61. Ball 1 is moving and ball 2 is still. Both balls have the same mass. What happens to the motion of the two balls if ball 1 strikes ball 2 head on in an elastic collision?
Answer: A
Ball 1 stops, and ball 2 moves at the velocity ball 1 had before the collision.
In an elastic collision between two objects of equal mass, if one object is initially at rest, the moving object transfers its velocity to the stationary object. Consequently, ball 1 comes to a stop, and ball 2 moves forward with the same velocity that ball 1 had prior to the collision.
A) Ball 1 stops, and ball 2 moves at the velocity ball 1 had before the collision.
This option accurately describes the outcome of an elastic collision where one ball is stationary and the other is in motion. The principle of conservation of momentum and kinetic energy in elastic collisions ensures that the moving ball transfers its entire velocity to the stationary ball, resulting in ball 1 stopping and ball 2 moving forward.
B) Ball 1 and ball 2 both move in the direction that ball 1 was initially moving, but ball 1 moves twice as fast.
This option is incorrect because it suggests that ball 1 continues moving at a faster speed after the collision, which contradicts the behavior of elastic collisions. In this scenario, ball 1 stops, and it is not possible for it to move faster than it originally did.
C) Ball 1 and ball 2 both move in the direction that ball 1 was initially moving, but ball 2 moves twice as fast.
This option is also incorrect. For an elastic collision involving equal masses, the second ball cannot move faster than the first ball's original speed; rather, it moves at that same speed. Hence, the outcome described here does not align with the principles governing elastic collisions.
D) Ball 2 remains at rest, and ball 1 moves at twice its original velocity.
This option is incorrect as well, as it implies that ball 1 gains speed after the collision while ball 2 remains stationary. In elastic collisions, the total momentum and kinetic energy are conserved, meaning ball 1 cannot accelerate if ball 2 is initially at rest.
Conclusion
The correct answer, option A, is definitive because it aligns with the laws of physics governing elastic collisions, particularly the conservation of momentum. All other options fail to accurately represent the outcomes based on the principles of motion and energy conservation in such collisions.