Types of Collisions - Online Tutor, Practice Problems & Exam Prep

Collisions can be categorized into elastic and inelastic types, with inelastic further divided into general inelastic and perfectly inelastic collisions. In all collisions, momentum is conserved, but energy conservation varies. Elastic collisions conserve both momentum and mechanical energy, while inelastic collisions conserve momentum but lose mechanical energy. Perfectly inelastic collisions involve objects sticking together post-collision. Understanding these distinctions is crucial for analyzing interactions, as they impact calculations involving momentum and energy loss.

Overview of Collision Types

Guys, remember that we said that interactions between objects can fall under either collisions or push away problems. But there are actually three types of collisions that you're going to have to be able to identify. I'm going to go over a conceptual overview of these types of collisions, and we'll talk about them in more detail later on. Let's go ahead and talk and take a look here. The two basic categories are elastic and inelastic. Inelastic collisions break down into two different categories. That's why we say that there are three types. What's common about all collisions is that momentum is going to be conserved in all collisions. We're always going to be able to use conservation of momentum. If you start out with 10 momentum, you have to keep the same 10 throughout these problems, no matter what type it is. The difference really comes in when you start to take a look at the energy. What really separates these two types is whether energy is conserved or not. An elastic collision is going to conserve energy. So if you calculate 20 joules of mechanical energy initially, you're going to end up with 20 joules of mechanical energy finally. That's the defining characteristic about them. So what happens is momentum and energy are conserved, but the objects don't stick to each other. And we'll talk about what that means in just a second here. An inelastic collision is going to conserve momentum, but it's not going to conserve mechanical energy. So you're always going to lose some mechanical energy here. So the setup is that you have these objects that are sort of crashing towards each other. You're going to conserve momentum. When you calculate the mechanical energy, there's always going to be some loss. Just making up numbers here. Here you have 20. Here you have 10. So there has been some mechanical energy that has been lost there. So this is sort of like a general inelastic collision. You have momentum conservation, not mechanical energy conservation, and the objects don't stick to each other. So basically, these two things are sort of going slower after the collision. An important subtype of these type of inelastic collisions is what's called a completely or perfectly inelastic collision. The setup is a little bit different here. But basically, you have one object that's going to hit another one, and those things are going to stick together, and they're going to move together as a system. The defining characteristic here is that objects move at the same velocity after they collide. They move together like this. Now this is really just a subtype. It's still an inelastic collision, so you still have some mechanical energy loss. So what happens is you have momentum conservation. You do not have mechanical energy conservation, but what's defining about these is that objects are going to stick together. Alright? So that's sort of a general overview of these types of problems. Now students always get confused between an elastic collision versus a totally inelastic collision versus a general inelastic collision. So what I always like to do, or sort of visualize, is a bouncy ball that's sort of going up, that's hitting the floor. And we want to take a look at the energy of that bouncy ball. If it's a completely elastic collision, we know that mechanical energy is going to be conserved. So if we drop this ball from 1 meter, it's going to fall down to the floor and it's going to rebound upwards, and it's going to rebound to the same height because there's no energy loss. So the ball returns to the same height. An inelastic collision always loses some mechanical energy. So if the ball, you know, falls down to the floor, the ball has to return to a lower height. It could be 0.1 meters. It could be 0.5 meters. It could be 0.9999. But if you ever have some energy loss, that's always going to be an inelastic collision no matter how close it is to 0 or 1 or something like that. Right? A completely inelastic collision is going to be something like the ball is going to fall to the floor, and it's just going to get stuck there. These two things are going to have to fuse together or stick to each other. Right? That's what's the defining characteristic about them. So these terms are often kind of confusing, completely elastic or completely inelastic or something like that. So what I always like to do is I kind of like to envision like a spectrum of how elastic a problem is. And the best way to tell which type it is, is to look first if it's completely inelastic. So if it's completely inelastic, you're going to be looking for if objects are sticking to each other. And if it's not one of those types of problems, if they don't stick to each other, you're going to go to the other side of the spectrum. You're going to figure out if the problem is completely elastic. And to do that, you're going to look at the mechanical energy. If you can calculate the mechanical energy and you figure out that it's conserved, then it's completely elastic. If it's not one of these two problems, if it's not completely inelastic and if it's not completely elastic, then it sort of falls into this sort of partially inelastic category here. So this is going to happen every time you have some mechanical energy loss. Alright? Hopefully that makes sense, guys. Let me know if you have any questions.

Here’s what students ask on this topic:

What is the difference between elastic and inelastic collisions?

In an elastic collision, both momentum and mechanical energy are conserved. This means that the total kinetic energy of the system before and after the collision remains the same. In contrast, in an inelastic collision, only momentum is conserved, while mechanical energy is not. Some of the kinetic energy is transformed into other forms of energy, such as heat or sound. A special case of inelastic collisions is the perfectly inelastic collision, where the colliding objects stick together and move with a common velocity after the collision.

How is momentum conserved in collisions?

Momentum is conserved in all types of collisions, whether elastic or inelastic. This means that the total momentum of the system before the collision is equal to the total momentum of the system after the collision. Mathematically, this can be expressed as:

$p_{\mathrm{initial}}=p_{\mathrm{final}}$

For a two-object system, this can be written as:

$m_1{v}_{\mathrm{1i}}+m_2{v}_{\mathrm{2i}}=m_1{v}_{\mathrm{1f}}+m_2{v}_{\mathrm{2f}}$

where $m_1$ and $m_2$ are the masses of the objects, and $v_{\mathrm{1i}}$, $v_{\mathrm{2i}}$, $v_{\mathrm{1f}}$, and $v_{\mathrm{2f}}$ are their initial and final velocities, respectively.

What is a perfectly inelastic collision?

A perfectly inelastic collision is a type of inelastic collision where the colliding objects stick together after the collision and move with a common velocity. In this type of collision, momentum is conserved, but mechanical energy is not. Some of the kinetic energy is converted into other forms of energy, such as heat or deformation. The defining characteristic of a perfectly inelastic collision is that the objects move together as a single entity after the collision. This can be represented mathematically as:

$m_1{v}_{\mathrm{1i}}+m_2{v}_{\mathrm{2i}}=(m_1+m_2)v_f$

where $v_f$ is the common final velocity of the combined mass.

How can you determine if a collision is elastic or inelastic?

To determine if a collision is elastic or inelastic, you need to check the conservation of mechanical energy. In an elastic collision, both momentum and mechanical energy are conserved. This means that the total kinetic energy before and after the collision remains the same. In an inelastic collision, only momentum is conserved, and some of the mechanical energy is lost to other forms of energy, such as heat or sound. You can calculate the initial and final kinetic energies of the system and compare them. If they are equal, the collision is elastic. If there is a loss of kinetic energy, the collision is inelastic.

What are some real-life examples of elastic and inelastic collisions?

Real-life examples of elastic collisions include the collision of billiard balls and the bouncing of a rubber ball on a hard surface. In these cases, both momentum and mechanical energy are conserved, and the objects do not stick together. Examples of inelastic collisions include car crashes and clay balls sticking together after impact. In these scenarios, momentum is conserved, but mechanical energy is lost to deformation, heat, and sound. A perfectly inelastic collision example is a lump of clay hitting another lump and sticking together, moving as a single mass post-collision.