The coefficient of restitution (often written as 'e') is a number that tells us how 'bouncy' an object is after it hits another object.

When two objects collide, they rarely bounce back with the exact same speed they had before the hit. Some energy is usually lost as heat or sound. The coefficient of restitution measures the ratio of how far apart the objects move after the collision compared to how fast they were moving toward each other before the collision.

Understanding the Formula

To find the value of 'e', you divide the speed of separation by the speed of approach. The formula is written as:

e = (Velocity of separation) / (Velocity of approach)

If two balls hit each other and bounce apart at the same relative speed they had before hitting, the coefficient is 1. We call this a perfectly elastic collision. If the objects stick together after hitting, the velocity of separation is zero, making 'e' equal to 0. This is called a perfectly inelastic collision.

Real-World Examples

Think about different types of balls to understand how 'e' works in real life:

• A superball: These are designed to be very bouncy. They have a high 'e' value, usually close to 0.9 or higher.
• A tennis ball: When you drop a tennis ball on concrete, it bounces back up quite high, but not to the exact height it started from. Its coefficient is less than 1.
• A lump of clay: If you throw a piece of soft clay at a wall, it sticks instantly. Because it does not bounce at all, its coefficient of restitution is 0.

Why Energy Matters

In the chapter of Work, Energy, and Power, we learn that energy cannot be destroyed, only changed. During a collision, 'e' helps us understand where that energy goes. When 'e' is less than 1, some of the object's kinetic energy—the energy of motion—is turned into other forms. Most of the time, this lost energy changes into a tiny bit of heat or the sound you hear when the objects strike each other. By calculating 'e', physicists can predict exactly how much movement will remain after any collision.