Forces in Sledding

Forces in Sledding 
In the winter, sledding is a common activity. However, physics is not the fist thought that comes to mind while sliding down the fluffy snow. Here is a video of my sister, Claire, enjoying herself while sledding. 

Here is a free body diagram of Claire's sledding track. 

Here are the Net Force Equations for her sledding track. 

Σ Fx =  f - mgcosθ = ma

Σ Fy =  N - mgsinθ = 0

To find Claire's acceleration, here are the steps I used 

Σ Fx =  f - mgcosθ = ma

Σ Fy =  N - mgsinθ = 0

N = mgsinθ 

f - mgcosθ / m = a

μmgsinθ - mgcosθ / m = a

Obviously, Claire's track couldn't be given measures. However, the basics of her track were projected on this blog. Snow friction results from a mixture of processes. Usually the snow and sled surfaces are partially separated by melt water but, when too much water is present, the contact area and friction increase. Sled thermal conductivity and color are very important. Heat is generated by friction and solar radiation absorption and is conducted away by both sled and ice particles. The remaining heat generates melt water, which acts as a lubricant. The important processes operate, not at the air temperature, but at the ski base temperature, which is highly dependent on such things as snow-surface temperature, load, and speed.