FBDs of Stacked Boxes: Understanding Force Distribution in Connected Objects

  • Thread starter InvisibleMan1
  • Start date
In summary, the problem was that Newton's third law was not able to solve the problem because the FBDs of the two objects were not the same. By thinking of the two objects as a single object, the problem was solved.
  • #1
InvisibleMan1
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To help me understand how a force is distributed over multiple connected objects, I have been trying to draw the FBDs of two stacked boxes which are sitting on the ground. I haven't been able to solve the problem however, and looking for the solution with Google did not turn up anything useful. I'm aware of Newton's third law, but I still have not been able to solve this... I'm at a loss, which is why I am posting here.

Here is an image of the problem:
fbd_problem.jpg


One attempt at solving it using Newton's third law ended up as (what appeared to be) an infinite loop of action-and-reaction forces going up and down the stack. I tried thinking of the two objects as a single object, but that just ended in guesswork without anything real concrete.

What would the FBD of A and the FBD of B look like, with all involved forces?
 
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  • #2
So A and B each feel a gravitational force (also resultant in reactionate forces meaning you have to draw two upward vectors in the Earth's core, but i think we're ignoring them here). Since A is not moving, it has to experience an equal (in magnitude) force upward: this can only come from B, and this force's reactionate brother is the force B experiences from A, the latter obviously pushing down. This force makes B extra heavy and thus the ground under B must deliver a force not only for B itself, but also the load B is carrying (this is indirectly what allows B to hold A up in its place). This last force from the ground to B also has a reactionate brother pushing from the blocks onto the ground (which is the force that would make for a weighing scale placed under B to react)

I hope this helps?
 
  • #3
That solved the problem, thanks :)
 

1. What does FBD stand for in relation to two stacked boxes?

FBD stands for "Free Body Diagram." It is a visual representation that shows the forces acting on an object or system, without any external influences.

2. How are FBDs useful in understanding the forces between two stacked boxes?

FBDs help to simplify complex systems and identify the forces at play. In the case of two stacked boxes, FBDs can show the normal force, weight, and friction between the boxes, which are crucial in understanding their stability and potential movement.

3. Can FBDs of two stacked boxes be used to calculate the net force between them?

Yes, FBDs can be used to calculate the net force between two stacked boxes. By summing up all the forces in the vertical and horizontal directions, we can determine the net force acting on the boxes.

4. How do you draw an accurate FBD of two stacked boxes?

To draw an accurate FBD of two stacked boxes, you need to identify all the forces acting on the system, including weight, normal force, and friction. Then, draw each force as an arrow, with its magnitude and direction, on a diagram that represents the boxes.

5. Can FBDs be used to predict the movement of two stacked boxes?

Yes, FBDs can be used to predict the movement of two stacked boxes. By analyzing the net force and its direction, we can determine whether the boxes will remain stationary or start to move. Additionally, FBDs can help in determining the minimum force needed to move the boxes or the angle at which they will start to slide.

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