Question

A block slides with constant velocity on a plane inclined at an angle theta the same block is post up the plane with initial velocity v
the distance covered by the block for coming to rest is

Answer 1

Ffr−frictionforce;θ−angleoftheinclinedplane;U−initialvelocity;t−timeaftertheblockstoped;a−decelerationoftheblock;Newton's second law for the blockwhen its moving down alongthe X-axisbefore it was projected (V=const⟹acceleration=0):x:Ffr−mgx=0Ffr=mgx(1)From te right triangle ABC:sinθ=mgxmg⟹mgx=mgsinθ(2)Newton's second law for the block when its moving up along the X-axis after it was projected. Force that acts of the block:x:Fnet=Ffr+mgx(3)(1)and(2)in(3):Fnet=mgx+mgx=2mgx=2mgsinθ(4)Loss of KE by block = work done by friction force + PE (final speed of the block = 0):mU22=Fnet∙d+mgd∙sinθ(5)(4)in(5):mU22=2mgdsinθ+mgd∙sin