The Physics of Hill Wipeouts on Colgate's Campus

As winter approaches and weather conditions become more slippery, the giant hills that elevate our beautiful campus become ever more dangerous. For example, as a fourth year student at Colgate, I can confidently argue that I see many more wipeouts on the hill that leads down to the library during the winter months in comparison with the fall and spring. People fall down the hill, whether it be from slippery snow, ice, rain, or mud, as their friends laugh at them and (sometimes) help them up. It was not until recently when I saw this graceful pattern start up again that I critically thought about the physics involved when students tumble down the infamous hill that leads to the front doors of Case Geyer Library. 

If we think about the forces that act on students as they walk down the hill to the library, we see a difference based upon weather conditions that impact the frictional force that opposes motion and more specifically, slipping and falling. In the warmer months of the year when there is no snow, ice, rain, or mud, students have an easier time walking down the steep hill that leads to the library. This is because as students walk down the hill, either on the pavement or in the grass, the forces of gravity, the normal force, and friction are all acting on them while their gravitational potential energy is converted into kinetic energy. 

Fy = may = FN - mgcosѲ → FN = mgcosѲ + may

Fx = max = mgsinѲ - Ffr = mgsinѲ - μFN → mgsinѲ - μ(mgcosѲ + may) = max → μ will decrease when friction decreases during winter months, which will increase acceleration in the x-direction, making it easier to slip and fall 

KE = -PE + WNC

1/2mv^2 = mgh - Ffr x displacement → when friction decreases, KE will increase

However, we cannot ignore the work of non-conservative forces at play. The key here that typically helps keep students from falling and thus opposes their motion down the hill is the force of friction. Because students are walking down a steep decline, the gravitational force is strong and as a result, one may feel as though they are speeding up as they get closer to the bottom of the hill. This is because the gravitational potential energy at the top of the hill is being converted into kinetic energy as one moves down the hill. The steeper the hill gets as one moves down it, the more they accelerate. However, the force of friction is also at play here as a non-conservative force, which means that not all of the gravitational potential energy is converted into kinetic energy. Especially when the ground is dry, this frictional force prevents students from falling down the hill by opposing forward motion and thus slowing people down and decreasing their kinetic energy. 

So, as you can imagine, when things like snow, ice, rain, and mud come into the picture, slipping becomes much more likely. This is because when we have these conditions, the frictional force, μFN, decreases. There is less traction between our shoes and the ground, causing us to slip and fall as our kinetic energy moving down the hill increases and the work of the non-conservative force decreases. I always find myself making a conscious effort to trudge down the hill at a slower pace when there are bad weather conditions to decrease my chances of falling, but I have never stopped to think about how physics plays a huge role in why I choose to do so until now!