Conservation of Kinetic Energy Example

Scenario

• A red snooker ball and a blue snooker ball, each with a mass of 160 g, are involved in a collision.
• The red ball is initially moving from left to right at 0.28 m/s, while the blue ball is moving from right to left at 0.12 m/s.
• After the collision, the blue ball moves from left to right at 0.18 m/s.

Calculate the velocity of the red ball after the collision.

• Total momentum before the collision is equal to the total momentum after the collision.
• Using the formula for momentum (p = mv), we have:
• Total initial momentum = Total final momentum
• (0.160 kg × 0.28 m/s) + (0.160 kg × (-0.12 m/s)) = (0.160 kg × V)
• (0.0448 kg m/s) - (0.0192 kg m/s) = (0.160 kg × V)
• (0.0256 kg m/s) = (0.160 kg × V)
• V = (0.0256 kg m/s) / (0.160 kg)
• V = -0.16 m/s
• The velocity of the red ball after the collision is approximately -0.16 m/s. The negative sign indicates that the direction is from right to left.

Use kinetic energy to determine whether the collision was elastic

• To determine if the collision is elastic or not, we need to calculate the kinetic energy before and after the collision.
• The equation for kinetic energy is KE = ½mv², where KE is kinetic energy, m is mass, and v is velocity.

Kinetic Energy Before the Collision

• For the red ball: KE_red = ½ × 0.160 kg × (0.28 m/s)² = 0.006272 J
• For the blue ball: KE_blue = ½ × 0.160 kg × (-0.12 m/s)² = 0.0009216 J
• Total kinetic energy before the collision: KE_initial = KE_red + KE_blue = 0.006272 J + 0.0009216 J = 0.0071936 J

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Conservation of Kinetic Energy Example

Kinetic Energy After the Collision

• For the red ball (with velocity -0.16 m/s): KE_red_after = ½ × 0.160 kg × (-0.16 m/s)² = 0.002048 J
• For the blue ball (with velocity 0.18 m/s): KE_blue_after = ½ × 0.160 kg × (0.18 m/s)² = 0.002304 J
• Total kinetic energy after the collision: KE_final = KE_red_after + KE_blue_after = 0.002048 J + 0.002304 J = 0.004352 J

Comparison of Kinetic Energies

• Total kinetic energy lost during the collision: ΔKE = KE_initial - KE_final = 0.0071936 J - 0.004352 J = 0.0028416 J
• The collision is inelastic because kinetic energy is not conserved. In this case, 0.0028416 J of energy is lost during the collision.

Summary

• The velocity of the red ball after the collision is approximately -0.16 m/s.
• The collision is determined to be inelastic because there is a loss of kinetic energy, with 0.0028416 J of energy being lost during the collision.