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A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground is
- a)1.48
- b)14.46
- c)39.04
- d)85.54
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160...
° above the horizontal through the hitch point.
To find the horizontal and vertical components of the pull force, we can use trigonometry:
horizontal component = pull force x cos(12°)
vertical component = pull force x sin(12°)
We don't know the value of the pull force, but we can find it by considering the equilibrium of forces on the tractor. The weight of the tractor acts downwards through its center of gravity, which is located at a distance of 1080 mm from the rear axle (since the weight is divided in a 30:70 ratio). The weight creates a moment (torque) about the rear axle, which is balanced by the moment created by the pull force about the same point:
weight x distance from rear axle = pull force x distance from rear axle
15.84 kN x (0.7 x 2160 mm) = pull force x (120 mm)
pull force = (15.84 kN x 0.7 x 2160 mm) / 120 mm
pull force = 211.25 kN
Now we can calculate the horizontal and vertical components of the pull force:
horizontal component = 211.25 kN x cos(12°) = 203.57 kN
vertical component = 211.25 kN x sin(12°) = 46.59 kN
The horizontal component represents the force that propels the tractor forwards, while the vertical component represents the force that lifts the front wheels off the ground. The ratio of these two forces is:
force ratio = vertical component / horizontal component
force ratio = 46.59 kN / 203.57 kN
force ratio = 0.229
This means that for every 1 kN of force that propels the tractor forwards, there is 0.229 kN of force lifting the front wheels off the ground. In other words, the tractor is not very well balanced for pulling, and may have traction problems if the ground is not level or has uneven traction.
To find the horizontal and vertical components of the pull force, we can use trigonometry:
horizontal component = pull force x cos(12°)
vertical component = pull force x sin(12°)
We don't know the value of the pull force, but we can find it by considering the equilibrium of forces on the tractor. The weight of the tractor acts downwards through its center of gravity, which is located at a distance of 1080 mm from the rear axle (since the weight is divided in a 30:70 ratio). The weight creates a moment (torque) about the rear axle, which is balanced by the moment created by the pull force about the same point:
weight x distance from rear axle = pull force x distance from rear axle
15.84 kN x (0.7 x 2160 mm) = pull force x (120 mm)
pull force = (15.84 kN x 0.7 x 2160 mm) / 120 mm
pull force = 211.25 kN
Now we can calculate the horizontal and vertical components of the pull force:
horizontal component = 211.25 kN x cos(12°) = 203.57 kN
vertical component = 211.25 kN x sin(12°) = 46.59 kN
The horizontal component represents the force that propels the tractor forwards, while the vertical component represents the force that lifts the front wheels off the ground. The ratio of these two forces is:
force ratio = vertical component / horizontal component
force ratio = 46.59 kN / 203.57 kN
force ratio = 0.229
This means that for every 1 kN of force that propels the tractor forwards, there is 0.229 kN of force lifting the front wheels off the ground. In other words, the tractor is not very well balanced for pulling, and may have traction problems if the ground is not level or has uneven traction.
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A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer?
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A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer?.
A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer?.
Solutions for A two wheel drive tractor, weighing 15.84 kN with a wheel base of 2160 mm, has the static weight divided between the front and rear axles in the ratio of 30 : 70 on a horizontal level surface. The hitch point is at a height of 700 mm from the ground and at a horizontal distance of 120 mm to the rear side from the center of the rear axle. Pull acts at an angle of 12° downwards from the horizontal. The maximum pull in kN, when the front wheels would just start rising from the ground isa)1.48b)14.46c)39.04d)85.54Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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