How Do You Analyze Forces in a Non-Slipping Book Stack Scenario?

In summary, the conversation discusses the scenario of a hand holding two books, ma and mb, with ma on top. The hand applies a pushing force at a 64° angle above horizontal to accelerate the books to the right. The conversation also mentions the variables involved, such as the reaction force, normal force, friction, gravity, and applied force. It also addresses the role of friction in preventing the top book from slipping and the relationship between the normal force in this scenario and if the books were stationary.
  • #1
nubshat
6
0
A hand supports two books, ma and mb, with ma on top. The hand accelerates the books p and to the right, with a pushing force directed 64° above horizontal. Assuming the upper book does not slip, draw a free body diagram for each book.

My attempt:
1NIx8Sk.png
 
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  • #2
Which book is on top? and it would help if you defined all of your variables that you have shown.
 
  • #3
ma is on top
R is the reaction force
n is the normal force
μn is friction
mg is gravity
|Fa| is the applied force
 
  • #4
What force is friction opposing in order to keep it from slipping?

What is your normal force (or contact force)? Is it the same in this situation as it would be if the books were stationary?
 
  • #5
Jesse H. said:
What force is friction opposing in order to keep it from slipping?

What is your normal force (or contact force)? Is it the same in this situation as it would be if the books were stationary?
I don't know that's the part I need help with
 
  • #6
In this problem friction acts only in the x direction. What other forces do you have acting in x? What do you know about those forces if the book doesn't slip?

It might help to say that the reaction force is the force that the bottom book is pushing up on the top book. So the reaction force is actually the y component of your applied force!
 
Last edited:

1. What is a free body diagram?

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

2. How do I draw a free body diagram?

To draw a free body diagram, start by identifying the object of interest and all the forces acting on it. Then, draw a simple sketch of the object and label each force with an arrow indicating its direction and magnitude. Remember to include all forces, including weight, normal force, friction, and applied forces.

3. Why are free body diagrams important?

Free body diagrams are important because they help us understand the forces at play in a given situation. By visualizing and analyzing these forces, we can determine the net force on an object and predict its motion or state of equilibrium.

4. Can I use a free body diagram for objects in motion?

Yes, free body diagrams can be used for objects in motion. In this case, the forces acting on the object may change as it moves, so it is important to consider the forces at different points in time and update the diagram accordingly.

5. Are there any tips for drawing accurate free body diagrams?

Yes, here are a few tips for drawing accurate free body diagrams:
- Start with a clear and simple sketch of the object
- Remember to include all forces, even those that may seem negligible
- Use arrows to represent the direction and magnitude of each force
- Label each force with a brief description
- Check your diagram for accuracy and consistency before using it for analysis

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