In a collision, momentum is always conserved, but kinetic energy is not. Sometimes, the kinetic energy in a collision is nearly conserved while in other collisions, it is hardly conserved at all. What is going on?

During a collision, energy changes form. As objects interact and collide, they change shape and are distorted. When this occurs, the kinetic energy of the colliding bodies is converted into potential energy, or dissipated as sound or heat. The extent to which the initial kinetic energy is converted to final kinetic energy during the collision determines the elasticity of the collision.

There is a spectrum of elasticity: collisions can range from being perfectly elastic to perfectly inelastic. As collisions become more and more inelastic, more and more kinetic energy is lost.




Perfectly Elastic Collisions

In a perfectly elastic collision, the total kinetic energy of the system is conserved.  Perfectly elastic collisions generally occur only at the subatomic level.

Inelastic Collisions

In an inelastic collision, some kinetic energy is lost, generally as sound or thermal energy.  This is a broad range and most collisions fall within this class.


Perfectly Inelastic Collisions

In a perfectly inelastic collision (also called completely inelastic), the colliding objects stick together upon impact. There is the greatest loss of kinetic energy in this type of collision.

 

Imagine throwing a perfectly spherical bouncy, elastic ball against the wall.

  1. Describe the shape of the ball before, during, and after the collision. 

  2. Describe what happens to the kinetic energy of the ball during the interaction. Is the kinetic energy of the ball conserved? If not, what happened to it?

    1. before:  spherical       during:   squished       after:   spherical  

    2. The kinetic energy of the ball is nearly conserved, with some kinetic energy being used as work done to momentarily change the shape of the ball.


Imagine throwing a blob of playdough against the wall.

  1. Describe the shape of the blob before, during, and after the collision. 

  2. Describe what happens to the kinetic energy of the blob during the interaction. Is the kinetic energy of the blob conserved? If not, what happened to it?

    1. before:   blob     during:    flat      after:    stays flat  

    2. The kinetic energy of the playdough is not conserved. Most of the kinetic energy is used in order to change the shape of the playdough permanently.


The Coefficient of Restitution (e) Defines Elasticity

Is there a range of elasticity in the collisions that were performed in previous lab simulation?  Recall that in each collision, a value known as e was recorded at the top of each table.  The e-value represents how elastic a collision is.  The closer the e-value is to 100% the more elastic a collision is.

Using the data from the previous lab, complete the table below.  Specifically,

            a. Record the total Ek initial , total Ek final , and e for each collision from the lab data tables.

            b. Calculate the percentage of loss in kinetic energy for each collision using: 

                % loss =∑Ek initial-∑Ek final∑Ek initial×100%

 

Collision

e

Total Ek Initial
(J)

Total Ek Final
(J)

 Loss in Ek

(%)

1

 

 

 

 

2

 

 

 

 

3

 

 

 

 


After you complete the table you should be able to determine the relationship between the percentage of loss in kinetic energy and the e-value.