner's mind, rather than clarifying things. The beginner ends up thinking there are many things at play when in fact they are all simply a result of a much more basic reason. That is just my opinion though because personally I don't like having to repeatedly take lots of things that look different and reduce them in my mind to one thing. I would prefer if the authors did that and I could just read the book without having to use my brain power to keep spotting equivalences.

I agree in the sense that the definition of coefficient of kinetic friction assumes it is independent of the mass. In practice, that may be true or it may not. That page does not in any way demonstrate that a mass-independent coefficient of friction is to be expected. In fact, the more you think about it the more likely it seems that the coefficient of friction would depend on the mass.

 

[Dale]

The reason I would prefer such remarks not to be included is ...

Your complaint here is simply a matter of style and personal preference. Every author will have a different style. If you don’t like this one then pick a different textbook or write your own with a style you prefer.