How to Identify the Type of Collision - Online Tutor, Practice Problems & Exam Prep

To determine the type of collision between two blocks, first check if momentum is conserved using the equation m_1 × v_1initial + m_2 × v_2initial = m_1 × v_1final + m_2 × v_2final . If momentum is conserved, check if the blocks stick together (completely inelastic) or have different final velocities. Finally, assess if the collision is elastic or inelastic by comparing total initial and final velocities. This systematic approach clarifies the collision type effectively.

How to Identify the Type of Collision

So we spend a lot of time talking through and solving problems of all the different types of collisions you have. But some problems like the one we're going to work out down here will give you a bunch of information, and they won't ask you to calculate an m or v. They'll just ask you to figure out what type of collision is happening. And to do that, I'm going to show you in this video, we're actually just going to use this flowchart over here, which is kind of just a series of checks. We're going to use the numbers given to us in the problem to check these equations. And based on the answers to those, we'll either know what type of collision it is, or we just keep on moving down the flowchart. And these checks are really based on just the characteristics of each type of collision. Alright? We're going to go through this step by step. Let's just jump right into this problem so I can show you how this works. Alright?

So in this problem, we have 2 blocks that are colliding with each other. We've got the masses of both of them, and we also have their initial and final velocities. So, actually, I'm just I already have this stuff drawn out. It's not what I'm interested in. I just want to figure out what type of collision it is. Alright? So that brings us to the first check in our flowchart, which is basically to use conservation of momentum to figure out if this collision is even possible in the first place. We're going to check whether the initial momentum of the system is equal to the final. And if it's not, then we can just stop right there because that means the collision's not possible or that means that the system is isolated. But if it is, if we do have momentum conservation, then we just keep going throughout the flowchart. Alright? So that's the idea. We're going to go ahead and just jump right into this first check. So this is basically just to check if m1v1initial+m2v2initial=m1v1final+m2v2final. We have all the numbers here, so we don't actually have to calculate anything. We just have to plug and chug all the numbers. So this is just going to be the mass of the first block, which is 2, initial velocity, which is 6, plus mass 1 or sorry, mass 2, which is 1, times the initial velocity, which is 2. And does that equal the right side, which is going to be the 2 times the final velocity, which is 3 plus, and then, one times the final velocity, which is 8 of the second block. Alright? Go ahead and plug this in, where you're going to see this is 12 plus 2, which means 14. That's this whole thing. And does 14 equal 6 + 8, which is also 14. And, actually, it does. So this is correct. This is a yes. We've done with this we're done with this check. And, basically, what that means here is that, it's not not possible. That this collision here is is actually possible because momentum conservation actually does occur. Alright? So initial equals final. So that means we actually just move on in the flowchart, which means we're going to move on to the second check. Alright?

So what we're going to do in this check over here is we're basically just going to figure out whether this is a completely inelastic collision or not. And really, what we're just going to do is focus on whether the objects are stuck together. There are 2 ways of figuring that out. Either we figure out that the final velocities of both the objects are the same, or we're going to look for keywords in our problem, like whether the objects are stuck, embedded, or lodged. Alright? So that's the second check. And if you look through the problem text, you'll actually read, nowhere in the problem does it say that these objects stick together or embedded or lodged. But that doesn't necessarily mean that they don't actually have the same final velocity. We're going to have to check if their final velocities are the same. So in other words, I'm going to check if v1final is equal to v2final. Again, I don't have to calculate anything. I already have those numbers here. This is really just 3 and 8. So clearly, we can see here that these things don't actually stick together because they have different velocities. So 3 is not equal to 8. This is a really, really simple check to do. Alright? So this is going to be a no. They do not stick together, which means that we actually go right into the second check into the 3rd check. Alright? So this is not a completely inelastic collision. And, by the way, what that means here with checks 1 and 2 is that we can already get rid of answer choices a and b. Alright?

