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The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W = 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The force Q acting in the +x direction, represents the traction force between the tire and the ground. The wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis with coordinate yD = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point G lies in the xy plane. Questions & Analysis: (a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and the bearing at A is a thrust bearing. Label all unknowns. (b) Is the assembly statically determinate or statically indeterminate? Explain. (c) Repeat Parts (a) and (b) if the bearings at A and B are self-aligning and the bearing at A is still a thrust bearing. (c) Invoke the free-body diagram from Part (c), and determine force Q and the reactions at the bearings. F = 5000 lb E X 4 in. C 24 in. w=1000 lb Z gear radius = 3 in. 18 in. y

The figure below depicts the tire, axle, and gear of a large tractor. The entire structure is in mechanical equilibrium. Bearings support the rotating axle at points A and C attached to the tractor's frame. A force FD = 5000 lb is applied in the -z direction at point G of a gear with a 3-in radius. The force W = 1000 lb in the +z direction represents a normal force resulting from the weight of the tractor. The force Q acting in the +x direction, represents the traction force between the tire and the ground. The wheel, axle, and gear assembly weigh 150 lb with center of gravity at point D, which lies on the y axis with coordinate yD = -18 in. Points A, C, D (not seen in the figure), and E lie in the yz plane. Point G lies in the xy plane. Questions & Analysis: (a) Draw the FBD for the wheel, axle, and gear assembly if the bearings at A and B resist moments and the bearing at A is a thrust bearing. Label all unknowns. (b) Is the assembly statically determinate or statically indeterminate? Explain. (c) Repeat Parts (a) and (b) if the bearings at A and B are self-aligning and the bearing at A is still a thrust bearing. (c) Invoke the free-body diagram from Part (c), and determine force Q and the reactions at the bearings. F = 5000 lb E X 4 in. C 24 in. w=1000 lb Z gear radius = 3 in. 18 in. y

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The image illustrates the tire, axle, and gear of a large tractor in mechanical equilibrium. Key components include: - **Supports**: Bearings at points A and C connecting the rotating axle to the tractor's frame. - **Forces**: - \( F_D = 5000 \, \text{lb} \) applied in the \(-z\) direction at point G of a gear with a 3-in radius. - \( W = 1000 \, \text{lb} \) in the \(+z\) direction representing the tractor's weight. - Force Q in the \(+x\) direction signifies traction between the tire and ground. The combined weight of the wheel, axle, and gear is 150 lb, with the center of gravity at point D (located on the y-axis with \( y_D = -18 \) in). Points A, C, D (not shown), and E are in the yz plane. Point G sits in the xy plane. ### Questions & Analysis: (a) **FBD (Free Body Diagram) for the Wheel, Axle, and Gear Assembly**: - Bearings at A and B resist moments, with A as a thrust bearing. - Label all unknown forces. (b) **Determination of Static Equilibrium**: - Evaluate if the assembly is statically determinate or indeterminate, with an explanation. (c) **Alternative Bearing Configuration**: - Redo Parts (a) and (b) assuming bearings at A and B are self-aligning, with A as a thrust bearing. (c) **Force and Reaction Calculation**: - Use the FBD from Part (c) to compute force Q and the reactions at the bearings. ### Diagrams Explanation: The diagram depicts the tractor assembly in the yz-plane with detailed measurements: - **Forces**: - \( F = 5000 \, \text{lb} \) directed downward on the gear. - \( W = 1000 \, \text{lb} \) represented as acting upward on the axle. - \( Q \) is shown horizontally acting on the wheel. - **Distances**: - Gear radius of 3 in. - Horizontal distance from gear to force F application is 4 in. - 18 in from A to the weight \( W \). - 24 in from the vertical force application to the traction force Q.
Transcribed Image Text:The image illustrates the tire, axle, and gear of a large tractor in mechanical equilibrium. Key components include: - **Supports**: Bearings at points A and C connecting the rotating axle to the tractor's frame. - **Forces**: - \( F_D = 5000 \, \text{lb} \) applied in the \(-z\) direction at point G of a gear with a 3-in radius. - \( W = 1000 \, \text{lb} \) in the \(+z\) direction representing the tractor's weight. - Force Q in the \(+x\) direction signifies traction between the tire and ground. The combined weight of the wheel, axle, and gear is 150 lb, with the center of gravity at point D (located on the y-axis with \( y_D = -18 \) in). Points A, C, D (not shown), and E are in the yz plane. Point G sits in the xy plane. ### Questions & Analysis: (a) **FBD (Free Body Diagram) for the Wheel, Axle, and Gear Assembly**: - Bearings at A and B resist moments, with A as a thrust bearing. - Label all unknown forces. (b) **Determination of Static Equilibrium**: - Evaluate if the assembly is statically determinate or indeterminate, with an explanation. (c) **Alternative Bearing Configuration**: - Redo Parts (a) and (b) assuming bearings at A and B are self-aligning, with A as a thrust bearing. (c) **Force and Reaction Calculation**: - Use the FBD from Part (c) to compute force Q and the reactions at the bearings. ### Diagrams Explanation: The diagram depicts the tractor assembly in the yz-plane with detailed measurements: - **Forces**: - \( F = 5000 \, \text{lb} \) directed downward on the gear. - \( W = 1000 \, \text{lb} \) represented as acting upward on the axle. - \( Q \) is shown horizontally acting on the wheel. - **Distances**: - Gear radius of 3 in. - Horizontal distance from gear to force F application is 4 in. - 18 in from A to the weight \( W \). - 24 in from the vertical force application to the traction force Q.
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