## Physics in a Winter Wonderland

Over the river and through the words, to grandmother’s house we go…
the horse knows the way to carry the sleigh through the white and drifting snow – oh!

As part of our family’s holiday season festivities, we went on a horse-drawn sleigh ride through the woods in northwest Pennsylvania. It was a terrific time, with low winds, just a very light dusting of now coming down, and 28 degree temperatures. As  Miss Micro-APlusPhysics (aged 16 months) drove the sleigh, I couldn’t help but think what a terrific multi-faceted physics problem our trip would make… finding the force of friction the horses had to overcome to keep us moving at a constant velocity through the woods, the power supplied, and the energy consumed.

Of course, being a physics teacher, I couldn’t just leave it there:

With nine people on the sleigh, all bundled up, I think we can estimate an average mass of about 70 kg per person (we had a couple lightweights, including the baby.) So, the mass on the sleigh was probably on the order of 650kg. The sleigh itself was made out of fairly solid boards with steel runners, and a quick attempt at lifting up a corner provided a feel for its weight — let’s estimate the sleigh at 550kg, giving us a total load of 1200kg. The weight of the load, then, settles in a 12,000N.

The horses pulled the sleigh from a horizontal tether, so that given the equilibrium condition of the sleigh, we know the normal force had to offset the weight, so the normal force of the snow on the sleigh is 12,000N. Now, to estimate the coefficient of friction.  From the NY Physics Regents Reference Table, we find the coefficient of kinetic friction for a waxed ski on snow as 0.05. This seems like a reasonable esimate for the frozen runner on the snow. Using ${F_f} = \mu N$ we find the force of friction as 600N.

For most of the 20-minute (1200s) journey the horses pulled us at a leisurely constant speed of approximately 1.5 m/s. Therefore, we can assume the applied force of the two LARGE Belgian horses as 600N. The power supplied can be calculated from P=Fv, or (600N)*(1.5 m/s) = 900W. And since they applied that power for roughly 1200s, the work done by the horses can be found from W=P*t=(900W)(1200s)=1,080,000 Joules, or the equivalent of 258 food calories (roughly the nutritional equivalent of one slice of pizza)!

A fun holiday activity providing another opportunity to highlight physics in the world around us.