When Does a Book Slide Off a Tilting Shelf?

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Homework Help Overview

The problem involves a book sliding off a tilting shelf, with specific parameters including the coefficient of static friction and the rate at which the shelf is lifted. The context is rooted in dynamics and the effects of changing angles on motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the angle of inclination and acceleration, with some suggesting the use of differentiation and free-body diagrams. There are varying interpretations of whether the angle or the vertical speed is constant, leading to questions about the appropriate equations to use.

Discussion Status

Several participants have offered insights into potential approaches, including the use of energy conservation and the need for a differential equation. There is an ongoing exploration of the implications of different assumptions regarding the motion of the shelf and the book.

Contextual Notes

Participants note the lack of clarity regarding whether the shelf is lifted at a constant angle or speed, which affects the analysis. The problem is framed within the constraints of a homework assignment, emphasizing the need for careful consideration of forces and motion without providing direct solutions.

  • #31
NihalSh said:
@Simon Bridge
I know about that technicality, but I was trying to avoid it. You already know this is a basic Physics question. The poster hasn't even studied rotation yet. I believe the question was set with a mindset that the student will apply conservation of energy (although you know why this cannot be applied). If someone has a better method to go about it, I would really appreciate it.
Pls take a look at my post #24.
 
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  • #32
haruspex said:
Pls take a look at my post #24.

yeah, looks like OP would have to solve that differential to get the precise result and would also have to get familiar with rotational variables!

Edit: If we use this method (which we should), the breakaway condition would change:

$$μ.g.Cos(ω.t)+(3.05).ω^2=g.Sin(ω.t)$$
 
Last edited:
  • #33
NihalSh said:
yeah, looks like OP would have to solve that differential to get the precise result and would also have to get familiar with rotational variables!

Edit: If we use this method (which we should), the breakaway condition would change:

$$μ.g.Cos(ω.t)+(3.05).ω^2=g.Sin(ω.t)$$
Good point.
 

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