Box on Box on Box free body diagram

In summary, the conversation discusses the circumstances under which the top box in a stack of three boxes will slip if a force is applied to the center box. It is mentioned that if the applied force is large enough, the static friction between the bottom and center box will be overcome and the middle box will slip over the bottom box. It is questioned if the top box can also slip out under these circumstances and a comparison is made to a playing card deck. The response states that both accelerations are in the same direction but not the same magnitude. The middle box may accelerate fast enough to make the top box seem immobile. The conversation ends with a thank you for a well-explained answer.
  • #1
wil3
179
1
Okay, so say that I stack three boxes, one on top of another. There is friction between all surface, including the bottom box and the ground.

If I apply a force to the center box only, is there any set of circumstances under which the top box will slip? I know that if the applied force is large enough, static friction between the bottom and center box will be overcome and the middle box will slip over the bottom box. Is there a way for the top box to slip out as well? I am trying to draw a free body diagram, but the only x-axis force I find on the top box is friction, which always points in the direction of the force applied to the center box. I know that the applied force can be great enough to overcome the static friction between the top and middle boxes, but it seems to me like the top box will still accelerate some in hte direction of the applied force. Is this accurate?

Think about this in terms of a playing card deck- if I take a deck of cards and set it on a table, and I pull out on random card halfway, if I flick it hard enough it will go flying out of hte deck without disturbing the cards above or below it.
 
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  • #2
wil3 said:
but it seems to me like the top box will still accelerate some in hte direction of the applied force. Is this accurate?

Yes.

Middle box:

[tex]F_{pull} - F_{f \ bottom} - F_{f \ top} = m_{middle} a_{middle}[/tex]

Top box:

[tex]F_{f \ top} = m_{top} a_{top}[/tex]

Both accelerations are in the same direction but they are not the same magnitude. And if the middle one accelerate fast enough wrt the top box, the top box will seem immobile (it won't have time to travel very far before the middle box is gone). Similarly, for the bottom box:

[tex]F_{f \ bottom} + F_{f \ ground} = m_{bottom} a_{bottom}[/tex]
 
  • #3
Thank you very much! Of all of the questions I have ever posted on Physics Forums, this is one of the few that I have received a complete, well-worded, and properly explained answer to.
 
  • #4
wil3 said:
Thank you very much! Of all of the questions I have ever posted on Physics Forums, this is one of the few that I have received a complete, well-worded, and properly explained answer to.

Thank you. I answer as much for myself than for others. It's exercise for the brain.
 
  • #5


I can confirm that your observations and understanding are accurate. In the scenario you described, the top box will indeed accelerate in the direction of the applied force, but it will not slip out completely unless the force is strong enough to overcome the friction between the top and middle boxes. This is similar to the playing card example, where the card will only fly out if the force applied to it is greater than the friction between the cards above and below it.

In terms of a free body diagram, the top box would have a force applied to it in the direction of the applied force, and a force of friction acting in the opposite direction. The middle box would also have a force applied to it in the direction of the applied force, and a force of friction acting in the opposite direction. The bottom box would have a force of friction acting in the direction of the applied force, as well as a normal force from the ground.

It's important to note that the amount of friction between the boxes will depend on the coefficient of friction between the surfaces in contact. If the coefficient of friction is high, it will take a larger force to overcome the friction and cause slipping. And if the coefficient of friction is low, even a small force may be enough to cause slipping.

In summary, your understanding of the forces at play in this scenario is correct. The top box will only slip if the applied force is strong enough to overcome the friction between it and the middle box. I hope this helps clarify the free body diagram and the concept of friction in this situation.
 

1. What is a free body diagram?

A free body diagram is a graphical representation that shows all the forces acting on an object. It is used to analyze the motion and equilibrium of an object.

2. What is the purpose of a "Box on Box on Box" free body diagram?

The purpose of a "Box on Box on Box" free body diagram is to show the forces acting on a system of three boxes stacked on top of each other, with each box having a different weight and forces acting on it. It helps in analyzing the forces and their effects on each box.

3. How do you draw a "Box on Box on Box" free body diagram?

To draw a "Box on Box on Box" free body diagram, you first need to identify all the forces acting on each box, such as weight, normal force, friction force, etc. Then, draw a box for each object and label the forces acting on it with arrows indicating their direction and magnitude. Finally, draw a dotted line connecting the boxes to show that they are in contact with each other.

4. What information can be obtained from a "Box on Box on Box" free body diagram?

A "Box on Box on Box" free body diagram can provide information about the forces acting on each box, such as the magnitude and direction of the forces, and their effects on the motion and equilibrium of the system. It can also help in identifying any unbalanced forces that may be causing the boxes to move or accelerate.

5. Why is it important to use a free body diagram in scientific analysis?

Free body diagrams are important in scientific analysis because they help in visualizing and understanding the forces acting on an object or system. They also aid in identifying any unbalanced forces that may be causing motion or changes in the system. By using free body diagrams, scientists can accurately analyze and predict the behavior of objects and systems under different conditions.

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