---
title: "Coefficient of Restitution | College Physics I Intro"
description: "Coefficient of restitution measures how bouncy a collision is in College Physics I, using the speed ratio before and after impact to show energy loss."
canonical: "https://fiveable.me/intro-college-physics/key-terms/coefficient-restitution"
type: "key-term"
subject: "College Physics I – Introduction"
unit: "Unit 8"
---

# Coefficient of Restitution | College Physics I Intro

## Definition

The coefficient of restitution, or e, is a number that tells you how elastic a collision is in College Physics I. It compares the objects’ relative speed after impact to their relative speed before impact.

## What It Is

The coefficient of restitution is the collision number, usually written as e, that tells you how much speed is recovered after two objects hit and separate. In College Physics I, you use it to describe how “bouncy” a collision is, but the real meaning is about relative velocity along the line of impact, not just how fast one object looks after the collision.

A common way to write it is as the ratio of the relative speed after the collision to the relative speed before the collision. If two objects move toward each other and then rebound, e compares how quickly they separate to how quickly they approached. A value of 1 means the collision is perfectly elastic, while 0 means the objects leave with no separation speed at all, which matches a perfectly inelastic collision where they stick together or move together after impact.

This number is tied to energy behavior, but it is not the same thing as kinetic energy itself. High e means less kinetic energy is turned into heat, sound, deformation, or internal energy during the collision. Low e means more of the initial motion gets converted into those other forms, which is why a squishy basketball and a lump of clay behave very differently.

You will usually see e in one-dimensional collision problems, especially when momentum alone is not enough to find the final velocities. Momentum conservation gives one equation, and the coefficient of restitution gives a second equation. Together, they let you solve for the unknown speeds after the collision.

A useful way to picture it is this: momentum tells you what the system must do overall, while restitution tells you how “springy” the contact is. For example, if two carts collide on a track, a large e means they rebound strongly. A small e means they crumple, compress, or stay together more after impact.

## Why It Matters

The coefficient of restitution shows up whenever you need to predict what happens after a collision, not just whether momentum is conserved. In College Physics I, that makes it a bridge between the momentum unit and the collision unit, because it adds one more piece of information about the interaction itself.

It matters most when the collision is not perfectly elastic. If you are solving a problem with a bouncing cart, a dropped ball, or two objects that hit and separate, e tells you how much of the approach speed comes back out as rebound speed. That lets you distinguish between a hard, springy collision and one that wastes a lot of mechanical energy.

This term also helps you interpret lab data. If you measure velocities before and after impact, you can estimate e and compare different materials. Steel-on-steel collisions usually have a larger e than collisions involving clay, foam, or other deformable materials.

In multi-step problems, e is the extra relationship that connects the collision’s physical behavior to the algebra. Without it, you often know momentum is conserved but still cannot determine every final velocity.

## Connections

### Elastic Collision

A perfectly elastic collision has e = 1, so the relative speed after impact matches the relative speed before impact. In that case, kinetic energy is also conserved. If a problem says the collision is elastic, restitution gives you a quick check on whether your final speeds make sense.

### Inelastic Collision

Inelastic collisions have e less than 1, which means the objects separate more slowly than they approached. The smaller the value, the more kinetic energy is transformed into heat, sound, or deformation. A perfectly inelastic collision, where objects stick together, has e = 0.

### Momentum

Momentum conservation still holds in collisions even when e is less than 1. That is why restitution is usually paired with momentum in problem solving. Momentum gives you the overall constraint, and e gives you the contact behavior that momentum alone does not tell you.

### [Kinetic Energy Loss](/intro-college-physics/key-terms/kinetic-energy-loss)

The coefficient of restitution is connected to how much kinetic energy disappears from the visible motion during impact. A lower e usually means a larger kinetic energy loss, because more energy goes into internal energy, sound, or permanent deformation. That is why e is useful for comparing real collisions.

## On the AP Exam

A problem set question will usually give you masses, initial velocities, and e, then ask for the final velocities after a collision. Your job is to pair momentum conservation with the restitution equation and solve the two equations together. If the objects bounce apart, watch the signs carefully so the relative velocity comes out right.

In a lab report, you may calculate e from measured approach and rebound speeds and then compare trials with different surfaces or materials. On a quiz, you might be asked to identify whether a collision is elastic, inelastic, or perfectly inelastic from the value of e. Sometimes the question is visual, so you need to read a motion diagram or velocity graph and decide how much bounce the collision shows.

## Coefficient of Restitution vs Conservation of Kinetic Energy

They are related, but not the same. Conservation of kinetic energy is a condition for elastic collisions, while the coefficient of restitution is a ratio that describes how much relative speed is recovered after impact. You can use e to spot whether a collision is elastic, but e itself is not energy.

## Key Takeaways

- The coefficient of restitution, e, measures how much relative speed remains after a collision compared with before it.
- A value of 1 means a perfectly elastic collision, while a value of 0 means a perfectly inelastic collision.
- In College Physics I, e is usually used with momentum conservation to solve collision problems.
- A smaller e means more kinetic energy is converted into heat, sound, deformation, or internal energy.
- You should interpret e along the line of impact, not as a general measure of how fast one object moves.

## FAQs

### What is the coefficient of restitution in College Physics I?

It is the ratio of relative speed after a collision to relative speed before the collision, measured along the line of impact. The value tells you how elastic the collision is. Higher values mean more bounce, and lower values mean more energy is lost from the visible motion.

### Is the coefficient of restitution the same as conservation of kinetic energy?

No. Conservation of kinetic energy is a statement about whether total kinetic energy stays the same, which only happens in elastic collisions. The coefficient of restitution is a number that describes the rebound speed, and it can be used to tell how far a collision is from perfectly elastic.

### How do you use e in a collision problem?

You usually combine the restitution equation with momentum conservation. Momentum gives one equation for the two unknown final velocities, and e gives the second equation. That is what lets you solve collisions where objects bounce apart or partially stick and move together differently afterward.

### What does e = 0 mean?

It means the collision is perfectly inelastic, so the objects have no relative separation speed after impact. They may stick together or move with the same final velocity. This is the extreme case of maximum kinetic energy loss in the collision model.

## Related Study Guides

- [8.4 Elastic Collisions in One Dimension](/intro-college-physics/unit-8/4-elastic-collisions-dimension/study-guide/7byodNWVQXcMsDsd)
- [10.6 Collisions of Extended Bodies in Two Dimensions](/intro-college-physics/unit-10/6-collisions-extended-bodies-dimensions/study-guide/VlSBD5D4L7Md3gih)
- [8.5 Inelastic Collisions in One Dimension](/intro-college-physics/unit-8/5-inelastic-collisions-dimension/study-guide/gIT11YebIOYHUK8i)
- [8.1 Linear Momentum and Force](/intro-college-physics/unit-8/1-linear-momentum-force/study-guide/nwMTvqoNTM5YaEFR)
- [8.2 Impulse](/intro-college-physics/unit-8/2-impulse/study-guide/q6RJW8KxH01qC9bZ)
- [8.6 Collisions of Point Masses in Two Dimensions](/intro-college-physics/unit-8/6-collisions-point-masses-dimensions/study-guide/yhTo9L5LjGQy6Ng5)

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