The physics:

The shooter plunger is pulled back by the knob on the outside of the cabinet, compressing a spring.

The force applied in pulling back on the shooter plunger is directly proportional to the compression on a spring which the shaft of the plunger goes through inside the cabinet (Hooke's Law). A simple scale is provided for the player to guage his compression distance from one shot to the next.

The compressed spring has stored potential energy which is then converted to kinetic energy in the shooter plunger upon release.

The front tip of the plunger strikes the ball and transfers much of its kinetic energy to the ball.

The impulse on the ball resulting from the shooter plunger force changes the momentum of the ball. Put another way, the force of the plunger tip on the ball accelerates it for a split second and it takes off with a final velocity once the force is no longer there.

If the original stored energy is sufficient to transfer enough kinetic energy to the ball, it will make it up the shooter lane and enter the playfield along the upper arch where it now has some gravitational potential energy to go along with some kinetic energy.

Most games have a "skill shot" which requires the player to pull the plunger back with just the right amount of force. It some cases the timing of the release is also important.