how large a force must puch the block if it's on the verge of sliding?

Question

a 5 kg block rests on a 30-degree incline. the coefficient of static friction between the block and the incline is 0.20. How large a horizontal force must push on the block if the block is to be on the berge of sliding (a) up the incline and (b) down the incline?

Answer 1

Hmmm...

a) Fcos(30)+mg(sin(30)- u mg (cos (30))

F=[mg(u mg (cos (30))-sin(30) ]/cos(30)
F=mg[u cos(30)-sin(30)]/cos(30)=
F=5 x 9.81[.2(.866)-.5]/.866=-18.5 N


b) Fcos(30)-mg(sin(30)- u mg (cos (30))

F=[u mg (cos (30))+mg(sin(30) ]/cos(30)
F=5 x 9.81[.5+.2(.866)]/.866=38.1 N

I hope it helps