Subtopic: Three point hitches – free link and restrained link operations
Question Statement:
A 2WD tractor weighing 15.84 kN, wheelbase 2160 mm, static weight on front:rear axle = 30:70 on level ground. Hitch point is 700 mm high and 120 mm to the rear of the rear-axle centre. Pull acts at 12° below horizontal. The maximum pull in kN, when the front wheels just start to rise, is:
Options:
(A) 1.48
(B) 14.46
(C) 39.04
(D) 85.54
Official Answer Key:
B
Step-by-Step Solution & Explanation
At incipient front-wheel lift, moments about the rear-wheel contact line balance: W_front-share-moment must equal the overturning moment from the pull P. Static front load = 0.30×15.84 = 4.752 kN, acting at 2160 mm ahead of the rear axle. Taking moments about the rear-axle ground contact: P[cos12°×700 + sin12°×120]... using P·(h·cos θ + horizontal offset·sin θ) = W_front × wheelbase: P(700cos12° + 120sin12°) = 4752×2160 (N·mm). cos12°=0.978, sin12°=0.208. LHS coefficient = 700×0.978+120×0.208 = 684.9+25.0=709.9 mm. P = 4752×2160/709.9 = 10,264,320/709.9 ≈ 14,459 N ≈ 14.46 kN. Answer: B.
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