THE MU OF THE SHOE

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November 23, 2024

For information on admission to Notre Dame Prep, please click here. 

Students in Notre Dame Prep physics class last week explored Newton's laws and applied them to a popular Irish Week game.

As part of their study of Sir Isaac Newton's Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), upper school students in Jennifer Pakkala's physics class decided it would be fun to apply what they learned to one of the most popular Irish Week games. 

Held annually around St. Patrick's Day in mid-March, Irish Week is a tradition that ranks among just about everybody’s favorites at Notre Dame Prep.

According to Pakkala, her students calculated the coefficient of friction for their shoes through an experiment, studied Newton's third law of motion and applied their findings in a strategy for winning a tug-of-war match. 

"In this research activity, students measured the force of kinetic (sliding) and static friction for each of the shoes of the group," she added. "They also measured the normal force pressing each shoe to the surface it rests upon." 

The maximum frictional force (ideal for tug-of-war) that exists between the individual and the floor is achieved when the shoe does not slide. 

Pakkala told the students, however, that just because a shoe is not sliding does not mean the frictional force is maximized. This is where the research questions and experiment came in. 

Research questions: 
What is the "mu" — which in physics (represented by the Greek letter µ), typically refers to the coefficient of friction between two surfaces in contact — of each shoe? And how does the mu impact the tug-of-war? What role does Newton's third law play in tug-of-war? 

Research experiment: 
1. Connect a wireless force sensor with vernier data analysis. When there are no forces acting on the sensor, zero it. In the lower right-hand corner where you see the force reading, click on it and select zero. 

2. Measure the weight of each shoe by hanging the shoe vertically from the force sensor. 

3. Connect a shoe to the force sensor and hold it upright. Click-collect about five seconds of data. Highlight the data, right click and select "view statistics." The mean value is the weight of the shoe.

4. Place straight-line a total of 0.5 kg mass in the shoe. Practice pulling the shoe with the force sensor using straight-line motion: Slowly and gently pull horizontally with a small force. Very gradually, taking one full second, increase the force until the shoe starts to slide, and then keep the shoe moving at a constant speed for another second. 

5. Record the force needed to start the shoe's motion. This is equal to the maximum force of static friction between the shoe and the surface.

6. Add a mass to the sneaker and repeat steps 4 and 5. Record the findings and repeat until there are five trials.

"The students finished the class with a classic tug-of-war in the E-wing hallway to 'field test' their research," Pakkala said. "See, physics can be fun!"

 

For information on admission to Notre Dame Prep, please click here.

Comments or questions? mkelly@ndpma.org

About Notre Dame Preparatory School
"At Notre Dame Prep, we inspire our students to become the best versions of themselves. We challenge them through an experience of academic excellence, focused on active, project-based learning. We invite them to explore a world of opportunities beyond the classroom. We guide them as they grow in spirituality within a community strong in its Catholic and Marist identity."

Notre Dame Preparatory School is a private, Catholic, independent, coeducational day school located in Oakland County. Notre Dame Preparatory School's upper school enrolls students in grades nine through twelve and has been named one of the nation's best 50 Catholic high schools (Acton Institute) four times since 2005. Notre Dame Prep's middle and lower schools enroll students in pre-kindergarten through grade eight. All three schools are International Baccalaureate "World Schools." NDP is conducted by the Marist Fathers and Brothers and is accredited by the Independent Schools Association of the Central States and the National Association of Independent Schools. For more on Notre Dame Preparatory School, visit the school’s home page at www.ndprep.org.