Collisions are short interactions where objects exert large forces on each other for a brief time. In physics, the key question is what stays the same before and after the collision. Total momentum is conserved in an isolated system, which makes collisions useful for studying motion in carts, balls, vehicles, and particles.
The main difference between elastic and inelastic collisions is whether kinetic energy is also conserved.
Understanding Physics: Elastic vs Inelastic Collisions
The force during a collision is usually far larger than the forces acting before it. It lasts for a very short time. The product of force and collision time is called impulse.
Impulse changes an object's momentum. Each object pushes on the other with equal size forces in opposite directions. These forces give equal and opposite impulses.
This is the physical reason the total momentum of the two-object system stays fixed when outside forces are too small to matter. Choosing the system matters. For example, friction from a track can affect a cart collision if the collision is slow or the track is rough.
An inelastic collision does not mean energy disappears. Energy is transferred into forms that are harder to see in the final motion. Objects may bend, compress, heat up, vibrate, or make sound.
A clay ball that hits a wall changes shape. A car bumper crumples. These changes take energy from the motion of the whole objects.
Even a bouncing ball loses some kinetic energy because the ball and floor deform during contact. A collision is closer to elastic when the objects spring back with very little permanent deformation, heating, or sound.
The amount of rebound gives useful evidence about the type of collision. In a nearly elastic head-on collision, objects separate rapidly after contact. In a strongly inelastic collision, their speeds relative to each other after impact are much smaller.
When objects stick, they leave with one shared velocity. This shared velocity can be surprising. A light fast object can noticeably change the motion of a heavy slow object, yet the heavy object usually has the greater effect on the final direction.
Mass and speed must both be considered. A small object moving very fast can carry substantial momentum.
When solving collision problems, start by drawing the situation before and after impact. Choose one direction as positive and keep that choice for every velocity. A leftward velocity is then negative if rightward is positive.
Write the momentum of every object, including objects initially at rest. Next, decide whether the problem states that the collision is elastic, inelastic, or perfectly inelastic. Use kinetic energy conservation only when the collision is elastic.
Check the final answer against common sense. If two objects stick, they must have the same final velocity.
If an object rebounds, its velocity changes sign. In laboratory work, measurements rarely show perfect conservation because of friction, air resistance, uneven tracks, and timing errors.
Key Facts
- Momentum of one object is p = mv.
- Total momentum is conserved in an isolated collision: m1v1i + m2v2i = m1v1f + m2v2f.
- Kinetic energy is KE = 1/2 mv^2.
- Elastic collision: total momentum and total kinetic energy are conserved.
- Inelastic collision: total momentum is conserved but total kinetic energy is not conserved.
- Perfectly inelastic collision: objects stick together, so m1v1i + m2v2i = (m1 + m2)vf.
Vocabulary
- Momentum
- Momentum is the quantity of motion of an object, equal to its mass times its velocity.
- Elastic collision
- An elastic collision is a collision in which total momentum and total kinetic energy are both conserved.
- Inelastic collision
- An inelastic collision is a collision in which total momentum is conserved but some kinetic energy changes into other forms.
- Perfectly inelastic collision
- A perfectly inelastic collision is a collision in which the objects stick together and move with one final velocity.
- Isolated system
- An isolated system is a group of objects with no net external force acting on it during the interaction.
Common Mistakes to Avoid
- Assuming kinetic energy is always conserved is wrong because only elastic collisions conserve total kinetic energy.
- Forgetting velocity signs is wrong because momentum is a vector, so motion in opposite directions must have opposite signs.
- Using conservation of momentum for one object alone is wrong because momentum conservation applies to the total system, not to each object separately.
- Thinking lost kinetic energy disappears is wrong because it is transformed into heat, sound, deformation, or internal energy.
Practice Questions
- 1 A 2.0 kg cart moving at 3.0 m/s collides elastically with a 1.0 kg cart initially at rest. If the 2.0 kg cart moves at 1.0 m/s after the collision, what is the final velocity of the 1.0 kg cart?
- 2 A 0.50 kg ball moving at 6.0 m/s collides with a 0.50 kg ball at rest. They stick together after the collision. What is their shared final velocity, and how much kinetic energy was lost?
- 3 Two collisions have the same initial masses and velocities. In one, the objects bounce apart, and in the other, they stick together. Explain which collision has more kinetic energy after the collision and why momentum can still be conserved in both.