Finding the pushing force needed to keep object from sliding down wall

[Timebomb3750]

This problem has been bugging me, seeing that my answer seems off. But who knows. Given the following measurements, find the required pushing force needed to keep a book from sliding down the wall.

Homework Statement

M= 2.88kg
Coefficient of static friction= .322

Homework Equations

Seeing that the book can't move, I figured that F=Normal force
mg=2.88kg(9.80 m/s^2)=28.2N
force of static friction=μsN

ƩFx=F-N=0
meaning F=N (Makes sense)

ƩFy=mg-fs=0
meaning mg=μs(N)
thus, N=(mg/μs)

The Attempt at a Solution

I did a simple substitution by setting F=(mg/μs)=(28.2N/.322)=87.6N

To me, that answer seems a little high. So, is my reasoning and/or answer correct?

 

[LawrenceC]

The answer must be greater in magnitude than the weight of the book because friction coefficient < 1. Your answer looks good to me.

 

[Timebomb3750]

The answer must be greater in magnitude than the weight of the book because friction coefficient < 1. Your answer looks good to me.

That's good to know. Thanks.