A rectangular box lies on a rough inclined surface The co- efficient of friction between the surface and the box mu Let the mass of box be m (a) At what angle of inclination 0 of the plane to the horizontal will box just start to slide down the plane ? (b) What isthe force acting on box down the plane if the angle of inclination of the plane is increases toalpha 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 unifrom speed ? (d) What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration a ?

A rectangular box lies on a rough inclined surface The co- efficient o

1.	A rectangular box lies on a rough inclined surface The co- efficient of friction between the surface and the box mu Let the mass of box be m (a) At what angle of inclination 0 of the plane to the horizontal will box just start to slide down the plane ? (b) What isthe force acting on box down the plane if the angle of inclination of the plane is increases toalpha 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 unifrom speed ? (d) What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration a ?
Answer» Solution :(a) As the box tends to slide down force of friction will ACT up the PLANE As is clear from box will just start slidding down , when ` mg sin theta = f = mu R = mu mg cos theta` or ` tan theta = mu or theta = tan^(-1) (mu) ` (b) When ANGLE of inclination is increased to `ALPHA gt theta` then net force acting on the box down the plane is ` F_(1) = mg sin alpha - f = mg sin alpha + f = mg (sin alpha+ mu cos alpha)` (In this case friction would act down the plane ) (d) If the box is to be moved with an upward acceleration a then upward force NEEDED ` F_(3) = mg (sin alpha+ mu cos alpha) + ma ` .