Section 4.4: Elastic Collisions
In an elastic collision, both momentum and kinetic energy are conserved. This section explains the principles and provides examples.
Elastic Collision Conditions:
- Momentum conserved: \( m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f} \)
- Kinetic energy conserved: \( \frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 = \frac{1}{2} m_1 v_{1f}^2 + \frac{1}{2} m_2 v_{2f}^2 \)
Example 1
Two balls, m1=2 kg moving at 3 m/s, m2=3 kg at rest. Find final velocities after elastic collision.
Use conservation of momentum and energy to solve: \( v_{1f} = 0.6 \, \text{m/s}, v_{2f} = 3.6 \, \text{m/s} \)
Example 2
A 5 kg ball moving at 4 m/s collides elastically with a 5 kg ball at rest. Find final velocities.
Since masses are equal and collision is elastic: \( v_{1f} = 0 \, \text{m/s}, v_{2f} = 4 \, \text{m/s} \)
Practice Problems
- A 2 kg ball at 5 m/s collides elastically with a 3 kg ball at rest. Find final velocities.
- Two equal-mass objects collide elastically, one at 6 m/s and the other at rest. Determine post-collision velocities.
- A 4 kg ball moving at 3 m/s hits a 2 kg stationary ball elastically. Find final velocities.
- 5 kg and 3 kg objects collide elastically. Initial velocities are 4 m/s and 2 m/s. Compute final velocities.
- Two balls, 2 kg and 2 kg, with velocities 3 m/s and -1 m/s, collide elastically. Find post-collision speeds.