Everywhere you look, you can find examples of energy transfer– boiling water on the stove, combusting gasoline to accelerate your car, a roller coaster moving along its track. While each of these examples have different mechanisms behind them,they all demonstrate the phenomena of energy transferring from one source to another.While we often think of energy being conserved throughout a system, work that is done by or on the system may alter the amount of energy available depending on the choice of system.

In this lab, you and your group are tasked with measuring the transfer of energy in mechanical systems and collisions. Energy in these systems often emerges as potential and kinetic energy,but they can also be quite complex, especially when considering any work present. By making qualitative and quantitative conclusions regarding energy transfer and work, you will also relate these phenomena to everyday life through examples you and your group identify that demonstrate safe ways to distribute energy.

In this lab, you will create a model of energy using two distinguishable bouncy balls. Using video tracking software to obtain your data, you can determine the initial energy and the total energy before and after the collision of the ball and the ground.The total energy of a system can be given as

= +

where PE is the potential energy of the system and KE is the kinetic energy. These are commonly written as

= ℎ

and

!

= 2

where

• m is the mass

• g is the acceleration of gravity

• h is the height

• v is the velocity.

Work (W), or the amount of energy that is added to or removed from the system ( ), can be calculated as

= =

where F is the force acting on an object over a distance of_x._

To do this lab, it will help to remind yourself how to use Tracker (http://physlets.org/tracker/) as well as develop an understanding of:

• How energy is transferred between kinetic and potential when objects fall

• How energy is transferred in collisions

• How work can increase or decrease the energy in a system and where that energy comes from/goes

• How the sign of the work equation depends on where the work is being done (i.e.,“Work done by” or “Work done on”)

Part 1 – Investigating a Bouncing Ball

The motion of a ball bouncing is one that is familiar to many. However, few consider the ways energy is being transferred from one state to another as it does so, or what forces interact on the ball as it moves. With your group, play with a bouncy ball and consider:

• What parameters can you change that affect the height of the bounce?

• Where is the energy transferring as the ball falls– from what form to which? What causes this?

• Where is the energy transferring as the ball hits the floor? What causes this?

• Can you describe what is causing the ball to change direction in terms of forces?

• Can you determine the relative size of the force for different bounces? On what parameters does this depend (initial speed, height, type of ball, etc.)?

Part 2 – Determining Losses

You and your group likely noticed that the ball doesn't reach the height from which you dropped it. Using a relatively bouncy ball, one that bounces less,and Tracker, determine how much energy is lost after bouncing. While doing so, consider:

• How much is lost after one bounce? After several?

• Is the energy lost after each bounce the same? Why or why not?

• Is the energy lost the same for each ball? Why or why not?

• Where does the energy go after each bounce?

• How accurate do you feel your values are? Can you determine sources of uncertainty in your experiment? Can you account for/minimize the impact from these sources?

• Is there a limit to the model you are considering (i.e., will you get the same relationship regardless of height)? Why or why not? It may be helpful to consider the assumptions that underlie the model you are using.

Part 3 – Air Resistance

One source we have looked at in the past for falling objects is air resistance. Therefore, you and your group may have identified this as a potential source for energy transfer. Using your data, determine how much energy is lost to air resistance.

• Does this account for the amount of energy you lost?

• How confident are you in the values you are obtaining?

• Is the energy lost the same for each ball? Why or why not?

If this doesn't account for the energy lost between bounces, your video likely holds even more information of energy transferring into or out of the system. Identify these instances occurring in your video. It may be helpful to check the total energy of the ball at various times to determine where the largest changes may occur. Are there particular instances that emerge, or a pattern you notice?

Part 4 – The Bounce

To investigate what occurs to the ball during the bounce,you and your group will likely have to take additional videos of this moment. If you choose to do so, it is recommended that you obtain as much information of the ball hitting the ground as you can (i.e., the slowest motion you can obtain and the shortest distance you can shoot from). From these videos, determine how much energy is lost in the system when the ball hits the floor. While doing so, it may be helpful to consider:

• What is the energy immediately before the collision? Immediately after?

• How large of an impact is this energy lost (i.e., what ratio of the total energy before impact is this lost)?

• Is this value the same for each ball? Why or why not?

• How does this ratio compared to the one you found between bounces in Part 2? (If you did not determine a ratio of energy lost at that time, it may be useful to do so now.)

Part 5 – Relating Energy Lost to Force

Your videos should have all of the information required to determine the force each ball felt as it hit the floor. If not, it may be helpful to retake the video in Part 4 , but consider throwing the ball at the floor with appreciable speed.

• What is the force felt on each ball as it hits the ground?

• What qualitatively is different between the two balls? Can this help you determine similarities and differences in these forces?

• How much force can each ball absorb?

• Where did the energy go while the ball hit the ground? What does that tell you about each material?

Determining the force felt or absorbed by various materials help engineers design better safety equipment seen every day. Considering the phenomenon you observed, can you and your group identify where you have seen similar examples before? Do your results align with how you understand these materials?

While conducting the experiment, consider the following questions:

• What video settings would give you the most useful data for analysis?

• How does uncertainty affect your measurements? How can you design your experiment to minimize uncertainty?

• How do your results compare to the expected values? Can you rectify any differences?