Answer to Question #139961 in Physics for Sydney

Question

A 6.00 kg block of wood is held motionless against a wall with a force of 65.0 N at an angle of 42.0o measured from the horizontal. What is the minimum coefficient of friction needed to prevent the block from moving

Answer 1

$$N=F\cos{42}\\mg=\mu N+F\sin{42}\\mg=\mu F\cos{42}+F\sin{42}\\(6)(9.8)=\mu (65)\cos{42}+65\sin{42}\\\mu=0.317$$