Question

A block can slide along an inclined plane in various directions (Fig. 16). If it receives a certain initial velocity v directed downwards along the inclined plane, its motion will be uniformly decelerated, and it comes to rest after traversing a distance l₁.

If the velocity of the same magnitude is imparted to it in the upward direction, it comes to rest after traversing a distance l₂. At the bottom of the inclined plane, a perfectly smooth horizontal guide is fixed. 

Determine the distance l traversed by the block over the inclined plane along the guide if the initial velocity of the same magnitude is imparted to it in the horizontal direction?

Answer 1

Each time the block will move along the inclined plane with a constant acceleration; the magnitudes of the accelerations for the downward and upward motion and the motion along the horizontal guide will be respectively

(Fig. 150). Here a is the slope of the inclined plane and the horizontal, and p is the coefficient of friction. Hence we obtain

The distances traversed by the block in uniformly varying motion at the initial velocity v before it stops can be written in the form

Taking into account the relations for the accelerations a₁ , a₂ and a, we can find the distance l traversed by the block along the horizontal guide: