Question

A block slides down an inclined plane of slope angle theta with constant velocity it is then projected up on on the same plane with an initial velocity v not have passed up the incline will it move before coming to rest

Answer 1

Since block is moving down the plane with constant speed

So here friction force on the block is counter balanced by weight along the incline plane while it is sliding down

$mgsin\theta = F_f$

now when block is pushed up the plane with initial speed "v"

then it has two forces along the incline plane opposite to the velocity

1. friction force

2. component of weight along the incline

so net force along the incline opposite to velocity

$F_{net} = - mgsin\theta - Ff = -2mg sin\theta$

deceleration of the block is given by

$a = - 2gsin\theta$

now we have

$v_f^2 - v_i^2 = 2 a d$

$0 - v^2 = 2*(-2gsin\theta)*d$

$d = \frac{v^2}{2gsin\theta}$

so above is the distance it will travel along the incline before it stop

Answer 2

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