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# A block is made to slide along a rough inclined plane. If it recieves a certain initial velocity v directed downwards along the incline, it comes to rest after a distance s1. If the same initial velocity is imparted in upward direction, it comes to rest after traversing a distance s2. There is a smooth path beside the rough path along the incline. If the same block is made to slide along this side in the upward direction, find the distance travelled by the block before coming to rest. A) 2s1s2/(s1+s2) B) (s1+s2)/2 C) (s1-s2)/2 D) (s1s2) 1/2

Kapil Kumar
12 Points
3 months ago
so the block will move along the inclined plane with constant accelaration each time.

a1 = µgcos∝ - gsin∝ , (accelaration for downward)
a2 = µgcos∝ + gsin∝ , (accelaration for upward)
a = µgcos∝

a is the slope of the inclined plane and the horizontal and p is the coefficient of friction. Hence we obtain

a = (a1+a2) / 2.

so distances covered by block in varying motion at the initial velocity v before it stops can be written as

s1 = V²/2*a1,
s2 = V²/2*a2,

s = V²/2*a

taking into accout the relations for the accelaration a1,a2, and a ...

s = 2s1s2/(s1+s2)