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

[Jpyhsics]

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

ΣF_xNapkin=F-fr_C-fr_T (where C is cup and T is table)
ΣF_xCup=fr_N (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?

 

[haruspex]

How can I proceed with this question? Do I have a correct FBD?

Your FBD looks fine.
What about the cup's acceleration?

 

[Jpyhsics]

Your FBD looks fine.
What about the cup's acceleration?

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

 

[haruspex]

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?

 

[Jpyhsics]

so would the cup acceleration be:
a_c=μ_kg ?
Which subsequently would be the acceleration of the napkin?

So would my solution in the picture make sense?

 

[haruspex]

so would the cup acceleration be:
a_c=μ_kg ?

μ_k is the kinetic friction between the napkin and the table.

 

[Jpyhsics]

Okay thanks!

 

[haruspex]

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.