Totally NOT Late Snow Day Blog

Totally NOT Late Snow Day Blog
By Yufan Lu
I live in an apartment complex in Johnston (with Jimmy).

I will measure the work required to move the snow on the parking lot in front of my apartment.
Length of the parking lot  42.7 m
Width of the parking lot 14.2 m
Height of the snow 0.3 m
Density of the snow 500 kg/m^3 (it really varies)
This means that there is approximately 182 m^3 of snow that weights 91000 kg.
Wow that is around 1000 Yufan
Such heavy

Anyway all snow is pushed to the edge. Like this:

So snows are pushed 7.1 m average.
Force to move the snow = mg = 891800N
Work required 7.1*891800 = 6331780 J

There's No Business Like Snow Business

I live in a large apartment complex, so on snow days, most of the snow gets plowed.  

However, we have to shovel out our own parking spaces, so for this assignment, I

determined the work it takes for me to shovel out a parking space filled with snow.  

First, I measured the length and width of the parking space, as well as the depth of the snow.  

After, I shoveled some of the snow to determine how high I lift it.

Length: 5.334 m

Width: 2.667 m

Snow Depth: 0.254 m

Height Lifted:  0.6858 m

After doing some research on www.accuweather.com, I found 10 cm of snow is equal to 1 cm of rain, and 1 cubic cm is
equal to 1 mL.  Using this, I determined the mass of snow in the parking lot.

V = 5.334 * 2.667 * 0.254 = 3.613 m3 of snow = 0.3613 m3 of water

Since 1 cubic meter = 1000 L, 0.3613 m3 = 361.3L of water.

According to www.convert-to.com, 1 L water = 1 kg, so 361.3 L water = 361.3 kg.

Then, I used the formula W = U = mgh in order to determine the amount of work it takes
to clear out the parking space.

W = U = 361.3 * 9.8 * 0.6858 = 2428 J

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.

This Is So Much Work...

Snow Blowing A Driveway

How much work is it actually?

❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄❄

Since my town got so much snow, no ordinary shovel could help my dad and I complete the arduous task of clearing our driveway. Therefore, we had no other option but to bring out the snow blower. Although it seems like considerably less work than having to shovel, there is work being done regardless, both by my dad on the snow blower, and the snow blower on the snow. 

1. Work Done by My Dad on the Snow Blower

Since the snow blower is on wheels, this approximation is way over the actual amount of work done by my dad. Also, this approximation only covers 1 strip of driveway, so the actual amount of work would be multiplied by 15 to cover the entire area. 

(Dimensions of my driveway are 25x30 ft, or 7.6x9.1 m)

2. Work Done by the Snow Blower on the Snow

This particular snow blower can clear 6 - 12 inches of snow at a time, and shoots it up to 12 meters away. By setting the snow in motion, it gives the snow kinetic energy, essentially doing work on it. 

To determine the change in kinetic energy (the work), I will have to approximate the weight of the snow being blown at any given moment, and determine its x-velocity by assuming that it is traveling the maximum 12 meters over the time it is in the air.

W = ΔKE = 1/2(m)(v^2) - 0

m ≅ 5.4 kg

v = 12m/1.5s = 8 m/s

W = 172.8 J (at any given instant)

Toro SnowMaster 724 QXE

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Sources:

https://www.toro.com/en/homeowner/snow-blowers/snowmaster-724-qxe-36002

https://socratic.org/physics/forces-and-newtons-laws/frictional-forces/determining-the-static-coefficient-of-friction-between-tires-and-snow

Working Hard or Hardly Working

Winter Storm Skylar

Living in one of the most North parts of Rhode Island can lead to a lot of snow that needs to be removed from the driveway. Over the past couple of days, this was especially true with winter storm Skylar dropping 18 inches of snow into our yard. Luckily, we own a snow blower which makes the clearing process much easier. However, due to the snowblower's limited height capacity, it is of utmost importance that the snow doesn't pile up too much rendering the snowblower useless. This is why my dad and I snow-blow our driveway multiple times throughout the storm.

To more closely examine how much work is done in clearing the driveway, I measured the dimensions and height of the snow before we went out and cleared the snow for a second time.

Length of Driveway: 52 ft 4 inches or 15.95 Meters

Width of Driveway: 21 ft or 6.4 Meters

Height of Snow: 5.5 inches or .14 Meters

During the storm my car was parked in the driveway so this must be subtracted from the work of the snowblower.

Length of Car: 15 ft or 4.57 Meters

Width of Car: 6 ft or 1.87 Meters

By doing some research, I found that snow weighed about .16 grams per cubic centimeter

Total weight of snow: 2,282.11 kg

Weight of Snow on car: 191.46 kg

This means that there was a total of  2090.65 kg of snow moved by the snowblower.
Total Time: 10.5 Minutes

Calculating the Work Done By Snowblower

To calculate the work of the snowblower, I will use the formula:

W =ΔKe

I already know the mass of the snow so now I just need to find the velocity that the snowblower shot the snow at. The snowblower shot the snow an average of  12 ft or 3.65 meters in about 1.5 seconds at an average angle of 45 degrees. 

