Question

you press a book against a vertical wall. express the force required to hold the book in place, $f_{applied}$, in terms of $w_{book}$ and $mu_{s}$. (1 point)
$f_{applied}=mu_{s}w_{book}$
$f_{applied}=mu_{k}w_{book}$
$f_{applied}=w_{book}/mu_{s}$
$f_{applied}=w_{book}/mu_{k}$

Explanation:

Step1: Analyze vertical - force equilibrium

The weight of the book $W_{book}$ acts downwards. The maximum static - friction force $F_f=\mu_sF_N$ acts upwards to balance the weight of the book to keep it in place. Here, the normal force $F_N$ is equal to the applied force $F_{applied}$ (since the book is pressed against the wall).

Step2: Set up force - equilibrium equation

In the vertical direction, for the book to be in equilibrium, $F_f = W_{book}$. And $F_f=\mu_sF_N$, where $F_N = F_{applied}$. So, $\mu_sF_{applied}=W_{book}$.

Step3: Solve for the applied force

Rearranging the equation $\mu_sF_{applied}=W_{book}$ for $F_{applied}$, we get $F_{applied}=\frac{W_{book}}{\mu_s}$.

Answer:

$F_{applied} = W_{book}/\mu_s$ (the third option)