A two-wheel drive tractor is pulling a load of 12 kN horizontally on a leveled surface at a forward speed of 5.0 km h⁻¹. The rolling radius of the traction wheel and wheel slip are 0.65 m and 20% respectively. If the rear axle torque is 9 kN m, the tractive efficiency is
Options:
(A) 56.7%
(B) 62.1%
(C) 69.3%
(D) 78.5%
Official Answer Key:
C
Step-by-Step Solution & Explanation
Actual travel speed v = 5.0 km/h = 1.389 m/s. Since slip s=20% reduces the wheel's actual advance per revolution, the theoretical (no-slip) speed v_t = v/(1−s) = 1.389/0.80 = 1.736 m/s. Theoretical angular speed ω = v_t/r = 1.736/0.65 = 2.671 rad/s. Input (axle) power = T·ω = 9000 × 2.671 = 24,038 W. Output (drawbar) power = Pull × v = 12,000 × 1.389 = 16,667 W. Tractive efficiency = Output/Input = 16,667/24,038 = 0.6933 = 69.3%, matching option (C).
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