Solve a problem

Momentum and collisionsPhysicsCollegeabout 1:05

A 5 kg ball at 1 m/s hits a 5 kg ball at -1 m/s in a perfectly elastic head-on collision. Find both final velocities: animated lesson

A narrated, step-by-step momentum and collisions video lesson with captions. Final answer: v₁ = -1 m/s, v₂ = 1 m/s (elastic; kinetic energy conserved).

SpeedLanguage

Chapters

Transcript

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
A 5 kg ball at 1 m/s hits a 5 kg ball at -1 m/s in a perfectly elastic head-on collision. Find both final velocities.
2. Step by step
1. $p = m_1u_1 + m_2u_2 = 5(1) + 5(-1) = 0\ \text{kg·m/s}$
  Total momentum before
2. $v_1 = \frac{(m_1-m_2)u_1 + 2m_2u_2}{m_1+m_2} = -1,\quad v_2 = \frac{(m_2-m_1)u_2 + 2m_1u_1}{m_1+m_2} = 1$
  Elastic collision: conserve momentum and kinetic energy
3. $KE_i = 5\ \text{J},\quad KE_f = 5\ \text{J},\quad \Delta KE = 0\ \text{J}$
  Kinetic energy before and after
3. The answer
$\text{v₁ = -1 m/s, v₂ = 1 m/s (elastic; kinetic energy conserved)}$
v₁ = -1 m/s, v₂ = 1 m/s (elastic; kinetic energy conserved)
4. Check
- Momentum before 0 = after 0 kg·m/s ✓
- Kinetic energy before 5 = after 5 J ✓

Transcript

The problem. Here is the problem: A 5 kg ball at 1 m/s hits a 5 kg ball at negative 1 m/s in a perfectly elastic head-on collision. Find both final velocities. One-dimensional collision; positive velocities point one way, negative the other.

Step by step. Total momentum before. Elastic collision: conserve momentum and kinetic energy. Kinetic energy before and after.

The answer. So the answer is v₁ equals negative 1 m/s, v₂ equals 1 m/s (elastic; kinetic energy conserved). Momentum is conserved in every collision when no external force acts. Kinetic energy is conserved only in elastic collisions; in a perfectly inelastic collision the objects stick together and the maximum possible kinetic energy is converted to heat, sound and deformation.

Check. Momentum before 0 equals after 0 kg times m/s, which checks out. Kinetic energy before 5 equals after 5 J, which checks out.

About momentum and collisions

Momentum, impulse and conservation of momentum in collisions.

A 5 kg ball at 1 m/s hits a 5 kg ball at -1 m/s in a…