Question

The coefficient of static friction between a book and a desk is 0.35 andthe coefficient of kinetic friction is 0.3. If the book weighs 0.5 kg, howmuch force does it take to get the book moving? How much friction isapplied to the book once it starts moving?

Answer 1

Given data:

* The coefficient static friction between the book and a desk is 0.35.

* The coefficient of kinetic friction is 0.3.

* The mass of the book is 0.5 kg.

Solution:

(a). The normal force acting on the book is,

`N=mg`

where N is the normal force or reaction of desk towards the book, m is the mass of book, and g is the acceleration due to gravity,

Substituting the known values,

`\begin{gathered} N=0.5*9.8 \\ N=4.9\text{ Newton} \end{gathered}`

The static friction of the book on the desk is,

`F_s=\mu_sN`
`\text{where }\mu_s\text{ is the static friction coefficient.}`

Substituting the known values,

`\begin{gathered} F_s=0.35*4.9 \\ F_s=1.715\text{ Newton} \end{gathered}`

Thus, the force required to move the book from the rest is 1.715 N.

(b). The friction experienced by the book when it start moving is,

`F_k=\mu_kN`
`\text{where }\mu_k\text{ is the coefficient of kinetic friction}`

Substituting the known values,

`\begin{gathered} F_k=0.3*4.9 \\ F_k=1.47\text{ Newton} \end{gathered}`

Thus, the friction applied to the book once it starts moving is 1.47 Newton.