#"given data :"#

#m:6 " "kg" mass of block"#

#g=9.81 " "N/(kg)#

#beta=(3pi)/8#

#mu_k=2/5#

#"The block appears as if it were given on an inclined plane."#

#"Please notice that the weight of of block is perpendicular"#

#"to the ground."#

#"You should split the weight of block into two components "#

#"The green vector "G_x " is parallel to the inclined plane."#

#"The orange vector "G_y " is perpendicular to the inclined plane."#

#G_x=mg*sin beta#

#G_x=6*9.81*sin beta#

#color(green)(G_x=54.38 )" "N#

#G_y=mg*cos beta#

#G_y=6*9.81* cos beta#

#color(orange)(G_y=22.52)" " N#

#"since it is perpendicular to the surface ,The " G_y " component causes friction."#

#color(red)(F_f=mu_k*G_y)#

#F_f=2/5*22.52#

#F_f=9" "N#

#"Since "G_x " greater than "F_f ," block is sliding down."#

#F_("net")=G_x-F_f=54.38-9#

#F_("net")=45.38 " "N#

#"it is necessary a 45 Newtons of force at opposite direction"#

#"so that it does not slide."#