ads wrote:

2 further questions

Should sum of mass after impact = ball (mass) before impact + pin (mass)?

The only way the sum of mass after, is different than the sum of mass before, is somehow part of the pin, or part of the ball is broken off and no longer considered part of the pin, or ball.

Bottom line the sum of the mass doesn't change.

But you don't look at the masses only, the issue is kinetic energy, which is a combination of mass, and velocity. KE = 0.5 * mass * velocity^2

You further break down the KE into it's orthogonal components (KE(y) down the lane, and KE(x) across the lane).

Such that if the ball was entering the pocket at a 6 degree angle of entry, then KE(x) = KE * sin(6 degrees), and KE(y) = KE * cos(6 degrees)

The sum of KE before impact = sum of KE after impact.

Also in terms of deflections.

for each object, you calculate the KE(x) which is 0.5 * mass * velocity^2 * sin(angle)

The sum for all objects after impact has to equal the sum for all objects before impact.

So if the ball had an entry angle of 6 degrees, and the only thing moving was the ball, the total KE(x) would be the balls KE in the (x) direction.

After impact, both the ball and the pin are moving, so the sum for KE(x) of the pin, and KE(x) of the ball has to equal the same KE(x) value that the ball had before impact.

ads wrote:

Plastic balls deflects much more than resin balls after impact with the pin (assuming same mass and velocity). Is it because of friction, entry angle or some other factors (e.g. plastic ball seldom arrives roll phase)?

Actually a plastic ball and a resin ball will deflect very close if not exactly the same amount.

The deflection occurs in a VERY short period of time.

The difference is what happens after that short time.

Again lets assume the ball has 6 degrees of entry angle, and will deflect 20 degrees.

After impact, the ball is back in the hook phase because the axis rotation (6 degrees left) is not in line with the path of the ball (20 degrees right) so the ball will not continue on a straight line.

How effective the ball is in this new hook phase is related to the cover stock material.

Before the ball has the opportunity to make significant changes in direction, it impacts the 3 pin on the left. So we go thru all those calculations again,

A proper strike ball will actually deflect right (off the head pin), then left (off the 3 pin) then right (off the 5 pin) then left (off the 9 pin).

If the ball deflects too much to the right off the head pin, or by hitting the head pin too far on the right, the 3 pin is sent back at an angle which doesn't drive the 6 pin either directly into the 10, nor by bouncing the 6 off the wall into the 10 pin.