Question

A force required just to prevent a body sliding down a rough inclined plane of angle  45° and cocfficient of friction 0.6 is F. The minimum force required to move the  body up the plane is

Ans 4F

Answer 1

$$F=-\mu mg \cos{45}+mg\sin{45}\\mg=\frac{F}{-\mu \cos{45}+\sin{45}}\\F_{up}=\mu mg \cos{45}+mg\sin{45}\\\\F_{up}=(\mu \cos{45}+\sin{45})\frac{F}{-\mu \cos{45}+\sin{45}}\\F_{up}=(0.6 \cos{45}+\sin{45})\frac{F}{-0.6 \cos{45}+\sin{45}}\\\\F_{up}=4F$$