Two boxes with masses m$1$ and m$2$ lean on each other on an inclined plane, with box m$2$ closer to the

floor than box m$1.$ The boxes are made of different materials such that the coefficient of kinetic friction

of box $1$ is u$1$ and the coefficient of kinetic friction of box $2$ is u$2($with p$1<$ U$2).$ The height of the

inclined plane is h and the length of the incline in l$.$ Initially you are holding box m$2$ such that neither box

is moving.

a$.$ In terms of the given quantities write an equation for the angle $0$ that the base of the

incline makes with the horizontal.

b$.$ Draw a co$-$ordinate system that has one axis parallel to the inclined plane $($call it x$\text{'})$ and

one axis perpendicular to the inclined plane $($call it y$\text{'}),$ and then determine the

coefficients of the gravitational acceleration with respect to the x$\text{'}$ and y$\text{'}$ directions of

this new co$-$ordinate system.