Ever noticed that when you kick the billiard ball off-center, there’s only one possible result?

Solution Link to heading

Step 1: Understanding the Situation Link to heading

  • We have two balls of equal mass.
  • One ball is moving; the other is stationary.
  • The collision is elastic, meaning no energy is lost, and the balls bounce perfectly.
  • The moving ball can hit the stationary ball directly in the center (head-on) or off-center (glancing).

Step 2: Momentum Link to heading

  • Momentum is the motion carried by an object and is conserved in all collisions.

  • We consider two directions:

    1. Forward direction (the original direction of the moving ball).
    2. Sideways direction (perpendicular to the original direction).

  • Before the collision, all the motion is in the forward direction.

  • After the collision, the momentum is shared between the two balls in both directions:

    • Some momentum goes forward for each ball.
    • Some momentum goes sideways if the hit is off-center.

Step 3: Energy Link to heading

  • Kinetic energy is also conserved in an elastic collision.
  • This means the total motion energy before and after the collision is the same.
  • The moving ball transfers some of its energy to the stationary ball, depending on how off-center the hit is.

Step 4: Types of Collision and Resulting Angles Link to heading

  1. Head-on collision:

    • The moving ball hits the center of the stationary ball.
    • Both balls move along the same straight line.
    • Angle between the balls: 0 degrees.

  2. Off-center collision:

    • The moving ball hits the side of the stationary ball.
    • The balls move away from each other at a right angle, forming a perfect “L” shape.
    • Angle between the balls: 90 degrees.

For collisions in between these two extremes, the angle will vary between 0 and 90 degrees, depending on exactly how far from the center the hit occurs.

Step 5: Summary Table Link to heading

Collision TypeAngle Between Balls
Head-on0°
Perfect Off-Center90°

Key Takeaways Link to heading

  • Elastic collisions conserve both momentum and energy.
  • Equal-mass balls striking off-center always produce a right-angle separation.
  • The exact angle depends on the impact point.
  • Using words, you can imagine the “moving ball” pushing the stationary one sideways, creating a neat perpendicular path.