A billiard player sends the cue ball toward a group of three balls that are initially at rest and in contact with one another. After the cue ball strikes the group, the four balls scatter, each traveling in a different direction with different speeds as shown in Figure P10.30. If each ball has the same mass, 0.16 kg, determine the total momentum of the system consisting of the four balls immediately after the collision.
FIGURE P10.30
Total momentum of four balls after the collision.
Answer to Problem 30PQ
The total momentum of the four balls after collision is
Explanation of Solution
The player sends a cue ball to hit on a group of four balls. All the four balls were initially at rest and after their collision with the cue ball each of them scattered to different directions.
Write the equation to find the total momentum of the four balls.
Here,
Refer figure 10.30 provided in the problem. The figure gives the coordinate system of the system of four balls.
Consider each ball and write the component form of velocity vector for each ball.
Write the equation to find the velocity vector for ball 1.
Here,
Write the equation to find the velocity vector for ball 3.
Here,
Write the equation to find the velocity vector for ball 6.
Here,
Write the equation to find the velocity vector for cue ball.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the total momentum of the four balls after collision is
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Chapter 10 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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