Question:hard

An inclined blade tillage tool of 25 cm wide and 10 cm long is operating at 25 cm depth in cohesionless soil with density equal to 1.25 \(\text{g}\cdot\text{cm}^{-3}\), and angle of internal friction of 39\(^\circ\). The normal load on the tool and coefficient of soil-metal friction are 1000 N and 0.3, respectively. The soil cutting resistance per unit length of cutting edge is 25 \(\text{N}\cdot\text{mm}^{-1}\). If the tool lift angle is 30\(^\circ\), the specific draft will be [Given: \(\cos 30^\circ = 0.866\)]

Show Hint

To save time on calculation:
\(1000 \times 0.5 = 500\).
\(300 \times 0.866 \approx 260\).
Sum = \(760\text{ N}\). This matches the target option perfectly.
  • 1385 N
  • 885 N
  • 760 N
  • 260 N
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Isolate the two forces that act on the blade face.
As the inclined blade moves through the soil at a lift angle of 30 degrees from the direction of travel, the soil pushes back on the blade with a normal reaction N perpendicular to the face and a friction force \( \mu N \) acting along the face, opposing the relative sliding of soil over the blade. Here \( N = 1000 \text{N} \) and \( \mu = 0.3 \).
Step 2: Resolve both forces along the direction of travel.
The horizontal (draft) component of the normal force is \( N \sin\alpha \) and the horizontal component of the friction force is \( \mu N \cos\alpha \), so the draft is \( D = N(\sin\alpha + \mu\cos\alpha) \).
Step 3: Substitute the numbers.
With \( \alpha = 30^\circ \), \( \sin 30^\circ = 0.5 \) and \( \cos 30^\circ = 0.866 \) as given, \( D = 1000 (0.5 + 0.3 \times 0.866) = 1000(0.5 + 0.2598) = 759.8 \text{N} \), which rounds to 760 N.
Step 4: Note the data that is not needed.
The soil density, angle of internal friction, blade dimensions and cutting resistance per unit length are all extra information for this particular calculation, since the draft here follows directly from the normal load, the friction coefficient and the lift angle alone.
\[ \boxed{760 \ N} \]
Was this answer helpful?
0

Top Questions on Soil Tillage Equipment