A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is `mu` . Let the mass of the box be m.
(a) At what angle of inclination `theta ` of the plane to the horizontal will the box just start to slide down the plane?
(b) What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to `a gt theta ` .
(c) What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed?
(d) What is the force needed to be applied upwards along the plane to `mu_k` kgf make the box move up the plane with acceleration a?

Explanation

(a) When the box just starts sliding
`mu = tan theta " or " theta = tan^(-1)mu`
(b) Force acting on the box down the plane
` = mg (sin alpha - mu cos alpha)`
(c) Force needed mg `(sin alpha + u cos alpha)`
(d) Force needed `= mg (sin alpha + u cos alpha ) + ma` .