Common Final Velocity in Inelastic Collisions

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• 0:04 What Is a Collision?
• 1:24 Conservation Laws
• 2:15 Momentum and Common Velocity
• 2:45 Practice Problems
• 5:59 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

When two objects collide and stick together, this is called an inelastic collision. In this lesson, learn how to recognize inelastic collisions and how to use conservation of momentum to find the common final velocity.

What Is a Collision?

While sitting on your front porch one day, you see two cars coming down the road. Suddenly, the car in front stops. The car behind doesn't notice and hits them from behind. The two cars both slide forward as one until the wreckage slowly comes to a stop. What just happened? The cars had a collision, right?

We all know that car crashes are collisions, but there are many other types of events that are also considered collisions in physics. For example, when you hit a baseball with a bat or kick a soccer ball, these are also collisions. What about if you run into your friend while you are both ice skating and you both slide across the ice together? Yes, this is also a collision. Whenever two or more objects hit each other in this way, then you have a collision.

We can classify collisions into one of two types depending on what happens to the objects immediately after the collision.

1. If the collision is inelastic, then the colliding objects stick together after the collision. The car crash you witnessed and the collision you had with your friend while ice skating would both be inelastic collisions.
2. In contrast, if the colliding objects bounce off each other and do not stick together, then the collision is considered to be elastic. Hitting a baseball or kicking a soccer ball are examples of elastic collisions.

Conservation Laws

Let's look more closely at what happens in an inelastic collision. When the two cars hit each other after the collision, they move together more slowly than the one car was moving beforehand. Therefore, the system has less kinetic energy after the collision than before.

What happens to the energy? Does it disappear? No, remember that you cannot create or destroy energy, but it can change forms. When the cars collided, there was likely some damage to each car. If you were to put your hand on the site of damage, it would be warm, maybe even hot. Some of the kinetic energy of the system was turned into thermal energy.

So even though the total energy of the system was conserved, kinetic energy was not. What was conserved in this collision, then? The physical quantity that is always conserved in collisions is momentum.

Momentum and Common Velocity

Momentum is equal to the mass of the object multiplied by its velocity. In any collision, whether it is elastic or inelastic, the total momentum of the system before the collision must be equal to the total momentum of the collision after the collision.

Since inelastic collisions involve objects that stick together after the collision, we say that the objects have a common final velocity. They are no longer two separate objects, but have merged into one larger object.

Practice Problems

Let's revisit the car crash you witnessed again and see what we can learn about it using conservation of momentum. Say the car in back had a mass of 1800 kg and was moving at 18 m/s originally. The car in front had a mass of 1500 kg, and was stopped. How fast were the two cars moving immediately after the collision?

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