Problem 4.39

F.B.D. ของวัตถุมวล m

จาก \(ΣF_{x}= 0\)

F

\(Fcos\theta - n = 0\cdots \cdots (1)\)

\(_{\theta}\)

\(f = \mu n = n\)

จาก \(ΣF_{y}= 0\)

mg

\(Fsin\theta + n - mg = 0n\cdots \cdots (2)\)

\((1) + (2) ;Fcos\theta + Fsin\theta - mg = 0\)

\(F =\frac{mg}{\cos \theta + \sin \theta}\)

\(F =\frac{mg}{\cos \theta  + \cos (90º - \theta )}\)

\(F =\frac{mg}{2\cos (45º)\cos (\theta  - 45º)}\)

F จะน้อยสุดเมื่อ \(cos(θ - 45º) = 1 \to \therefore F =\frac{mg}{2}\;\blacksquare\)