Question Bank • QB_FM_088 NAT • 2 Marks

Section 2: Farm Machinery

Farm Machinery

Subtopic: Soil tillage

Question Statement:

According to Gorjatchkin's formula, draft of a moldboard plow is given by $D = f W_p + k a b + \epsilon a b v^2$. A plow bottom of width $b = 30\text{ cm}$ and depth $a = 15\text{ cm}$ has static soil resistance coefficient $k = 4.0\text{ N/cm}^2$ and dynamic resistance coefficient $\epsilon = 0.002\text{ N}\cdot\text{s}^2/\text{cm}^4$. If the weight component $f W_p$ is $250\text{ N}$, calculate the total draft in $\text{N}$ at a forward speed of $2\text{ m/s}$ ($200\text{ cm/s}$).

Answer Key:

2410

Step-by-Step Solution & Explanation

Given: - Furrow cross-section $a \times b = 15 \times 30 = 450\text{ cm}^2$ - $f W_p = 250\text{ N}$ - Static soil resistance $k a b = 4.0 \times 450 = 1800\text{ N}$ - Speed $v = 200\text{ cm/s}$ - Dynamic resistance $\epsilon a b v^2 = 0.002 \times 450 \times (200)^2 = 0.002 \times 450 \times 40000 = 360\text{ N}$ Total draft: $D = 250 + 1800 + 360 = 2410\text{ N}$
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