A specially set 40 cm Five-bottom disc plow was used for a ploughing operation. If there was a 5% overlap in cutting width and the entire disc formation left a trapezoidal furrow cross section having a top width of 310 cm and a depth of 10 cm. Unit draft was 0.6 kgcm-2 while operational speed was 5 km/h. Determine the volume of soil worked in 3 hours
To determine the volume of soil worked, we need to calculate the total area of the furrow cross-section and then multiply it by the length of the furrow.
First, let's calculate the actual cutting width of the plow:
Actual cutting width = 40 cm - (5% overlap) = 40 cm - (0.05 * 40 cm) = 40 cm - 2 cm = 38 cm
The area of the trapezoidal furrow cross-section can be calculated using the formula:
Area = (1/2) * (top width + bottom width) * depth
Area = (1/2) * (310 cm + 38 cm) * 10 cm = 17.4 m²
To convert the area to cm², we multiply it by 10,000:
Area = 17.4 * 10,000 cm² = 174,000 cm²
Now, let's calculate the volume of soil worked in 3 hours:
Operational speed = 5 km/h = (5,000 m / 3600 s) m/s = 1.389 m/s
Length of furrow in 3 hours = operational speed * time = 1.389 m/s * (3 hours * 60 minutes/hour * 60 seconds/minute) = 1.389 m/s * 10,800 s = 15,000 m
Volume = Area * Length = 174,000 cm² * 15,000 cm = 2,610,000,000 cm³
Since the unit draft is given in kg/cm², we need to convert the volume from cm³ to m³:
Volume = 2,610,000,000 cm³ = 2,610,000 dm³ = 2,610 m³
Therefore, the volume of soil worked in 3 hours is 2,610 m³.