# The 2010 Physics Ig Nobel: Physics of Preventing Winter Slips and Falls

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d is the maximum distance someone can take before they fall, N1 and N2 are the reaction forces and f1 and f2 are the friction forces on each foot and h is the height of the center of mass above ground.

## The Physics of Walking on Ice

The molecular layer of ice reduces static friction and makes it easy to slip and fall. To prevent this, people do what is often called the “penguin shuffle”; walkers take small steps and attempt to keep their center of gravity over their front legs.

The reason for this is firmly grounded in physics, seen as ITT lecturer Mr. Manish Verma derives the equations of motion on the 123iitjee YouTube channel.

By analyzing a free body diagram, Verma shows the torque a person undergoes as he is about to fall.

We can reduce the friction felt to a single variable f. We now see that the step size is proportional to friction. Increase static friction and we can take longer steps

We can solve for d, the maximum step,

We can simplify f2f1 to a frictional force, f. By increasing friction, f, a person can take longer steps without falling down. This offers a possible explanation as to why socks over shoes work so well when walking on ice-the socks possibly absorb or push away the molecular layer of water thereby increasing static friction.

Solving for d and we see what variables affect the maximum step size before a person falls. We see this is dependent on static friction.

This in turn increases the step length someone is able to take. Being able to walk with a larger step means that people can walk more naturally and with greater confidence and are thus less likely to slip and fall or get in an accident.

## A Simple Though Not Stylish Solution

The idea of wearing socks over shoes may seem silly, especially among the fashion conscious but Dr. Parkin and her colleagues show that this cheap and simple intervention prevents some accidents. It must be noted that, though effective, it does not replace a good pair of boots as the socks tend to absorb water especially when the ice is damp.

Among others, Parkin has commented that socks don’t perform well when wet. This fits with what the physics equations say. Wet socks don’t have as strong as an effect on the quasi-liquid layer as dry socks and this decreases static friction; you must make smaller steps or you are likely to fall. This captures the spirit of the Ig Nobel in many ways; the experiment seems funny – but it makes you think about some very serious physics.

Resources

Neshyba, S., Nugent, E. et all. Molecular Dynamics Study of Ice−Vapor Interactions via the Quasi-Liquid Layer. (2009). The Journal of Physical Chemistry. Accessed October 29, 2013.

North West Public Health Observatory. Falls involving ice and snow, transport accidents and respiratory conditions: the impact of winter (2009/10) on emergency hospital admissions in the North West. (2012). Accessed October 29, 2013.

Parkin, L., Williams, S. M., & Priest, P.Preventing winter falls: A randomised controlled trial of a novel intervention. (2009). The New England Medical Journal. Accessed October 29, 2013.

Rosenberg, R. Why Is Ice Slippery? (2005). Physics Today. Accessed October 29, 2013.

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