A fixed tower crane needs to be carefully balanced with no tipping. A crane at a...

  

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A fixed tower crane needs to be carefully balanced with no tipping. A crane at a construction site is about to lift a load of mass, ML. The crane's dimensions are shown if the figure. Assume the crane's arm (i.e. jib) has uniform mass, MArm, and has a total length L. The arm is raised a distance y with respect to the ground. The cables that connect the ends of the arm to the top of the tower exert negligible tension. Cables of negligible mass and length c support the load and is located a distance a away from the pivot point, P. The crane's counterweight has a mass of Mc and is greater than ML. Where must the crane's counterweight be placed, x, from the pivot point when the load is lifted from the ground distance d? Note: the counterweight is typically moved via sensors and motors to precisely Counter- weight Mc -x- Pivot point, P This Photo by Unknown Author is licensed under CC BY-NC y MLoad d MArm compensate the load. Your solution should be in terms of the variables provided and g. [Hint: Some dimensions are more useful than others] 1. Draw a diagram representing the physical situation. Identify and label all relevant forces. 2. What principle(s)/concept(s) will you need to help solve the problem? 3. What assumption(s)/approximation(s) do you need to make to better help you solve the problem? 4. Identify your system(i.e. objects experiencing a change) 5. Identify the surroundings (i.e. objects causing the change) 6. In words, describe the general strategy you will take to solve the problem. How will you apply the principles and assumptions/approximations you identified? 7. Solve the problem. Clearly and neatly work out the solution. A fixed tower crane needs to be carefully balanced with no tipping. A crane at a construction site is about to lift a load of mass, ML. The crane's dimensions are shown if the figure. Assume the crane's arm (i.e. jib) has uniform mass, MArm, and has a total length L. The arm is raised a distance y with respect to the ground. The cables that connect the ends of the arm to the top of the tower exert negligible tension. Cables of negligible mass and length c support the load and is located a distance a away from the pivot point, P. The crane's counterweight has a mass of Mc and is greater than ML. Where must the crane's counterweight be placed, x, from the pivot point when the load is lifted from the ground distance d? Note: the counterweight is typically moved via sensors and motors to precisely Counter- weight Mc -x- Pivot point, P This Photo by Unknown Author is licensed under CC BY-NC y MLoad d MArm compensate the load. Your solution should be in terms of the variables provided and g. [Hint: Some dimensions are more useful than others] 1. Draw a diagram representing the physical situation. Identify and label all relevant forces. 2. What principle(s)/concept(s) will you need to help solve the problem? 3. What assumption(s)/approximation(s) do you need to make to better help you solve the problem? 4. Identify your system(i.e. objects experiencing a change) 5. Identify the surroundings (i.e. objects causing the change) 6. In words, describe the general strategy you will take to solve the problem. How will you apply the principles and assumptions/approximations you identified? 7. Solve the problem. Clearly and neatly work out the solution.