Finding minimum force to pull the napkin out from under the tea cup

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Homework Help Overview

The problem involves determining the minimum force required to pull a napkin out from under a tea cup, considering the masses of both objects and the coefficients of friction between them and the table. The context is rooted in dynamics and frictional forces.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the forces acting on the napkin and the tea cup, including frictional forces and the relationship between their accelerations. Questions are raised about the correctness of free body diagrams (FBD) and the equations used to describe the system.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's FBD and questioning the reasoning behind the equations presented. There is a recognition of the need to clarify the relationship between the accelerations of the cup and the napkin.

Contextual Notes

Participants note the coefficients of kinetic and static friction and their relevance to the problem, while also highlighting potential misunderstandings in the equations proposed.

Jpyhsics
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Homework Statement


There is a table, and a napkin on it. The napkin has a mass mn=71.6 g. On the napkin, there is a tea cup with mass mc=104.6 g. What is the minimum force required for someone to pull the napkin out from under the tea cup? Assume that between the table and the napkin the friction is µk= 0.484, while the coefficient of static friction between the tea cup and the napkin is µs=0.705. Express your answer in Newtons.

Homework Equations


F=ma

The Attempt at a Solution


ΣFxNapkin=F-frC-frT (where C is cup and T is table)
ΣFxCup=frN (where N is napkin)

I have also included a photo of my FBD
How can I proceed with this question? Do I have a correct FBD?
 

Attachments

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Jpyhsics said:
How can I proceed with this question? Do I have a correct FBD?
Your FBD looks fine.
What about the cup's acceleration?
 
haruspex said:
Your FBD looks fine.
What about the cup's acceleration?
Would the acceleration of the cup be equal to the acceleration of the napkin?
 
Jpyhsics said:
Would the acceleration of the cup be equal to the acceleration of the napkin?
Yes, or only very slightly less. So what equation can you write?
 
so would the cup acceleration be:
ac=μkg ?
Which subsequently would be the acceleration of the napkin?

So would my solution in the picture make sense?
 

Attachments

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Jpyhsics said:
so would the cup acceleration be:
ac=μkg ?
μk is the kinetic friction between the napkin and the table.
 
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Likes   Reactions: Jpyhsics
Okay thanks!
 
Jpyhsics said:
Okay thanks!
Not sure how to interpret that response. I am telling you that your equation in post #5 makes no sense... and wondering if it was a typo.

Edit: I have marked the thread unsolved.
 
Last edited:

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