On page one of this lesson you were asked this question: in a collision between two automobiles, is it better for the occupants if the collision is elastic or inelastic?

Now that you know the differences between elastic and inelastic collisions, you should be ready to complete the necessary analysis to answer this question. Below are descriptions of experiments using a ball pendulum and a block pendulum.

In one version of the experiment, a bouncy ball attached to a long string collides with a wooden block that is also suspended by a long string. In other words, a bouncy-ball pendulum collides with a wooden-block pendulum. Before the collision, the bouncy ball has all the kinetic energy because the wooden block is at rest.  After the collision, both objects have some kinetic energy.

The following diagram summarizes typical results:


          

In another version of this experiment, the bouncy ball is replaced with a ball of clay.  Before the collision, the ball of clay has all the kinetic energy because the block of wood is at rest.  After the collision, both objects have some kinetic energy.  The following diagram summarizes typical results:

 

 



The results for the pendulum experiment illustrate how the properties of the materials impact the transfer of kinetic energy in a collision. Some of the initial kinetic energy was used to do work to change the shape of the clay ball, so there was less kinetic energy available for the objects after the collision.

An automobile collision is more like the collision between the clay ball and the block than the bouncy ball and the block. Some of the initial kinetic energy is used to do work to change the shape of the crumple zones of the vehicle.  The amount of kinetic energy transferred from one vehicle to the other depends upon the amount of work that is done to change the shape of the vehicles. Although this energy transfer has nothing to do with impulse, the resulting impulse that acts on each vehicle in a collision is strongly influenced by how the transfer of kinetic energy occurs between the two vehicles. You can see why by returning to typical data from the experiments of the two pendulums.

In the case of the bouncy ball and the wooden block, typical data for the collision is shown in the following diagram:



 

 


bouncy ball

  

← Before the collision →

 

← After the collision →

wooden block

  

 

When we calculate the impulse for the bouncy ball and the block each has the same magnitude but opposite direction.

Impulse of the bouncy ball  

 

Impulse of the block

 

 


When a clay ball collides with a wooden block, the velocity values are significantly reduced due to the lower values of kinetic energy. The following diagram shows typical results:


 

 


clay ball

  

← Before the collision →

 

← After the collision →

wooden block

  

 

However, even though kinetic energy was lost the change in momentum for each is the same just opposite in direction.

 Impulse of the clay ball

 Impulse of the block


Explain why it would be better to be in a vehicle that is in an inelastic collision with another object rather than a vehicle in an elastic collision with another object.

Inelastic collisions involve a significant reduction in the kinetic energy of the objects after the collision since very little bouncing or reversal of direction occurs. This means that the overall change in velocity is less, so the change in momentum is less. Therefore, less impulse is required to cause that change in momentum. In addition, the time interval for the inelastic collision is increased because crumpling takes time. As was mentioned in the previous module, if the time interval for an interaction lengthens, then the force required reduces to achieve the same impulse.