Land growing continuous grain corn as a cash crop loses soil at a rate of

14.0 metric tonnes ha-1 yr-1. This is a fertile soil, which has an organic matter content of 3.8% and nitrogen content of 0.35% (both by mass).

a)Calculate how long it will take to erode the entire Ah horizon of this soil. Assume an initial Ah thickness of 7 inches and a bulk density of 1.25 g cm-3 prior to the onset of cultivation

b)If the entire Ah horizon is lost, calculate how many kg of manure you would need to add per hectare in order to replace the lost organic matter if manure is assumed to be 100% organic matter .

Math - Ramya's work so far, Thursday, November 12, 2009 at 11:32am

Ok, so when your trying to find volume you multiply 7 inches by the 14 ton/ha/y. I know u need to convert it but my question is do i need to take the tones part into account or can i do it like this :

7 inches *( 217000434.00 in^2)<--[ that is 14 ha into inches sqaured].... and get the volume?

Math - bobpursley, Thursday, November 12, 2009 at 12:18pm
lost soil=soil mass
14000kg/10000m^2 yr * time=7in*1m/39.37in*1.25E3kg/m^3

time=7/39.37 * 1.25E3 /(14) years

check that. It seems to me to be easier working it in metric.

HELLO, sorry to bug u again ,but u said 14 years. i was just wondering shouldnt it be 1.4 years instead?..im not completely sure however i still wanted to make sure.. thank you!

To calculate how long it will take to erode the entire Ah horizon of the soil, you can follow these steps:

a) Convert the thickness of the Ah horizon from inches to meters:
- There are 0.0254 meters in 1 inch, so you multiply 7 inches by 0.0254 to get the thickness in meters: 7 * 0.0254 = 0.1778 meters

b) Calculate the volume of soil lost per year:
- The rate of soil loss is given as 14.0 metric tonnes ha^-1 yr^-1, which means 14.0 metric tonnes of soil are lost per hectare per year.
- To convert this to kilograms per square meter (kg/m^2), divide by 10,000 (since there are 10,000 m^2 in 1 hectare): 14.0 metric tonnes / 10,000 = 1.4 kg/m^2.

c) Calculate the time it takes to erode the entire Ah horizon:
- Let's use the formula: soil mass = lost soil * time
- Since the initial soil mass is the volume of the Ah horizon, we can use the formula: soil mass = volume * bulk density.
- The bulk density is given as 1.25 g/cm^3.
- To convert this to kg/m^3, multiply by 1000: 1.25 * 1000 = 1250 kg/m^3.
- The volume of the soil is the area multiplied by the thickness, so it is 1.4 kg/m^2 * 0.1778 m = 0.248 m^3.

Now, we can solve for time:
soil mass = volume * bulk density * time
0.248 m^3 = 0.248 m^3 * 1250 kg/m^3 * time
Dividing both sides by 0.248 m^3 * 1250 kg/m^3 gives: 1 = time
Therefore, it will take 1 year to erode the entire Ah horizon of this soil.

I apologize for the confusion earlier. It seems there was a mistake in the calculation. The correct answer is indeed 1 year, not 14 years.

Now let's move on to the second part of the question.

To calculate how much manure is needed to replace the lost organic matter, you can follow these steps:

b) Calculate the amount of organic matter lost per hectare per year:
- The organic matter content is given as 3.8% (by mass) or 0.038.
- The loss of organic matter is proportional to the loss of soil, which is 14.0 metric tonnes ha^-1 yr^-1.
- Multiply the organic matter content by the soil loss rate to get the amount of organic matter lost per hectare per year: 0.038 * 14.0 = 0.532 metric tonnes.

c) Calculate the amount of manure needed to replace the lost organic matter:
- If manure is assumed to be 100% organic matter, then the amount of manure needed is equal to the amount of organic matter lost.
- Convert the amount from metric tonnes to kilograms: 0.532 metric tonnes * 1000 = 532 kg.

Therefore, you would need to add 532 kg of manure per hectare to replace the lost organic matter.