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### Course: Mechanics (Essentials) - Class 11th > Unit 8

Lesson 4: How to measure the speed of a bullet using a block of wood and a string?# Inelastic collision review

Review the key concepts and skills for inelastic collisions. Understand how to determine if a collision is elastic or inelastic.

## Key terms

Term (symbol) | Meaning | |
---|---|---|

Inelastic collision | Collision which conserves momentum but not kinetic energy. | |

Totally inelastic collision | Collision where the objects stick together and have the same final velocity. Also called a perfectly inelastic collision. | |

Explosion | Reverse inelastic collision where momentum is conserved and kinetic energy increases. |

## How to determine if a collision is elastic or inelastic

If objects stick together, then a collision is perfectly inelastic. When objects don’t stick together, we can figure out the type of collision by finding the initial kinetic energy and comparing it with the final kinetic energy. If the kinetic energy is the same, then the collision is elastic. If the kinetic energy changes, then the collision is inelastic regardless of whether the objects stick together or not. In either case, for collisions with no external forces, momentum is conserved.

## Examples of inelastic collisions

The ballistic pendulum is a device in which a projectile such as a bullet is fired into a suspended heavy wooden stationary block. Some kinetic energy gets transformed into heat and sound, and some is used to deform the block. However, momentum is conserved. Consequently, the block swings away at some speed after the collision.

We can use both of these conservation laws to solve for different unknowns, depending on what variables we are given. For example, we can use the maximum height of the swing to determine the kinetic energy of the block after the collision, then using conservation of momentum we can find the initial speed of the projectile.

Another example of an inelastic collision is dropped ball of clay. A dropped ball of clay doesn’t rebound. Instead it loses kinetic energy through deformation when it hits the ground and changes shape. Likewise, cars are designed to crumple when they collide. A car crash transforms some of the car’s initial kinetic energy into heat, sound, and the deformation of the car.

## Common mistakes and misconceptions

**People sometimes think that objects must stick together in an inelastic collision.**However, objects only stick together during a perfectly inelastic collision. Objects may also bounce off each other or explode apart, and the collision is still considered inelastic as long as kinetic energy is not conserved.**Sometimes people think kinetic energy is only lost during inelastic collisions.**Collisions are considered inelastic when kinetic energy is not conserved, but this could be from either a loss or gain or kinetic energy. For example, in an explosion-type collision, the kinetic energy increases.**It is common for people to try to conserve energy in a collision.**We can only do this if we are told the collision is perfectly elastic.

## Learn more

For deeper explanations of inelastic collisions, see our video elastic and inelastic collisions.

To check your understanding and work toward mastering these concepts, check out properties of elastic and inelastic collisions.

## Want to join the conversation?

- What exactly causes objects to stick together after a perfectly inelastic collision?(1 vote)
- Hi,

Actually, having a perfectly inelastic collision is kinda requires the two objects stick together by definition.

Below is some math to prove it. If you want to skip the math, go to "Skip to here!"

(warning: solid algebra with bad formatting):

Let object A have mass M, initial velocity VI, final velocity VF; let object B have mass m, initial velocity vi, final velocity vf.

By the equation of kinetic energy, in the system of A and B,

ΔKE=0.5M(VF^2-VI^2)+0.5m(vf^2-vi^2).

=0.5(M·VF^2+m·vf^2)+C.

(C=0.5(M·VI^2+m·vi^2), which is a constant)

By the conservation of momentum, M·VF+m·vf=M·VI+m·vi=K.

(K is another constant)

Therefore VF=(K-m·vf)/M. Substituting in ΔKE gives:

ΔKE=0.5((K-m·vf)^2/M+m·vf^2)+C.

Simplifying:

0.5/M·(K^2-2Km·vf+m^2·vf^2+m·vf^2)+C.

(Skip to here!)

Because a perfectly inelastic collision means a maximum loss in kinetic energy, we are looking for a min in ΔKE (note that ΔKE is negative, so a smaller value means a larger change in magnitude).

Using vertex of a parabola (precal..?) or minimum of a function (calc) gives us vf=K/(M+m), plugging vf into VF=(K-m·vf)/M gives us that:

vf=VF=M·VI+m·vi/(M+m).

Since the final velocity of the objects is the same, they stick together.(15 votes)

- What is an example of an explosive inelastic collision?(3 votes)
- There are a couple of great examples in this thread:

https://physics.stackexchange.com/questions/126302/is-there-any-example-of-an-inelastic-collision-where-final-kinetic-energy-of-the(0 votes)

- Is mechanical energy conserved during an explosion?(1 vote)
- Yes, energy is conserved. In a bomb there are special chemicals that react to cause an explosion. This means that there is chemical potential energy stored in the chemical bonds. After the explosion, some of that initial potential energy turns into the kinetic energy of shrapnel, some into heat, some into light, and some into sound. Thus, energy is conserved.(3 votes)

- Isn't a collision where Kinetic Energy increases called a super elastic collision?(1 vote)
- For a 1 dimensional perfectly inelastic collision. Is there a way to calculate v2i given m1, m2, v1i, the coefficient of kinetic friction, and the distance the objects moved until they were at rest?(1 vote)
- In an inelastic collision, where does the kinetic energy go?

Is a deformation of the mass considered a kind of energy?

Is most of the energy converted to thermal and sound?(1 vote) - How do we calculate inelastic collisions?(1 vote)
- Do we look at the entire system or only one object in the system when looking to see if a collision is elastic or inelastic? Like lets say you shoot a block, to you look at the Ke of the bullet alone or of both the bullet and the block?(1 vote)
- Why is mechanical energy conserved in the ballistic pendulum after the bullet enters the ball? Isn't the force of tension doing work on the bullet-ball system? And when an external force works on a system, isn't mechanical energy not conserved?(1 vote)
- I think in the article they were saying that momentum was conserved not mechanical energy. Mechanical energy isn't conserved because some is lost to the heat, sound, and deformation in the block as mentioned.(1 vote)

- In the examples of inelastic collisions part of the article, it mentions that you can find final kinetic energy of the block by using the maximum height of the swing, how would we do this?(1 vote)