Section 4.5: Inelastic Collisions
In inelastic collisions, momentum is conserved but kinetic energy is not. Often, colliding objects stick together after impact.
Inelastic Collision Conditions:
- Momentum conserved: \( m_1 v_{1i} + m_2 v_{2i} = (m_1 + m_2) v_f \)
- Kinetic energy is not conserved: some energy converted to heat or deformation
Example 1
A 2 kg object moving at 3 m/s collides inelastically with a 3 kg object at rest. Find final velocity if they stick together.
\( v_f = \frac{m_1 v_{1i} + m_2 v_{2i}}{m_1 + m_2} = \frac{2*3 + 3*0}{2+3} = 1.2 \, \text{m/s} \)
Example 2
Two cars of masses 1000 kg and 1500 kg collide and stick together. First car at 20 m/s, second at 10 m/s. Find final velocity.
\( v_f = \frac{1000*20 + 1500*10}{1000+1500} = \frac{20000+15000}{2500} = 14 \, \text{m/s} \)
Practice Problems
- A 5 kg ball at 4 m/s collides inelastically with a 3 kg ball at rest. Find final speed.
- Two carts, 2 kg and 3 kg, collide and stick together. Initial velocities 3 m/s and 0 m/s. Find final velocity.
- A 10 kg object moving at 8 m/s collides with a 15 kg object at 2 m/s. They stick together. Determine final velocity.
- Cars of 1200 kg and 1000 kg collide inelastically. Initial velocities 15 m/s and 5 m/s. Find final velocity.
- Two blocks of 4 kg and 6 kg collide and stick. Speeds before collision 3 m/s and 2 m/s. Compute final velocity.