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
μ
s
.(1 point)
Responses

F
applied
=
μ
k
W
book
upper F subscript applied baseline equal mu subscript k baseline upper W subscript book baseline

F
applied
=
μ
s
W
book
upper F subscript applied baseline equal mu subscript s baseline upper W subscript book baseline

F
applied
=
W
book
/
μ
s
upper F subscript applied baseline equals upper W subscript book baseline divided by mu subscript s baseline

F
applied
=
W
book
/
μ
k
upper F subscript applied baseline equals upper W subscript book baseline divided by mu subscript k baseline
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Answer 1

To hold a book against a vertical wall, you need to apply a force that offsets the gravitational force acting on the book, which is its weight (\( W_{book} \)). The force of static friction that helps to prevent the book from sliding down is defined by the static friction coefficient (\( \mu_s \)) and the normal force (\( F_{applied} \)) that you apply against the wall.

The static friction force (\( F_{friction} \)) can be expressed as:

\[
F_{friction} = \mu_s \times F_{normal}
\]

Since the applied force is also the normal force when pushing the book against the wall, we can replace \( F_{normal} \) with \( F_{applied} \):

\[
F_{friction} = \mu_s \times F_{applied}
\]

For the book to stay in place, this frictional force must be equal to the weight of the book:

\[
F_{friction} = W_{book}
\]

Combining the two equations, we have:

\[
\mu_s \times F_{applied} = W_{book}
\]

To solve for \( F_{applied} \):

\[
F_{applied} = \frac{W_{book}}{\mu_s}
\]

Therefore, the correct expression for the force required to hold the book in place is:

\[
F_{applied} = \frac{W_{book}}{\mu_s}
\]

This corresponds to the option:

**\( F_{applied} = \frac{W_{book}}{\mu_s} \)**