The animation simulates a billiard shot to demonstrate the law of conservation of momentum. A white cue ball can be aimed at colored object balls, with the collisions showing momentum transfer between the balls.
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Description of the Animation
The animation shows a billiard table with a white cue ball and six colored object balls arranged in a classic triangular formation. When the cue ball strikes the object balls, momentum is transferred according to the law of conservation of momentum:
[ vec{p}_{text{gesamt}} = sum m_i vec{v}_i = text{konstant} ]
In elastic collisions between two balls of equal mass, momentum is transferred along the line of impact. The velocity components perpendicular to the line connecting the centers remain unchanged, while the components along this line are exchanged.
- Momentum arrows: Black arrows indicate each ball’s current direction and speed. The arrow length is proportional to the momentum.
- Elastic collisions: During collisions, momentum and kinetic energy are conserved – an idealized model without energy loss through deformation.
- Wall reflection: At the cushions, the velocity component perpendicular to the wall is reversed.
Interactive Control
The animation offers various control options:
- Aiming: Click and drag on the cue ball to set the direction and strength of the shot. The black arrow shows the planned shot direction.
- Execute shot: Starts the simulation with the selected shot direction.
- Reset: Resets all balls to their starting positions.
- Rolling friction μ: Determines how quickly the balls slow down due to friction. At μ = 0 the balls roll indefinitely.
Physical Background
The law of conservation of momentum is one of the fundamental conservation principles of physics. In a closed system, the total momentum remains constant regardless of internal interactions. Billiards is particularly well suited for illustrating this, as the balls have approximately equal mass and the collisions are nearly elastic.
The simulation also shows the transition from sliding friction to static friction: If the ball’s speed drops below a threshold, the ball comes to a complete stop – a realistic behavior observed in everyday rolling objects.