Let's move into the final check, which is basically trying to figure out whether the collision is elastic or inelastic. Remember, what happens is you have 3 types of collisions, either a perfectly inelastic collision, an elastic collision, or by default, if it's none of those 2, then it actually has to be somewhere in the middle of the spectrum, which is an inelastic collision. And to do that, we're going to have we're basically just going to check the elastic equation, if the total velocity of the first object is equal to initial and final is equal to the total velocity of the second object. Alright? And depending on the answer to that, we'll know what type of collision we're dealing with. That's the 3rd check. We're just going to do v1initial+v1final is equal to the total velocity of the second, which is v2initial+v2final. Alright. So this is just going to be basically the initial velocity and final velocity of the first, which is 6 plus 3. Does this equal the total velocity of the second object, which is 2 +8? Well, we check this. This is actually just going to be 9, and over here, we're going to have 10. So these things are not equal to each other. So what that means, by the way, if it's a no, then it actually just means that it's not an elastic collision. And so if it's none of the other things above, if the collision is possible but it's not perfectly inelastic and it's not elastic, then by default, we're already done with our flowchart because we know that this is just going to be a regular inelastic collision. Alright? So that's how to use this flowchart. You kind of just go down and work the steps. As soon as you know what type it is, you're done. You'll have to continue with the rest of the flowchart. If you make it all the way to the bottom, then that means that by default, the collision is inelastic. Alright? Hopefully this made sense. Thanks for watching, and let's get some practice.

Two toy carts collide head-on on a frictionless surface. Cart A has a mass of 0.50 kg and an initial velocity of 2m/s. Cart B has a mass of 0.30kg and initial velocity –2m/s. After the collision, the final velocities of A and B are –1m/s and 3m/s, respectively. What type of collision was this?

• A. Collision Not Possible
• B. Completely Inelastic
• C. Elastic
• D. Inelastic

Here’s what students ask on this topic:

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

To determine if a collision is elastic or inelastic, you need to check two main criteria. First, verify if momentum is conserved using the equation:

$m_1\times v_1\mathrm{initial}+m_2\times v_2\mathrm{initial}=m_1\times v_1\mathrm{final}+m_2\times v_2\mathrm{final}$

If momentum is conserved, check if kinetic energy is also conserved. For an elastic collision, both momentum and kinetic energy are conserved. For an inelastic collision, only momentum is conserved, and kinetic energy is not.

What is the difference between elastic and inelastic collisions?

The main difference between elastic and inelastic collisions lies in the conservation of kinetic energy. In an elastic collision, both momentum and kinetic energy are conserved. This means the total kinetic energy before and after the collision remains the same. In an inelastic collision, only momentum is conserved, while kinetic energy is not. Some of the kinetic energy is converted into other forms of energy, such as heat or sound, during the collision.

How can you tell if a collision is completely inelastic?

A collision is completely inelastic if the colliding objects stick together after the collision, moving with a common final velocity. To determine this, check if the final velocities of both objects are the same or look for keywords in the problem statement such as "stuck," "embedded," or "lodged." If the objects have the same final velocity, the collision is completely inelastic.

What is the first step in identifying the type of collision?

The first step in identifying the type of collision is to check if momentum is conserved. Use the equation:

$m_1\times v_1\mathrm{initial}+m_2\times v_2\mathrm{initial}=m_1\times v_1\mathrm{final}+m_2\times v_2\mathrm{final}$

If the initial momentum equals the final momentum, the collision is possible, and you can proceed to the next steps to determine the specific type of collision.

What equations are used to identify the type of collision?

To identify the type of collision, you use the following equations:

1. Conservation of Momentum:

$m_1\times v_1\mathrm{initial}+m_2\times v_2\mathrm{initial}=m_1\times v_1\mathrm{final}+m_2\times v_2\mathrm{final}$

2. Check for Completely Inelastic Collision:

Are the final velocities of both objects the same?

3. Check for Elastic Collision:

$v_1\mathrm{initial}+v_1\mathrm{final}=v_2\mathrm{initial}+v_2\mathrm{final}$

These equations help you systematically determine the type of collision.