Oblique Collisions

In an oblique collision, the velocity of the object is not along the line of impact. This requires resolving velocities into components parallel and perpendicular to the surface or line of centres.

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1 Oblique Impact with a Smooth Wall

When a particle hits a smooth wall obliquely:

• The component parallel to the wall is unchanged (the wall is smooth, so no friction).
• The component perpendicular to the wall obeys Newton's law of restitution: the perpendicular rebound speed = e times the perpendicular approach speed.

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2 Worked Example 1

A ball hits a smooth wall at 30 degrees to the wall with speed 12 m s^(-1). The coefficient of restitution is 0.8. Find the speed and direction after the bounce.

Solution:

Perpendicular component (towards wall): 12 sin 30 = 6 m s^(-1)

Parallel component (along wall): 12 cos 30 = 6 sqrt(3) m s^(-1)

After bounce:

• Perpendicular: 0.8 * 6 = 4.8 m s^(-1) (away from wall)
• Parallel: 6 sqrt(3) m s^(-1) (unchanged)

Speed after = sqrt(4.8^2 + (6 sqrt(3))^2) = sqrt(23.04 + 108) = sqrt(131.04) approximately 11.4 m s^(-1)