Larry,
Thanks for this response, exactly what I was looking for, however, in trying to understand this, I can't help but have several questions. You may not have all the answers, so if anyone else wants to jump in feel free.
First, mass is defined as the weight of the cue. Is acceleration simply the speed of the stroke at impact? Acceleration is usually thought of as something like the rate of change in speed (like in a car goes from 0-60 in 5 seconds), which is different than speed at a given point, isn't it?
So, in trying to understand your conclusion that the same stroke (assuming one can apply the same stroke) applied with two different cue weights will produce different results (i.e. a cueball that goes faster or slower, a cueball that travels farther or less far) seems to need further explanation.
So, here's what we have. A cueball can't go farther unless it goes faster. A cueball can't go faster unless it goes farther. These seem true, no?
For our conclusion to be true, a heavier cue will move the cueball faster than the actual stroke speed, while a lighter cue will move a cueball slower than the actual stroke speed. Therefore, there must be a cue weight that moves the cueball at the same speed as the actual stroke speed, no?
That weight would seem to represent the optimal weight for a cue because it produces a result that is in precise tune with my stroke. Additionally, lighter cues, because they produce a cueball speed slower than the stroke speed, require more effort, and heavier cue weights require less effort.
All of the above seems to make sense to me, with the possible exception that a cue can actually cause the cueball to travel faster than the actual stroke speed. Care to elaborate on this, anyone?[/
When playing one pocket, the weight of a cue stick is best suited to personal preference and feel. Playability and touch is something that has to be decided by the individual using the cue. The weight/force ratio is a personal thing, as is the wrap, the tip, the ferrule, & the mm of the shaft used.
As to the delivery, or imparted speed, ie; propulsion, it seems not to compare with other sports where light vs. heavy or speed equating to force has a greater impact.
A light baseball bat swings faster and faster equals farther in baseball...
Club head speed, not weight determines distance in golf...
If someone had super strength and could swing either of these two at the same speed only weighing twice as much, which balls would travel farther? According to F=MA the heavier bat and the heavier golf club would out distance the lighter weaponry by far... That could very well be true, but, :sorry. I don't buy it...