Chapter 6: Q.58 (page 157)

A person with compromised pinch strength in his fingers can exert a force of only $6.0 N$ to either side of a pinched object, such as the book shown in FIGURE $P 6.58$ . What is the heaviest book he can hold vertically before it slips out of his fingers? The coefficient of static friction between his fingers and the book cover is $0.80$ .
FIGURE P6.58

Expert verified

The weight of the heaviest book is $0.979 k g .$

Step by step solution

The maximum force that fingers can exert: $6 N$ .

Coefficient of static friction between friction and book: $0.80$ .

$\begin{aligned} F = m g \\ F_{f} = μ N = μ m g \end{aligned}$

The maximum force exerted by each finger is there are two normal forces on either side of the book that is in $x$ direction. So

The friction force, that tries to hold the book $F_{f} = 2 μ_{s} n$ .

The downward force, $F = m_{max} g$ .

For the heaviest book that can behold vertically before it slips out of his finger can be calculated by equating both the equations.

$\begin{aligned} F_{f} = F \\ m_{max} g = 2 μ_{s} n \\ m_{max} = \frac{2_{μ_{s} n}}{g} = \frac{2 \times 0.8 \times 6}{9.8} = 0.979 kg \end{aligned}$

The weight of the heaviest book is $0.979 K g$ .

The weight of the heaviest book that can behold vertically before it slips out of his fingers is $0.979 k g$ .

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