Elastic and Inelastic Collisions
Introduced| English |
|---|
| elastic collision/ɪˈlæstɪk kəˈlɪʒn/ |
| inelastic collision/ɪnɪˈlæstɪk kəˈlɪʒn/ |
| perfectly inelastic collision/ˈpɜːfektlɪ ɪnɪˈlæstɪk kəˈlɪʒn/ |
| energy lost/ˈenədʒi lɒst/ |
Pool balls versus clay
- Two pool balls click off each other and both keep rolling briskly.
- Two lumps of clay smack together and stop dead, stuck as one.
- Both obey the same momentum law -- yet feel completely different.
- The difference is what happens to the energy.
Momentum yes, energy maybe
- Momentum is conserved in every collision -- always.
- Kinetic energy is not always conserved -- some can turn to heat, sound, or dents.
- That single difference sorts collisions into two families.
Momentum is conserved in every collision, elastic or not.
Yes -- momentum is always conserved (no net external force). Only kinetic energy may or may not be.
Elastic versus inelastic
- An elastic collision 弹性碰撞 conserves kinetic energy too (ideal, like hard spheres).
- An inelastic collision 非弹性碰撞 loses some kinetic energy to other forms.
- Most real collisions are at least a little inelastic.
In which collision is kinetic energy conserved?
Only an elastic collision conserves kinetic energy. Momentum, though, is conserved in all of them.
Select all true statements about collisions.
Momentum always holds; kinetic energy holds only when the collision is elastic.
Perfectly inelastic
- A perfectly inelastic collision 完全非弹性碰撞 is the extreme case: the objects stick together and move off with one common velocity.
- Momentum conservation alone gives that final velocity.
- The clay lumps are the classic example.
Elastic or inelastic?
Momentum is always conserved, but kinetic energy is not. Sort each collision.
A $3\ \text{kg}$ cart at $4\ \tfrac{\text{m}}{\text{s}}$ sticks to a stationary $1\ \text{kg}$ cart. Their common speed afterward (in m/s)?
$3(4) = (3 + 1)v_f$, so $v_f = 12/4 = 3\ \tfrac{\text{m}}{\text{s}}$.
A collision where the objects stick together is called perfectly ____.
In a perfectly inelastic collision the objects move off with one common velocity.
Finding the energy lost
- Compare total kinetic energy before and after the collision.
- Any drop is the energy lost 损失的能量 -- gone to heat, sound, or deformation.
- In a perfectly inelastic collision this loss is the largest.
Before a collision the total KE is $20\ \text{J}$; after it is $14\ \text{J}$. How much energy was lost (in J)?
Energy lost $= 20 - 14 = 6\ \text{J}$, gone to heat, sound, or deformation.
A $2\ \text{kg}$ cart at $3\ \tfrac{\text{m}}{\text{s}}$ hits and sticks to a stationary $4\ \text{kg}$ cart.
- Momentum: $2(3) = (2 + 4)v_f$, so $v_f = 1\ \tfrac{\text{m}}{\text{s}}$.
- KE before $= \tfrac{1}{2}(2)(9) = 9\ \text{J}$; after $= \tfrac{1}{2}(6)(1) = 3\ \text{J}$ -- so $6\ \text{J}$ was lost to heat.
Never assume kinetic energy is conserved unless a collision is stated to be elastic. Using energy conservation on an inelastic collision gives a wrong answer -- momentum is the law that always holds.
Momentum is conserved in every collision; kinetic energy only in an elastic collision. An inelastic collision loses some energy; a perfectly inelastic collision (objects stick together) loses the most. Compare KE before and after to find the energy lost to heat and sound.