Solving 3D Statics Problem with Two Equal Mass Rods

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In summary, the conversation discusses a 3-d system with two equal rods of unknown mass and length. The rods are connected by a small rod and the question asks to find the reactions of each rod by summing the moments around point O. The suggestion is to draw diagrams and use the cross product or right rule to solve the problem.
  • #1
bigdaddynate
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I have attached a sketch of a 3-d system. There are two rods of equal length (35cm) and equal mass. The masses are equal but unknown (mass of rod #1 = mass of rod #2). Please note that rod #2 is attached to rod one by a small connecting rod (3cm in length). Also note that the width of all rods is arbitrary. The question asks to sum the moments around point O & find the reactions of each rod.

statics.gif


(Please click on image for a larger view)

I would really appreciate any input or advice on how to go about this problem. Thanks in advance.
 
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the image isn't showing up. Try uploading it to fileshack or something.

All i can say for now is draw a diagrams and label all your force. If they ask you to sum moments at a points then you will have to use the cross product or right rule.
 
  • #3


Thank you for sharing your problem with us. I would approach this problem by first defining the system and all the forces acting on it. In this case, we have a 3D system consisting of two equal mass rods connected by a small rod, with unknown masses and arbitrary widths. We also have a point O around which we need to sum the moments.

To solve this problem, we can use the principles of statics, which state that the sum of all forces acting on a system must be zero and the sum of all moments about any point must also be zero. In this case, we have two unknown forces - the reactions of each rod - and we need to find them by summing the moments around point O.

To do this, we can use the equation M = Fd, where M is the moment, F is the force, and d is the distance from the point to the line of action of the force. We can start by drawing a free body diagram of the system and labeling all the forces acting on it. Then, we can write out the equations for the sum of moments around point O, using the distances and angles given in the sketch.

Once we have the equations, we can solve for the unknown forces by using algebraic methods or by using a computer program. It is important to note that the arbitrary widths of the rods may affect the distribution of the forces and the resulting reactions, so it may be necessary to consider them in the equations.

In conclusion, to solve this 3D statics problem, we need to carefully define the system, draw a free body diagram, and use the principles of statics to write and solve equations for the sum of moments around point O. I hope this helps and good luck with your problem!
 

1. What is a 3D statics problem?

A 3D statics problem involves analyzing the equilibrium of forces and moments acting on a three-dimensional object or system. This can include determining the forces and moments acting on individual components within the system, as well as the overall equilibrium of the entire system.

2. How do two equal mass rods affect the solution of a 3D statics problem?

Two equal mass rods can be seen as a symmetrical system, meaning that the forces and moments acting on each rod will be equal and opposite. This can simplify the problem by reducing the number of unknowns and making it easier to calculate the equilibrium conditions.

3. What are the general steps for solving a 3D statics problem?

The general steps for solving a 3D statics problem are as follows:

  1. Draw a free-body diagram of the system, including all external forces and moments.
  2. Apply the equations of equilibrium to determine the unknown forces and moments.
  3. Check the equilibrium conditions to ensure that the system is in static equilibrium.
  4. If necessary, repeat the process for individual components within the system.

4. What are some common challenges when solving 3D statics problems with two equal mass rods?

One common challenge is ensuring that the forces and moments are correctly identified and accounted for in the free-body diagram. Another challenge can be determining the correct direction and magnitude of the forces and moments, as they may be different for each rod in the system.

5. What are some real-world applications of solving 3D statics problems with two equal mass rods?

Some examples of real-world applications include analyzing the forces and moments acting on a bridge or building structure, determining the stability of a vehicle or aircraft, and calculating the forces and moments on a crane lifting a heavy load.

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