Working in the Snow (Kind of)

Working in the Snow!

I live in a rural part of Cranston, and my driveway is very long and made of gravel. Due to the gravel we cannot have a snowblower and our driveway is too long to be shoveled. 

[Here is a picture for reference]

Instead we get our driveway plowed by a truck, which goes much faster than shoveling. In order to calculate the work of a snowplow there were a few estimations I had to make first:

Length of Driveway: ~ 100 meters
Width of Driveway: ~ 6 meters

Amount of Snow: ~ 13 inches or 0.3302 meters

Weight of snow: ~ 320. 369 kg per cubic meter

Speed of truck: ~ 10 mph or 4.44 meters per second

Width of plow: ~ 2.5 meters

Diagram of snow on driveway:

Total mass of snow = 186.2 x 320.4 = 59620.5 kg

Total force required to move = 59620.5 x 9.8 = 584,281 N

Total Displacement of the snow = average of 2 meters for each drive (to edge of driveway)

Work of the snowplow = F x d = 584281 x 2 = 1,168,562.04 J

If the snowplow is covering 4.4 meters per second that means that it would be covering an area of 4.44 x 2.5 square meters which is 11.1 meters each second. The total area is 563.9 so the time spent plowing would be 563.9 / 11.1 which is about 50 seconds. 

Power = Work / Time = 1168562.04 / 50 = 23,002.4 watts or 30.8 horsepower

In conclusion, the snowplow had significantly more power than I could have, which made the job go very quickly and was relatively easy. My family and I still went outside and enjoyed the snow throughout the storm.