Section 5.9: Review Examples
This section consolidates key concepts from momentum, collisions, explosions, and disintegration. Focus on momentum conservation and problem-solving using vector and scalar components.
Example 1
A 3 kg object moving at 5 m/s collides inelastically with a 2 kg object at rest. Find the final velocity of the combined mass.
Total momentum before: \(3*5 + 2*0 = 15\text{ kg·m/s}\)
Combined mass: 5 kg
Final velocity: \(v_f = 15/5 = 3 \text{ m/s}\)
Example 2
A 4 kg object at rest explodes into two fragments: 1 kg moves at 3 m/s right, find velocity of 3 kg fragment.
Total momentum before explosion: 0
Momentum conservation: \(0 = 1*3 + 3*v_2 \Rightarrow v_2 = -1 \text{ m/s (left)}\)
Example 3
Two ice skaters push off each other on frictionless ice. Masses: 50 kg and 40 kg. Skater 1 moves at 2 m/s. Find speed of skater 2.
Initial momentum: 0
50*2 + 40*v2 = 0 → v2 = -2.5 m/s
Practice Problems
- 5 kg object at 4 m/s collides inelastically with 3 kg object at 2 m/s. Find final velocity.
- Object explodes into three fragments: 2 kg, 3 kg, 5 kg. Two velocities given. Find third using momentum conservation.
- Two skaters, 60 kg and 45 kg, push apart. One moves at 1.5 m/s. Find the other’s speed.
- Projectile of 10 kg explodes at top of trajectory into 3 kg and 7 kg. Find velocities if one fragment moves at 4 m/s.
- Two objects collide elastically. m1=2 kg, v1=3 m/s; m2=3 kg, v2=-1 m/s. Find velocities after collision.
- Rocket ejects 20 kg fuel at 100 m/s. Rocket mass 80 kg. Find rocket velocity after fuel ejection.
- 3 kg and 2 kg particles move at right angles. Compute resultant momentum before collision.
- Explosion in 2D: a stationary object splits into 2 unequal masses at 90°. Find unknown velocity given one fragment’s velocity.
- Inelastic collision of 3 objects along x-axis. Find final velocity of combined system.
- Two carts on frictionless track collide. Momentum vectors given. Find final vector magnitude and direction.