Vx = D / t

Vx = 2.433 m/s

Cos θ = adjacent / hypotenuse

Velocity = 2.433 / cos(45) =

3.441 m/s

W = .5 * 2,282 * 3.441^2 - 0

W = 12,377.2 J

Therefore, the snowblower did 12,377.2 Joules of work to clear the snow. 

Overall, this is a lot of work that I am thankful I did not have to do by hand. While it may be annoying to have to go out multiple times during the storm, it is much easier than using a shovel to clear the driveway. While, there were parts that the snowblower couldn't reach, it was easy to grab a shovel and move the rest aside. This may seem like a lot of work but, thanks to our snowblower, I was hardly working. 

Works Cited 

“Volume to Weight Conversion.” Volume to Weight Conversions for Common Substances and Materials, www.aqua-calc.com/calculate/volume-to-weight.

All Work and Snow Play

Living in the city can make snow removal interesting.  By interesting, I mean there are many cement surfaces to clear and few places to put the snow.  To remove the snow, my parents and I shovel as much snow onto the back lawn with the remaining snow going on the edge of the sidewalk.  Occasionally we borrow my grandfather's snowblower, but for this storm we shoveled the snow.

Here are some pictures of the areas we had to clear.  In these pictures, my dad had already gone out and shoveled (because he's impatient).

Calculating Work

Volume

To calculate the work my family did to remove the snow, the volume of the snow we moved had to be calculated.  These measurements will be obtained from the online property card for my house and satellite imagery.

According to the online property card for my house, the back patio has an area of 156 square feet, or 14.5 square meters.  The driveway has a length of 43 feet, and a width of about 9 feet.  This translates to an area of 36.0 square meters.

The remaining area that must be shoveled is the sidewalk, which has an length of 35 feet (adding up the length of my house and the width of the driveway) and a width of about 10 feet.  This means the sidewalk has an area of about 32.5 square meters.

The last thing that needs to be factored in is the two cars parked in the driveway, each having an area 8.78 square meters.

In all, the area the snow covered was:

14.5 + 36.0 + 32.5 - 2(8.78) = 65.4 square meters

According to weather reports, Providence received 12.3" of snow, or 0.31 meters.  Therefore, the volume of snow in total that had to be moved was 20.3 cubic meters.

Mass and Volume of a Shovelful

The next thing that needs to be calculated is the volume of one shovelful.

One shovelful is about 12 inches by 18 inches in area with an average height of about 5 inches, which calculates out to 0.0177 cubic meters.

According to this website, the density of settled snow is between 200 and 300 kg/m³.  For argument's sake, I will use a density of 250 kg/m³.  Therefore, using the density formula, the mass of one shovelful 4.425 kg.

Work of One Shovelful
Using the formula W = mgh, the work done to lift snow 3 feet, which is about how far one vertically moves snow with each shovelful.

W = mgh = (4.425)(9.8)(0.91) = 39.5 Joules

Total Work
To calculate total work, we must multiply the work of one shovelful by the number to shovelfuls needed to move all the snow in my yard.  If each shovelful can move about 0.0177 cubic meters of snow, and there is a total of 20.3 cubic meters, using division the estimated number of shovelfuls needed to move all the snow would be 1147! (yikes!)  According to those calculations, the total work done my entire family to move all the snow is:

W_Total = 39.5(1146) = 45302 J = 45.3 kJ


Time Lapse
Here's a time-lapse of me shoveling.  It came out blurry thanks to a Ziploc bag.  It worked to keep my phone dry, but not to keep the video clear.

sNOw DAYS OFF

Working Hard, or Hardly Working?

This week was supposed to be my relaxed week. I just finished my indoor season at nationals this past weekend. So, no running, no exercise for a week! What makes this week even better is that we got a snow day so I had more of an excuse to do nothing. But, knowing that my cars (and physics grade) depended on it, I got the motivation to go clear my driveway.

We have a snowblower, so we used that for the majority of our clearing. However, there were some stubborn piles of snow that we attacked with the shovel.

How much work would we have done if we shoveled all of it? We had to move the snow off of the driveway. There was about 10 inches of snow (.254 m) when we went out. Our driveway is 20 m x 10 m. On average, newly fallen snow is around 100 kg per cubic meter. There was 50.8 meters cubed of snow on the driveway. Multiplied by the density, the total mass of this snow was 5080 kg.

Let's assume we moved the snow an average of 15 m. Some blocks moved more than this, but some were less. The force we applied to the snow to move it was at least that of its weight, 5080*9.8= 49,784 N. Moving it 15 meters, it takes 746,760 J to move all that snow. This might be on the conservative side, because we actually applied more than the force of gravity to the snow (in order for it to accelerate)

All I can say is, bless whoever made snowblowers. That is too many joules for me. Apparently, 746,760 J is 178 kilo calories. So in order to shovel the whole driveway, I could have burned off two tablespoons of peanut butter. Or I can just eat the peanut butter anyways and resume my Netflix binge watching, and let the snowblower do all the hard work.

Here is some bonus footage of me shoveling some snow that the blower couldn't get to.