#"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."#