Two billiard balls with identical masses and sliding in opposite directions have an elastic head-on collision. Before the collision, each ball has a speed of 20 cm/s. Find the speed of each billiard ball immediately after the collision.
To find the speed of each billiard ball immediately after the collision, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. In this case, since both billiard balls have identical masses, we can assume their masses to be equal, let's say "m".
Let's label the velocities of the first ball (moving to the right) before and after the collision as v1i and v1f, respectively. Similarly, for the second ball (moving to the left), the velocities before and after the collision are v2i and v2f, respectively.
The law of conservation of momentum states that the total momentum of a closed system before the collision is equal to the total momentum after the collision. Mathematically, we can express this as:
(m * v1i) + (m * v2i) = (m * v1f) + (m * v2f)
Since the masses are equal and opposite in direction, we can rewrite the equation as:
v1i + v2i = v1f + v2f
Given that the velocity before the collision (v1i and v2i) is 20 cm/s and since the collision is elastic, we can use the fact that the relative velocity between the two balls changes sign but remains constant.
Now, let's label the final velocity of the first ball as v1f' and the final velocity of the second ball as v2f'. Since v1f' will be in the opposite direction to v2f', we can say that v1f' = -v2f'.
Substituting this relationship into the equation, we have:
v1i + v2i = v1f' - v2f'
Substituting the given values:
20 cm/s + (-20 cm/s) = v1f' - (-20 cm/s)
0 cm/s = v1f' + 20 cm/s
Therefore, the final velocity of the first ball (v1f') is -20 cm/s, and the final velocity of the second ball (v2f') is 0 cm/s.
Thus, immediately after the collision, the first ball comes to rest, and the second ball continues to move in the same direction with a speed of 20 cm/s.