Solving Snow Shovelling Problem - 10m x 1.5m

[standardflop]

Hey,

The problem:
"At a given day there there are 10cm of snow in your sidewalk. Estimate how much work is required to remove this snow when you sidewalk has a length =10m and a width= 1.5m. Assume that a liter snow weighs about the same as 100ml water. Discuss any assumptions youve made."

if you plan to remove the snow (so it won't disturn your neighbours) youll have to move it from the center of the width and out to both sides. The work required to move snow from the center of the sidewalk equals W=F*x, where x is distance and F is the force you push the snow with m_snow*a_snow minus friction (neglected).. how should i proceed? I think one could derive an diff. equation and integrate it, but i don't see how..

Thanks

 

[lightgrav]

If you neglect friction, how much Force is required to push 1 kilogram sideways?

This is a "concept" question, not a "compute it" question.
I would avoid integration by multiplying (total * average).
Whether you use total Force and average distance, or
total distance and average Force, is up to you.

 

[quicknote]

for your question. I would approach this problem by first calculating the volume of snow that needs to be removed from the sidewalk. With a length of 10m and a width of 1.5m, the total area of the sidewalk is 15 square meters. Multiplying this by the depth of snow (10cm or 0.1m) gives us a volume of 1.5 cubic meters.

Next, we can use the assumption that 1 liter of snow weighs the same as 100ml of water to convert the volume of snow into its weight. 1.5 cubic meters of snow is equivalent to 1,500 liters, which would weigh 150,000 grams or 150 kilograms.

To calculate the work required to remove this snow, we can use the formula W = F * x, as you mentioned. However, we need to first determine the force (F) required to push the snow. This force would be equal to the weight of the snow (150kg) multiplied by the acceleration due to gravity (9.8 m/s^2), which gives us a force of 1,470 Newtons.

Now, we need to determine the distance (x) over which this force must be applied. As you mentioned, the snow would need to be moved from the center of the sidewalk to both sides, so a total distance of 5m. Therefore, the work required to remove the snow would be 1,470 * 5 = 7,350 Joules.

As for your question about integrating a differential equation, I do not believe it would be necessary in this case. We can simply use the basic formula for work, W = F * x, to calculate the required work.

One assumption I have made in this calculation is that the sidewalk is flat and there are no obstacles or uneven surfaces that would require additional force or work to remove the snow. Additionally, the weight of snow may vary slightly depending on its density, but for the purposes of this estimation, we can assume it is equal to the weight of water. Overall, this approach should provide a good estimate for the work required to remove the snow from the given sidewalk dimensions.