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

In summary, the conversation discusses the minimum force required to pull a napkin out from under a tea cup on a table, taking into account the mass of the napkin and cup, as well as the friction coefficients between the table and napkin, and the napkin and cup. The conversation also includes a discussion on the acceleration of the cup and how it relates to the napkin's acceleration. The proposed solution in the conversation is questioned and the thread remains unsolved.
  • #1
Jpyhsics
84
2

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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  • #2
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?
 
  • #3
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?
 
  • #4
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?
 
  • #5
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?
 

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  • #6
Jpyhsics said:
so would the cup acceleration be:
ac=μkg ?
μk is the kinetic friction between the napkin and the table.
 
  • Like
Likes Jpyhsics
  • #7
Okay thanks!
 
  • #8
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:

1. What is the purpose of finding the minimum force to pull the napkin out from under the tea cup?

The purpose is to determine the minimum amount of force needed to successfully remove the napkin without knocking over the tea cup.

2. Can this experiment be applied to other objects besides a tea cup and napkin?

Yes, this experiment can be applied to any object that is resting on a smooth surface and can be lifted by pulling on a napkin or cloth underneath it.

3. What factors affect the minimum force needed to pull the napkin out from under the tea cup?

The weight of the tea cup, the type of surface it is resting on, the texture and thickness of the napkin, and the angle and direction of the pulling force can all affect the minimum force needed.

4. How can this experiment be useful in real-world applications?

This experiment can be useful in scenarios where delicate objects need to be moved without being directly touched, such as in a laboratory setting or when handling fragile items. It can also help in determining the stability of objects on different surfaces.

5. Is there a specific method or technique to use when finding the minimum force to pull the napkin out from under the tea cup?

There is no one specific method, but it is important to keep all variables constant and to perform multiple trials to ensure accurate results. Additionally, using a force gauge or measuring the displacement of the napkin can help in finding the minimum force needed.

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