I think there's a bit of fuzzy thinking here and there in this thread. Acceleration due to gravity does not change with mass. F=ma, and force due to gravity is proportional to mass, so the acceleration is constant. Clearly, when the hammer strikes the string, both the hammer compresses to some extent, and the string is displaced. The rebound of the string and the hammer will both help accelerate the hammer away from the string. How much? Well, that becomes a bit complex. It depends on the lossiness of the hammer felt, and the hardness and mass of the hammer as acted upon by the frequency content of the string. The mass of the hammer, the springiness of the string, and the springiness of the felt combine to form a somewhat complex spring/mass system. I think, despite the complexities of the system, that a lighter hammer will always bounce away from the strings more quickly than a heavier hammer. The quicker rebound will damp the upper harmonics of the string less, and, other things being equal, will cause a brighter tone. Of course, other things don't need to remain equal, and hammer shape and felt hardness can be tailored to bring out the desired tone. I realize that my description is far less detailed than this topic deserves, but I hope it's a bit helpful.
Not sure whether this is (in part, at least) a response to my observation that larger hammers will produce faster key return or not, but I'll amplify.
Of course, attraction by gravity is a constant regardless of the velocity of an object or its direction of travel. Left to its own, an object of any size will fall toward the earth at exactly the same speed.
piano hammers are not objects left to their own. On their return stroke they are driving a load and greater weight will either drive a greater load or drive the same load at a higher speed. There is more potential energy due to gravity in a larger object than a small one. This is easily understood by first dropping a marble from waist height on one's toe and then dropping a brick from the same height. Both objects will arrive at the toe traveling at exactly the same velocity. However, no one will have any doubt about which one will strike with greater force. Perhaps we have difficulty remembering this truth because although history records the experiment at the tower of Pisa that the weights traveled at the same speed, it does not record the size of the divot the different weights made when they hit the ground.
So, in any situation where there is work to be done ( in the case of a piano action, returning the key to its starting point) a larger weight will accomplish the work faster than a smaller weight. Our thinking is further complicated by the fact that there are multiple return scenarios in a piano action. Here are at least three:
1) Hammer blow light enough and held long enough that the hammer doesn't seat in the backcheck but remains at the "top"-- resting on the rep lever after jack escapement.
In this case the only source of energy to return the key is the attraction of gravity to the hammer. A heavier hammer will absolutely return the key faster than a light hammer given the same action set up in the same way
2) Hammer blow strong enough to rebound and set into the backcheck with the note held long enough for seating to happen.
A heavier hammer will seat more deeply into the backcheck than a hammer of the same construction
that weighs less. In this case, return will be faster than scenario #1 because energy has been harvested by the rep spring which is returned upon key release. In addition, since the hammer/shank/knuckle acts as a mass and weight stabilized fulcrum for the rep lever to press against, thus driving the wippen downwards and the key upwards, a heavier and more massive hammer will allow the spring to drive key return more effectively whereas a lighter hammer will tend to pop upwards thereby wasting the stored energy of the spring. Additionally, the hammer that is checked further down has less distance to travel to its rest point.
3) Strong staccato blow that is not held so that the hammer is held by neither the backcheck nor the rep lever.
In this case, the driving force to return the key will be the weight of the hammer -- which will be greater with a heavier hammer -- PLUS the return of energy from the springiness of the hammer. So, two variables here... hammer weight and hammer felt springiness. None of the above means that I advocate heavy hammers as an intrinsic good
. Rather, I hope people can understand that all parameters have BOTH negative and positive tradeoffs. If we are not aware of the tradeoffs, we can potentially create scenarios where performance is not ideal. Whatever action setup approach we use, we need to be aware of how we are blending the tradeoffs to achieve a satisfactory result.
Another factor which people seem not to account for is that hammer felt springiness is a variable
. Not all hammers are equally springy. In the case of the Cadenza hammers by Isaac, the formula for the felt is so springy that it cannot be used by any other hammer maker. In a similar manner, Classical West hammers use a synthetic elastomer "underfelt" that accomplishes much the same thing.