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 0 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 make the box move up the plane with acceleration a ?

A rectangular box lies on a rough inclined surface. The coefficient of

1.	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 0 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 make the box move up the plane with acceleration a ?
Answer» SOLUTION :Considerdiagram SHOWNIN figure (a ) For bxjuststartsto sliding downslope `F = mg sin theta` `N=m g COS theta` `(f )/(N )= tan theta` `MU = tan theta` `theta= tan ^(-1)(mu)` ( b)Whenangle ofinclinationincreasedto `alpha gttheta` Resultantforcebe `F_(1)` `F_(1)= mgsin alpha- f` (c ) Tokeepboxstationaryor movingwithuniformspeedupwardforceir requiredHerefrictionforcewouldbed indownwarddirection (d ) Whenbox isto bemovedwithaccelerationa upwardalong theplanenet forcebe `F_(3)` frictionwouldbe indownwarddirection `F_(3)= mg (sinalpha+ mu cos alpha )+ ma`