Impulse

You have observed collisions in many aspects of life. Whether intentional– dribbling a basketball or tackling a football player – or accidental – a fender bender while driving home or dropping your phone – collisions are a part of daily life. The severity of these collisions – whether the player is injured or whether the phone's screen will break– is determined by measurable parameters of the impact. Qualitatively, you probably have a sense of how hard you would have to bump heads with someone before it hurt or how high you can safely drop your phone without breaking it.All of these examples illustrate how the severity of a collision is related to its impulse or force.

In this lab, you will investigate multiple collisions to make qualitative and quantitative conclusions regarding forces during a collision. These conclusions will help you relate to the way a collision “feels” – for instance, why concussions are so prominent in modern sports.

In this lab, you will create a model of the relationship between the height of a dropped ball and the force it feels when bouncing off the ground.Using video tracking software to obtain your data, you can determine the acceleration an object feels during the collision, often referred to in “g”s, referring to the acceleration due to gravity. Impulse (I) is defined as the force (F) an object feels over some amount of time (∆ ), or the change in momentum (∆ ),

= ∆ = ∆

This collision can be related to the acceleration(a) the object felt using Newton's Second Law

=

where m is the mass of the object.

By determining the acceleration (i.e., the g's) that a bouncing ball feels, qualitative conclusions can be drawn as to how we experience other forces – from the sensation of riding a roller coaster to the force necessary to cause a concussion. (While it is not know exactly how much force is required to cause a concussion, there is evidence that it can be caused with accelerations less than 100 g's [Hernandez, F., Wu, L.C., Yip, M.C. et al. Ann Biomed Eng (2015) 43:1918.] http://link.springer.com/article/10.1007/s10439-­‐014-­‐1212-­‐4/fulltext.html.)

Studying impulse and momentum of collisions is a focus of many researchers, especially those in sports medicine. From analyzing the impulse of collisions that cause concussions, scientists are able to contribute not only to fundamental science,such as basic brain and body-­‐kinetics research, but also in engineering better safety equipment.

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:

• What it means to measure something in “g”s

• Impulse and momentum changes and how both are related to the force an object experiences

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

• How energy is transferred in collisions

Part 1 – Investigating a Bouncing Ball

The motion of a ball bouncing is one that is familiar to many. However, few consider the forces interacting on the ball as it hits the floor. With your group, play with a bouncy ball and consider:

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

• 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 – Measuring the Force of Impact of a Bouncing Ball

Building on your observations from Part 1 , your group is tasked with quantifying the size of the force acting on a ball as it bounces.By investigating the dynamics of a ball bouncing off the floor, you can analyze the size of the impact. With your group, design an experiment to determine the amount of “g”s a ball feels when bouncing off the floor. For the sake of this investigation, it is recommended that you choose a ball that bounces well. While determining your video parameters, keep in mind that the amount of time the ball experiences a force is an important value. While doing so, consider

• What parameters will you need to measure in order to determine the impulse?

• How will you determine how long the ball is in contact with the floor?

• How accurate are your measurements? How certain are you that you are obtaining the appropriate value?

• What assumptions or estimations are you making in this process?

• What are potential sources of uncertainty? Can you consider them during your design process?

Part 3 – Relating Force to Height of Ball Dropping

From Part 2 you should have a sense for the magnitude of the impulse felt by the dropped ball. However, you likely noticed from Part 1 that height also plays a role in size of the bounce and thus the magnitude of the impulse.Conduct an experiment with your group to model how the height the ball is dropped from affects the impulse of the ball.

• How does the height you drop the ball from affect how high it bounces back? Considering how energy is transferred, can you describe this relationship?

• 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.

• Does your data represent your hypotheses well?

• What sources of uncertainty potentially affect your measurements? What has the largest effect?

Part 4 – Relating Impact Force to Concussive Blows

Concussions, especially those in sports, have become very prevalent in the media and are a source of concern for many athletes. From the audience perspective, it is typically impossible to tell which impacts are minor and which can potentially cause major damage. There are many resources available that relate acceleration felt by forces athletes experience to brain injuries. Looking at your data from Part 3 , determine from what height you can drop the ball such that it undergoes enough acceleration to potentially cause injury.

• Is there a known value for a concussive force?What about acceleration? How will you relate this to your data?

• How confident are you with your height value?

• What sources of uncertainty are you considering?

• What does your intuition tell you about falling from that height? Would you feel comfortable landing on your head from that distance? Why or why not?

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?