## Friday, June 12, 2015

### Sliding on Ice: The Case of Two Hockey Pucks

The concept of friction is essential to all skating on ice, whether it is for hockey, speed, or figure skating. Ice provides a reduced-friction surface, which allows humans to glide, rather than stick to the floor. Synthetic ice, consisting of slippery plastic, also reduces friction. The friction of synthetic ice can be lowered further by applying soapwater, or other slippery liquids.

For gliding motion to occur, two types of friction must be overcome: initial non-moving (static) friction, and moving (kinetic) friction.

The following graphs, excerpted from Volume 1 of The Science of Hockey, show the effect of force on motion of an official hockey puck.

Discussion Questions
1. Describe the magnitude of each force in Graph 1. For what amount of time is each force applied?
2. Describe the motion of the puck in Graph 2, using words.
3. How far does the puck travel? In what direction?
4. Are the graphs coordinated in the time dimension?

The following graphs, excerpted from Volume 1 of The Science of Hockey, compare the force required to move two types of pucks on synthetic ice (HDPE plastic).

Discussion Questions
1. Is the total force different in these two graphs? If so, why?
2. Is the initial force different in these two graphs? If so, why?
3. What is the average force is applied to each puck?
4. Calculate the work involved for each puck.
5. Why does the practice hockey puck perform differently on synthetic ice than an official puck? (Hint: The practice hockey puck is normally used on concrete floors.)

Additional free graphs on the science of ice skating are available in a free pamphlet from the publisher's webpage.

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series
• The Science of Ice Skating
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks
Anthologies of 28 Graphs
• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports

Schottenbauer Publishing

### The Science of Jumping

What happens when an ice skater jumps? The answer can be modeled in various levels of difficulty. One the simplest level, assume that the skater is simply a point mass object, without movement within the body. In this analysis, acceleration occurs in three planes, leading to changes in altitude and rotation.

On the most complex level, the skater's body must be analysed as separate components moving in relation to the center of mass, which for most humans is approximately in the center of the abdomen or hips.

Discussion Questions
1. What everyday motions are related to skating?
2. If skater motion were to be studied by making comparisons between graphs, which types of motions should be compared?

Volume 4 of Glide, Spin, & Jump: The Science of Ice Skating contains graphs of acceleration, force, and vertical distance in a series of motions completed by the author.

Graphs of Motion
• Standing to Squatting Position
• Jumping with No Rotation
• Rotation with No Jumping
• Skating Jumps on Land
• Skating Jump on Synthetic Ice

Jumps on Land
• Half Jumps
• Stag
• Waltz
• Ballet
• Mazurka
• Half Axel
• Single & Double Jumps
• Salchow
• Loop
• Toe Loop
• Flip
• Lutz
• Axel

The following two graphs are excerpted from Volume 4 of Glide, Spin, & Jump: The Science of Ice SkatingNotice that these jumps, completed in a purely vertical direction on land, are simpler to analyze, because they lack the horizontal translational motion across the ice.

Discussion Questions
1. What are the major differences between these graphs?
2. In these graphs, how can direction be determined? What direction is up?
3. In each graph, what occurs in the vertical direction?
4. In the lower graph, what is the pattern of acceleration in the horizontal plane during the rotations?
5. In each graph, what sort of tilt (side to side) occurs?
6. Is it better to locate the wireless device on the stomach or chest? Why?
7. Describe the role of knee motions during each of the above jumps, and their effects on acceleration.
8. What is the role of non-relevant movements (such as the motion of breathing) in these graphs, if any?
9. What is the role of error or random motion in these graphs, if any?
10. Are these clean (technically correct) jumps? If not, what would the acceleration pattern be during a clean jump?
11. What would a fall look like in a graph of acceleration?
12. What would the graphs look like if the jumps were completed on the ice?

Additional free graphs of ice skating are available in a free pamphlet from the publisher's webpage. A humorous cartoon animation of an ice skater, showing approximate force vectors, is available from the publisher's YouTube channel.

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series
• The Science of Ice Skating
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks
Anthologies of 28 Graphs
• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports