I think you are overcomplicating things with physics that no violinist really needs to know in order to play violin. You are always going to be imparting a force on the violin, and how you get that force can vary. My teacher has taught me to use the natural weight of the arm with a relaxed arm, but I imagine that some successful violinists come from above more with a higher elbow, and the way they impart force is more "active", if you will. I wouldn't play that way, since it seems like it would result in more tension over time.
Heifetz had a pretty high elbow, and he had shoulder problems later in his career (related?). Midori seems like she has a very active right arm with a slightly high elbow - Is that an adaptation for someone with an arm that doesn't weigh that much? Oistrakh had big hamhocks, and he seemed to have a pretty low elbow.
When my teacher talked about hearing and seeing Szeryng play in person, she said that his elbow didn't seem to be as high as it looked (at least relative to the violin), because he held the violin quite high, but then again, he could apparently play quite well when he was sloshed, so maybe it doesn't always pay to imitate the Gods.
At the tip: pressure (More so on the G than in the E string.)
In my humble experience.
It's just easier to talk about bow "pressure" and know how it feels and what you are doing!
Rotate hand counter-clockwise so force is applied at the index finger to push down on the bow.
Is that about right science majors?
I would say weight and pressure are less correct; whereas, force, rotate and push are closer to what is being done. Semantics?
The strings simply do not care how the pressure is achieved. Only that it occurs.
You, as the player, have several options for applying pressure to the strings through the bow hairs.
You can let gravity pull down on the bow because it has mass.
You can pinch your thumb and forefinger together to rotate the bow harder into the strings.
You can rest the mass of your hand and arm on the bow to let gravity push more pressure into the strings.
You can bend you wrist into the bow to push more pressure into the strings.
You can rotate your forearm into the bow to add more pressure.
You can throw the bow into the strings using a thrust of your fingers.
In terms of bow speed, you are applying a sheer pressure to the strings which is a function of the bow speed (duh) and how much pressure you are putting into the strings. In other words the sheer pressure due to bow speed is limited by how much downward pressure is being forced into the strings.
So if you want to play really loud, you need to increase both pressure into the strings as well as the speed across the strings.
I am sure there are other things I haven't thought of.
In ALL cases except strictly using the weight of the bow, you will feel a corresponding increase in the pressure of the bow against your forefinger. This is the primary feedback mechanism you use to judge how much pressure you are applying to the strings.
Perhaps a more interesting question is, "WHICH method should one use to apply string pressure?" I think it depends on the bowing technique one is executing.
An excellent source the relates different pressure techniques to bowing techniques, check out
http://www.violinmasterclass.com/en/masterclasses/right-hand/bow-grip
Thus force and weight in this context can be used interchangeably.
Chemistry students often get confused about the difference between weight and mass. The weight depends on the gravitational field, the mass doesn't. That's why weights on the moon are a fraction of what they are on earth. It's a largely academic distinction because most of us do not operate in environments of partial terrestrial gravitation.
Therefore weight and mass can be used interchangeably.
Pressure is force per unit area to which the force is applied. Since the contact area between your strings and your bow is roughly constant, at least in the limit of small changes in force, then force is proportional to pressure.
Therefore force and pressure can be used interchangeably.
The reason these different terms matter to us was explained adequately by Adrian Heath above.
I learned that tone, at least as far as the right hand is concerned, is a combination of contact point (bowing "lane"), downward force/pressure/weight, and bow speed. Fischer has described the interplay of these factors masterfully.
I believe that many violinists feel that "pressure" is directly downward toward the string, whereas "weight" is more about how your arm draws the bow both downward and laterally in some kind of smooth, organized way. However, from the perspective of Newtonian mechanics, that non-perpendicular force/motion can be decomposed into two orthogonal vectors, one of which contributes to downward "pressure" and the other to lateral "bow speed". Thus the three variables described by Fischer are sufficient.
My teacher used to tell me to "play through the string" which is obviously a nonsensical statement in terms of what is physically possible but it definitely gives a nice sort of imaginary feeling for what we can do to accomplish a good sound.
Having said this I do still use the word press with regards to the index finger when teaching articulation so...
edit: How about this scenario - one person says they press with their index finger, the person next to them says they apply arm weight. Are they contracting the same muscles the same amount? If they're not how do they differ?
Ranting aside, I think these words like "weight" vs. "pressure" are more psychology than physics. They make you think about the task in different ways, so that two similar-sounding words have very different results. A word like "pressure" might encourage tensing up, or pressing too hard - while terms like "weight" or "sinking into the string" might prompt you to set up those linkages of joints and muscles in your arm and hand in a way that works much better.

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