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

## 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.

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

• IMG_109F6D002955-1.jpeg
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haruspex
Homework Helper
Gold Member
How can I proceed with this question? Do I have a correct FBD?

Would the acceleration of the cup be equal to the acceleration of the napkin?

haruspex
Homework Helper
Gold Member
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:
ackg ?
Which subsequently would be the acceleration of the napkin?

So would my solution in the picture make sense?

#### Attachments

• IMG_E3E262A0D1DA-1.jpeg
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haruspex
Homework Helper
Gold Member
so would the cup acceleration be:
ackg ?
μk is the kinetic friction between the napkin and the table.

Jpyhsics
Okay thanks!

haruspex