Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A vertical conveyor reaper is to be used for harvesting wheat crop at a height of 30 mm above the ground. The ultimate tensile strength and diameter of the crop stem are 35 N mm⁻² and 3 mm respectively. The friction coefficient of knife edge for wheat crop is 0.346 and the maximum oblique angle of the counter shear is 17°. The crop stem is of homogenous solid with a uniform circular section.
Options:
(A) 1.55
(B) 3.09
(C) 4.64
(D) 6.19
Official Answer Key:
B
Step-by-Step Solution & Explanation
For a circular cross-section, section modulus Z = πd³/32 = π(0.003)³/32 = 2.651×10⁻⁹ m³. Bending moment capacity M = σ_ult·Z = 35×10⁶ × 2.651×10⁻⁹ = 0.0928 N·m. The horizontal force applied at height h=30 mm above ground (base of stem, treated as a cantilever fixed at ground level) causing this bending moment: F = M/h = 0.0928/0.030 = 3.09 N, matching option (B).
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