# Elastic and inelastic collisions

##### Intros

###### Lessons

##### Examples

###### Lessons

**Solving word problems with momentum and elastic/inelastic collisions**- Two cars collide head-on and stick together. The cars are stationary after colliding.

- Is total momentum conserved?
- Is total energy conserved?
- Is the collision elastic or inelastic?

- Identify each situation as an inelastic or elastic collision.

- One car crashes into another, bouncing apart with a loud bang.
- A hammer strikes a piece of steel, bouncing off and producing sparks.
- A He atom collides with a H atom, bouncing off and maintaining overall kinetic energy.

- Two cars collide head-on and stick together. The cars are stationary after colliding.
- $\bold{\sum\vec{E}_i = \sum\vec{E}_f}$ $\bold{ ; }$ $\bold{\sum\vec{p}_i = \sum\vec{p}_f:}$
**Conservation of energy and momentum in elastic and inelastic collisions**- 3.6×10
^{4}kg train car A travelling at 5.40 m/s [E] collides with stationary 5.20×10^{4}kg train car B. The train cars bounce apart, and after the collision, train car A travels at 1.70 m/s [E]. Determine if this collision is elastic or inelastic. - 0.50 kg steel ball A travelling [E] with a kinetic energy of 0.49 J collides with stationary 0.75 kg steel ball B head-on. After the collision, ball A travels at 0.28 m/s [W]. Assuming the collision is elastic, find the velocity of ball B after the collision.
- A "ballistic pendulum" is a method used to measure the velocity of a bullet. A 5.60 g bullet is fired at a 1.24 kg wooden block suspended as shown in the diagram, and the block rises to 0.250 m higher than its initial position at the peak of its swing.
- Find the velocity of the bullet when it hits the block.
- Calculate how much of the kinetic energy is lost in this inelastic collision. Explain what happens to this energy.

- 3.6×10

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###### Topic Notes

In this lesson, we will learn:

- Meaning of elastic and inelastic collisions
- What happens to kinetic energy in a collision?
- Understanding perfectly inelastic collisions
- Problem solving with elastic and inelastic collisions

__Notes:__- Total momentum and total energy are conserved in collisions. However, kinetic energy is not always conserved, since it can be converted into other forms of energy.
__Elastic collision:__collision where no kinetic energy is lost__Inelastic collision:__collision where part of the kinetic energy is converted to other forms of energy__Perfectly inelastic collision:__collision where the maximum possible amount of kinetic energy is converted to other forms of energy; objects stick together.

**Conservation of Momentum**

$\sum\vec{p}_i = \sum\vec{p}_f$

$\vec{p}_i:$ initial momentum, in kilogram meters per second (kg·m/s)

$\vec{p}_f:$ final momentum, in kilogram meters per second (kg·m/s)

**Conservation of Energy**

$\sum\vec{E}_i = \sum\vec{E}_f$

$\vec{E}_i:$ initial energy, in joules (J)

$\vec{E}_f:$ final energy, in joules (J)

**Kinetic Energy**

$KE = \frac{1}{2}mv^2$

$KE:$ kinetic energy, in joules (J)

$m:$ mass, in kilograms (kg)

$v:$ speed, in meters per second (m/s)

**Potential Energy**

$PE = mgh$

$PE:$ potential energy, in joules (J)

$g:$ acceleration due to gravity, in meters per second squared (m/s^{2})

$h:$ height, in meters (m)

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