🔖 Topics

  • Elastic collisions in one and two dimensions
  • Inelastic collisions in one and two dimensions

🎯 Objectives

  • Calculate the properties of objects undergoing elastic collisions using conservation of momentum and energy
  • Calculate the properties of objects undergoing inelastic collisions using conservation of momentum and energy

📋 Sequence

  • Inelastic collision example problems
  • Elastic collision example problems

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

Inelastic Collision: A 2.0 kg object is at rest on a frictionless surface when it is hit by a 3.0 kg object moving at 8.0 m/s. The two objects stick together after they collide.

  • What is the speed of the combination after the collision?
  • What is the total kinetic energy of the combination before the collision?
  • What is the total kinetic energy of the combination after the collision?
  • Why are the energies different? Have we violated conservation of energy?

Elastic Collision: Two billiard balls, each with a mass of 0.20 kg, collide. Ball one moves with an initial velocity of 6 m/s, and ball two is initially at rest. After the collision, ball one comes to a complete stop.

  • What is the velocity of ball two after the collision?
  • What is the total kinetic energy of the combination before the collision?
  • What is the total kinetic energy of the combination after the collision?

Collision in Two Dimensions: Two objects slide over a frictionless horizontal surface. The first object, mass \(m_1\) = 5 kg, is propelled with speed \(v_{i1} = 4.5 {\rm m/s}\) toward the second object, mass \(m_2\) = 2.5 kg, which is initially at rest. After the collision, both objects have velocities which are directed \(\theta = 30^\circ\) on either side of the original line of motion of the first object.

  • What are the final velocities of the two objects?
  • What is the total kinetic energy of the combination before the collision?
  • What is the total kinetic energy of the combination after the collision?
  • Is the collision elastic or inelastic?

✅ Partial Solutions

N/A

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.