A two-wheel drive tractor weighing 21 kN has a wheel base of 2.1 m. The CG of the tractor is 0.7 m ahead of rear axle centre. The tractor is pulling a single-axle trailer with gross trailer weight of 50 kN on a leveled concrete road while maintaining the line of pull parallel to the ground surface. The tractor hitch point is 42 cm behind the rear axle centre and 52.5 cm above the ground surface. During operation, 20% of the gross trailer weight is transferred to the tractor hitch point. If the coefficient of rolling resistance for each of the tractor and trailer wheels is taken as 0.04, and their ground reactions are assumed to pass through their respective wheel centres, the dynamic ground reaction against the tractor rear wheels in kN is
Options:
(A) 14.0
(B) 24.0
(C) 24.5
(D) 26.4
Official Answer Key:
D
Step-by-Step Solution & Explanation
Step 1 — static weight transfer from the hitch load: vertical load transferred to the hitch, W_h = 0.20×50 = 10 kN, acting 42 cm behind the rear axle. Taking moments about the front axle (wheelbase=2.1 m, tractor's own CG is (2.1−0.7)=1.4 m from the front axle):
R_rear(from weights) = [21×1.4 + 10×(2.1+0.42)]/2.1 = [29.4+25.2]/2.1 = 26.0 kN.
Step 2 — additional transfer from the horizontal pull force: the tractor must overcome the trailer's own rolling resistance to tow it: trailer net weight on its wheels = 50−10=40 kN, so trailer RR = 0.04×40 = 1.6 kN = the horizontal pull the tractor must exert. This pull acts at the hitch height (0.525 m above ground), creating an additional forward-pitching moment that further loads the rear axle: extra transfer = Pull×hitch height/wheelbase = 1.6×0.525/2.1 = 0.4 kN.
Total dynamic rear reaction = 26.0+0.4 = 26.4 kN. Answer: (D).
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