First slide

Static friction

Question

What is the maximum value of the force F such that the block shown in fig. does not move ?

Moderate

A

20 N
B

25 N
C

30 N
D

40 N

Solution

See fig.
$For no motion, F = \cos 60^{\circ} \leq f$
$where f = μN = μ (mg + Fsin 60^{\circ})$
$\begin{array}{l} ∴ Fcos 60 \leq (mg + Fsin 60^{\circ}) \\ \frac{F}{2} \leq \frac{1}{2 \sqrt{3}} (\sqrt{3} g + \frac{F \sqrt{3}}{2}) \\ or \frac{F}{2} \leq g or F_{max} = 2 g = 20 N . \end{array}$

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