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Old Oct 22nd 2017, 10:53 AM   #1
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Join Date: Oct 2017
Posts: 7
Book friction problem

Problem
Suppose you are holding a heavy physics book upright between your
hands as shown in the figure to the right. The mass of the book is 4.00 kg.
When your right hand applies a force of 50.0 N normal to the book
as shown, the book remains at rest.

b.)What is the minimum possible value of the coefficient of
static friction between your hands and the book? Assume the
coefficient of static friction between your left hand and the book
is the same as the coefficient of static friction between your right
hand and the book.

Known information
n1=50N
m=4.00kg
Fnet=0

Free Body Diagram
Book friction problem-book-physics-problem.png

Attempt at a solution

$\displaystyle x:n2-n1=0 (1)$
$\displaystyle y:Fs1+Fs1-mg=0 (2)$
$\displaystyle Fs≤sn (3)$

$\displaystyle (1) =>n2=n1=50N$
$\displaystyle (3) =>Fs=(50)$
$\displaystyle (2) => 100=mg$
$\displaystyle (2) => s=(4*9.80)/100$
$\displaystyle (2) => s=.392$

The concept I'm wondering about is the minimum value of the coefficient of static friction. Was I right to set Fs=n after I had figured out that the normal forces are the same in magnitude? If not I'm not really sure how to go about this.
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Old Oct 22nd 2017, 12:34 PM   #2
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Join Date: Apr 2015
Location: Somerset, England
Posts: 684
Your approach is generally correct.
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