Section 4.6: Problem-Solving Strategies

This section focuses on systematic strategies for solving momentum and collision problems efficiently.

Key Strategies:
  • Identify system of particles and isolate objects involved in collision.
  • Determine whether collision is elastic or inelastic.
  • Apply momentum conservation along appropriate directions.
  • For inelastic collisions, remember objects may stick together.
  • Check kinetic energy changes to identify elastic or inelastic cases.

Example 1

Two carts, 3 kg and 2 kg, move toward each other at 4 m/s and 3 m/s respectively. They collide inelastically. Outline steps to find final velocity.

  1. Identify system: carts A (3 kg) and B (2 kg).
  2. Collision type: inelastic (stick together).
  3. Momentum conservation: \( 3*4 + 2*(-3) = (3+2)v_f \)
  4. Compute: \( v_f = (12-6)/5 = 1.2 \, \text{m/s} \)

Example 2

A 5 kg ball moving at 6 m/s collides elastically with a 5 kg stationary ball. Outline the approach to find velocities after collision.

  1. Identify system: Ball A (moving), Ball B (stationary).
  2. Collision type: elastic.
  3. Momentum conservation: \( m_A v_{Ai} + m_B v_{Bi} = m_A v_{Af} + m_B v_{Bf} \)
  4. Kinetic energy conservation: \( \frac12 m_A v_{Ai}^2 + \frac12 m_B v_{Bi}^2 = \frac12 m_A v_{Af}^2 + \frac12 m_B v_{Bf}^2 \)
  5. Simultaneously solve for \( v_{Af} \) and \( v_{Bf} \).

Practice Problems

  1. Two carts of 2 kg and 3 kg collide inelastically with speeds 5 m/s and 2 m/s. Find final speed.
  2. A 4 kg and 6 kg object collide elastically. Initial velocities 3 m/s and 0 m/s. Find final velocities.
  3. A 5 kg ball moving at 7 m/s hits a stationary 5 kg ball elastically. Outline steps to find velocities after collision.
  4. Two cars, 1200 kg and 1000 kg, collide inelastically. Velocities 15 m/s and 5 m/s. Determine final velocity.
  5. Objects of masses 3 kg and 4 kg collide inelastically, initial velocities 2 m/s and -1 m/s. Find final speed.
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