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 is μ. Let the mass of the box be m.(a) At what angle of inclination θ 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 α > θ?(c) What is the force needed to be applied upwards along the plane ot 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 make the box move up the plane with acceleration a?
Answer» (a) θ = tan^-1 (μ) (b) if α > θ, angle of inclination of plane with horizontal, it will slide down. (c) To keep box either stationaries or just move it up with uniform velocity F₂ = mg sin α + f or mg(sin α + μ cos α) (d) force applied to move box upward with acceleration a, mg(sin α + μ cos α) + ma

A rectangular box lies on a rough inclined surface. The co-efficient of friction between the surface and the box is μ. Let the mass of the box be m.(a) At what angle of inclination θ 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 α > θ?(c) What is the force needed to be applied upwards along the plane ot 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 make the box move up the plane with acceleration a?

Answer»

(a) θ = tan^-1 (μ)

(b) if α > θ, angle of inclination of plane with horizontal, it will slide down.

(c) To keep box either stationaries or just move it up with uniform velocity

F₂ = mg sin α + f or mg(sin α + μ cos α)

(d) force applied to move box upward with acceleration a,

mg(sin α + μ cos α) + ma