Question

A body of mass 2 kg is lying on a rough inclined plane of inclination 30°. Find the magnitude of the force parallel to the incline needed to make the block move (a) up the incline if the push is applied horizontally and not parallel to the incline.

Answer 1

If the Push will be applied horizontally, the the component of the Force along the Incline will be, FCos30°.

Mass of the body = 2 kg.

(a) . Force required to move the block up the Incline = mgsin30 + μ(mgcos30 + F Sin30)

Force = mgsin30 + μmgcos30 + μFSin30°

Fcos30°=µmg.cos30°+µFsin30°+ mg.sin30°

F(cos30°-µsin30°) = µmg.cos30°+mg.sin30°

F(√3/2 - 0.20 × 0.5) =0.20 × 2 × 9.8 × √3/2+ 2 × 9.8 × 0.5

F(1.732-0.20)/2 = 0.20 × 9.8 × 1.732 + 9.8  

0.766F = 13.195  

F = 13.195/0.766

F = 17.23 N    

Hope it helps.