Collisions

It all depends on the angle of contact between the cue ball and the object ball. For a thin cut, the cue ball retains practically all of its force and very little is transferred to the object ball while for a straight in shot, the cue ball loses practically all it's force because it's all transferred to the object ball. For angles in between it varies, with a 45 degree cut being about 50/50 (50% retained, 50% transferred to the object ball). Of course, this is assuming center-ball hits. You can alter the transfer of energy with spin and english, such as applying follow on a straight in shot, etc. And when it comes to that, it becomes a matter of feel.
 
How can players determine how much of their power is being delivered from their cue stick to object (not the cue ball).

Practice hitting various cut shots at such a speed that the OB rolls up to the pocket and stalls out on the lip of the pocket. Any more CB speed and the OB would drop. Hit a couple thousand of these and you will get a feel for how <lack of> hard you have to hit the CB to pot the OB.

Any more speed than the above, and you are trying to do something with the CB AFTER OB contact. That is, "You don't have to hit it any harder than what will pot the ball".

The cue ball is the mechanism that transfers the energy from your stroke to the rack or object ball. A demonstration of what I am talking about is to place an object ball close to a side pocket and another close to the corner pocket. Position the cue ball on the table so that after pocketing the side ball, it rolls toward the corner pocket. If you get the experiment right, what you get to see is that the cue ball hardly transfers any force to the side ball, even though you hit it strongly. The point is sometimes force plays a significant role but in extreme circumstances the angle the balls collide at play a more influential role in achieving a desired outcome.

The amount of energy transfered has to do with the Cosine of the angle of contact--thin means little energy is transfered, thick means lots of energy is transfered. Dead on and the CB actually comes to a stop at impact and rolls only because of the remaining spin.
 
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