Exercise 4: Coefficient of restitution
The last way that we will quantify the energy change as your ball bounces is by determining a parameter known as the coefficient of restitution. Restitution refers to how something is restored or returned. So, the coefficient of restitution measures how much speed is returned to an object after a collision. Mathematically, it is defined as the ratio of the speeds,
where 
is the speed of the ball right before it collides with the ground, and 
is the speed of the ball right after the collision, as it leaves the ground. The | | represents taking the ‘absolute value’ of the velocities. So if you calculate e = 0.5, that means the ball leaves the ground half as fast as it initially hit the ground. You may then conclude that half of the speed was ‘lost’ during the collision with the ground.
Exercise 4.1 (2 marks)
i) What value of e would correspond to energy being completely conserved?
ii) What value of e would correspond to energy being completely lost?
Select the correct answer(s) directly on Crowdmark.
Exercise 4.2 (3 marks)
With your data from Exercise 2 (where you used the hard surface), plot a new graph of e vs Collision Number. Set your y-axis to go between 0 and 1.0.
Helpful hints: Be careful to use the correct speed for 
when calculating each new value of e. For example, the first e we can calculate is that of the 2nd bounce. The speed that the ball leaves the ground with after the first collision (i.e. the first speed recorded in the table from Exercise 2.2) is the same as the speed before the second collision. Furthermore, the speed that the ball leaves the ground with after the second collision is then the same speed before the third collision (i.e. the second speed in the table).
Submit your completed graph with the correct y-axis for your first experiment (hard surface).
Think about it:
Choosing to compare the speed of your ball between collisions may seem like an odd choice, since earlier we were more concerned with how much energy the ball retains between bounces. However, this choice is practical because
i) Speed is often relatively easy to calculate
ii) In many cases, the speed before and after a collision will be directly related to the energy returned to an object.
In the case of this lab, you can equivalently write e directly in terms of the kinetic energy K.
Exercise 4.3 (1 mark)
Exercise 4.4 (1 mark)
Use the equation for e and your plot from 4.2 to determine what fraction of energy is lost from collision to collision. What is that fraction in terms of e?
Helpful hint: For a constant e value, the same fraction of energy is lost on each collision. Was your plot from 4.2 relatively constant?
Select the correct answer(s) directly on Crowdmark.
Before you continue!
Before continuing, be sure you have completed (4.1) to (4.4), which will be graded and submitted through Crowdmark.
