Question

A man hold a book weighing 20N in vertical position between the hands and keeps it free from falling by pressing both hands against the book with force of 50N each. The coefficient of friction between the book and the hand would be?

Answer 1

The book tends to fall down so the frictional force is acting upwards. But since the book is not falling down if 50 N from each hand is applied to it, we can say that the frictional force,

$\displaystyle\longrightarrow\sf{f\geq20\ N\quad\quad\dots(1)}$

It can be greater than or equal to the weight of the book.

The reaction acting between the book and the hand is usually equal to the applied force i.e,

$\displaystyle\longrightarrow\sf{R=50\ N}$

Let $\displaystyle\sf{\mu}$ be the coefficient of friction between the hand and the book. Then,

$\displaystyle\longrightarrow\sf{f=\mu R}$

$\displaystyle\longrightarrow\sf{f=50\mu\quad\quad\dots(2)}$

From (1) and (2),

$\displaystyle\longrightarrow\sf{50\mu\geq20}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\mu\geq\dfrac{2}{5}}}}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\mu\geq0.4}}}$

For minimum coefficient of friction,

$\displaystyle\longrightarrow\sf{\underline{\underline{\mu_{min}=0.4}}}$