GATE AG 2019 • Q57 NAT • 2 Marks

Section 3: Farm Power

Tractors and Power Tillers

Subtopic: Mechanics of tractor chassis

Question Statement:

Tractors and Power tillers: Type, selection, maintenance and repair of tractors and power tillers; tractor clutches and brakes; power transmission systems – gear trains, differential, final drives and power take-off; mechanics of tractor chassis; traction theory; three point hitches - free link and restrained link operations; steering and hydraulic control systems used in tractors; tractor tests and performance; human engineering and safety considerations in design of tractor and agricultural implements. A two-wheel drive tractor is taking a turn with radius of curvature 5.0 m. The minimum horizontal distance between the tipping axis and line of action of the CG is 800 mm. The angle between the line of action of centrifugal force and perpendicular direction to the tipping plane is 15°. If the vertical distance of the CG from ground level is 900 mm, the limiting speed (km/h) to prevent overturning (rounded to 2 decimals) is ______.

Official Answer Key:

24.00 to 24.45

Step-by-Step Solution & Explanation

Overturning about the tipping axis is prevented as long as the restoring moment of the tractor's weight (acting through the lateral offset d of the CG from the tipping axis) exceeds the overturning moment of the centrifugal force (acting at height h, with its line of action inclined at θ to the perpendicular of the tipping plane). At the limiting (critical) speed the two moments balance: Fc·cosθ·h = W·d, with Fc = mV²/R and W = mg: (mV²/R)·cosθ·h = mg·d ⟹ V² = g·d·R /(h·cosθ) V² = 9.81 × 0.800 × 5.0 / (0.900 × cos15°) = 39.24/(0.900×0.9659) = 39.24/0.8693 = 45.14 V = 6.719 m/s = 6.719 × 3.6 = 24.19 km/h. Answer: within 24.00–24.45.

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