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Momentum and collisionsPhysicsHigh schoolabout 1:05

A 1200 kg object moving at 15 m/s collides and sticks to a 800 kg object moving at -10 m/s. What is their common velocity?: animated lesson

A narrated, step-by-step momentum and collisions video lesson with captions. Final answer: v = 5 m/s (perfectly inelastic; 150000 J of kinetic energy lost, 85.71%).

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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 1200 kg object moving at 15 m/s collides and sticks to a 800 kg object moving at -10 m/s. What is their common velocity?
2. Step by step
1. $p = m_1u_1 + m_2u_2 = 1200(15) + 800(-10) = 10000\ \text{kg·m/s}$
  Total momentum before
2. $v = \frac{m_1u_1 + m_2u_2}{m_1+m_2} = \frac{10000}{2000} = 5\ \text{m/s}$
  Perfectly inelastic: the objects move together
3. $KE_i = 175000\ \text{J},\quad KE_f = 25000\ \text{J},\quad \Delta KE = -150000\ \text{J}$
  Kinetic energy before and after
3. The answer
$\text{v = 5 m/s (perfectly inelastic; 150000 J of kinetic energy lost, 85.71\%)}$
v = 5 m/s (perfectly inelastic; 150000 J of kinetic energy lost, 85.71%)
4. Check
- Momentum before 10000 = after 10000 kg·m/s ✓

Transcript

The problem. Here is the problem: A 1200 kg object moving at 15 m/s collides and sticks to a 800 kg object moving at negative 10 m/s. What is their common velocity? One-dimensional collision; positive velocities point one way, negative the other.

Step by step. Total momentum before. Perfectly inelastic: the objects move together. Kinetic energy before and after.

The answer. So the answer is v equals 5 m/s (perfectly inelastic; 150000 J of kinetic energy lost, 85.71 percent). 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 10000 equals after 10000 kg times m/s, which checks out.

About momentum and collisions

Momentum, impulse and conservation of momentum in collisions.

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