One end of a thin uniform rod of mass m and length 31 rests against a smooth vertical wall. The other end of the rod is attached by a string of length 1 to a fixed point O which is located a distance 21 from the wall. A horizontal force of magnitude F₁ is applied to the lower end of the rod as shown. Assuming the rod and the string remain in the same vertical plane perpendicular to the wall, find the angle 0 between the rod and the wall at the position of static equilibrium. Notes: This quiz is going to walk you through a sequence of steps to do this. It won't give you the answers, but it will hopefully get you to see how to approach problems like this so that you have a working reference/template in the future. This is actually a modified version of a problem from the textbook (6.3). Note that in that problem, is not actually given. It has been introduced for convenience as we move through solving the problem, and should not show up in the final answer. DO NOT DO PROBLEM 6.3. It is not the same problem and if you submit that for your answer, IT WILL BE WRONG F1 F2 = mg 22 مه 1) Write a simple equation for virtual work in terms of F₁, Sr₁, F2, and Sr2. Remember what the virtual work must ultimately equal in a statics problem. DO NOT EVALUATE THIS EQUATION YET. 2) Write position vectors r₁ and 12 from the point O to the points of force application (i.e., to the point where F₁ is applied, AND to the point where F2 is applied). This may require some geometry magic. 3) Compute the variation of each of your position vectors from part 1 using 0 and as generalized coordinates. a. NOTE: YOU SHOULD STILL HAVE VECTORS WHEN DONE b. OTHER NOTE: DO NOT TRY TO SIMPLIFY ANYTHING 4) Using the variation you computed in part 4, compute the dot products that you wrote in part 1 5) Derive a constraint equation that relates 1, 0, and 0. a. HINT: Consider the horizontal distance from the wall to the end of the rod 6) Compute the variation of your constraint equation, and solve for dø as a function of Se 7) Combining your results from parts 4 and 6, obtain an equation that can be solved for the equilibrium angle eq of the bar. DO NOT SOLVE THE EQUATION

One end of a thin uniform rod of mass m and length 31 rests against a smooth vertical wall. The other end of the rod is attached by a string of length 1 to a fixed point O which is located a distance 21 from the wall. A horizontal force of magnitude F₁ is applied to the lower end of the rod as shown. Assuming the rod and the string remain in the same vertical plane perpendicular to the wall, find the angle 0 between the rod and the wall at the position of static equilibrium. Notes: This quiz is going to walk you through a sequence of steps to do this. It won't give you the answers, but it will hopefully get you to see how to approach problems like this so that you have a working reference/template in the future. This is actually a modified version of a problem from the textbook (6.3). Note that in that problem, is not actually given. It has been introduced for convenience as we move through solving the problem, and should not show up in the final answer. DO NOT DO PROBLEM 6.3. It is not the same problem and if you submit that for your answer, IT WILL BE WRONG F1 F2 = mg 22 مه 1) Write a simple equation for virtual work in terms of F₁, Sr₁, F2, and Sr2. Remember what the virtual work must ultimately equal in a statics problem. DO NOT EVALUATE THIS EQUATION YET. 2) Write position vectors r₁ and 12 from the point O to the points of force application (i.e., to the point where F₁ is applied, AND to the point where F2 is applied). This may require some geometry magic. 3) Compute the variation of each of your position vectors from part 1 using 0 and as generalized coordinates. a. NOTE: YOU SHOULD STILL HAVE VECTORS WHEN DONE b. OTHER NOTE: DO NOT TRY TO SIMPLIFY ANYTHING 4) Using the variation you computed in part 4, compute the dot products that you wrote in part 1 5) Derive a constraint equation that relates 1, 0, and 0. a. HINT: Consider the horizontal distance from the wall to the end of the rod 6) Compute the variation of your constraint equation, and solve for dø as a function of Se 7) Combining your results from parts 4 and 6, obtain an equation that can be solved for the equilibrium angle eq of the bar. DO NOT SOLVE THE EQUATION

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.10P

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